Bio

Bio

Brad is Max H. Stein Professor of Humanities and Sciences, Professor of Statistics, and Professor of Biostatistics with the Department of Biomedical Data Science in the School of Medicine; he serves as Co-director of the Mathematical and Computational Sciences Program. He has held visiting faculty appointments at Harvard, UC Berkeley, and Imperial College, London. A recipient of a 2005 National Medal of Science for his contributions to theoretical and applied statistics, especially the bootstrap sampling technique, in 2014 he was awarded the Guy Medal in Gold by the Royal Statistical Society. Together with David Cox of the University of Oxford, Efron was honored as a Laureate in the 2016 edition of the BBVA Foundation Frontiers of Knowledge Awards, ?for revolutionizing statistics and making it into an indispensable tool for other sciences.?

Academic Appointments

Administrative Appointments

  • Professor of Biomedical Data Science, Stanford School of Medicine Department of Biomedical Data Science (2015 - Present)
  • Chairman, Stanford University Department of Statistics (1998 - 1999)
  • Chairman, Stanford University Faculty Senate (1998 - 1999)
  • Chairman, Stanford University Advisory Board (1996 - 1997)
  • Chairman, Stanford University Department of Statistics (1993 - 1994)
  • Chairman, Stanford University Department of Statistics (1991 - 1994)
  • Max H. Stein Professor of Humanities and Sciences, Stanford University (1988 - Present)
  • Associate Dean, Stanford University School of Humanities and Sciences (1987 - 1990)
  • Co-director, Stanford University Mathematical and Computational Science Program (1980 - Present)
  • Professor, Stanford University Department of Statistics (1972 - Present)
  • Professor of Biostatistics, Stanford School of Medicine Department of Health Research and Policy (1972 - 2015)
  • Visiting Scholar, Imperial College London Department of Mathematics (1971 - 1972)
  • Associate Professor, Stanford University Department of Statistics (1968 - 1972)
  • Visiting Lecturer, Harvard University Department of Statistics (1967 - 1968)
  • Assistant Professer, Stanford University Department of Statistics (1964 - 1967)

Contact

Links

Research & Scholarship

Current Research and Scholarly Interests

My main project during the last two years has been "Computer Age Statistical Inference", a book written in collaboration with Trevor Hastie. Our goal is to review the development of statistical thinking since the introduction of electronic computation in the 1950s. Individual chapters concern progress in important topic areas, emphasizing the interplay between computational methods and inferential ideas. The survival analysis chapter, for example, traces the steps from life tables, the Kaplan-Meier estimator, and the Mantel Haenszel log rank test to the proportional hazards model.

The book proceeds in three parts: Part 1 reviews classical inference, Bayesian, frequentist, and Fisherian. Part 2 covers developments from 1955 through 1995, empirical Bayes, James-Stein estimation, ridge regression, generalized linear models, jackknife and bootstrap methods, objective Bayes and MCMC, plus several other topics. Part 3 concerns 21st century topics, false discovery rates, sparse modeling and the lasso, support vector machines, neural networks, random forests, and other modern data analytic algorithms. First drafts of Parts 1 and 2 are now complete. Part 3 is in progress, and we hope to complete work in 2016.

The broader impact of my other work over the previous few years has been to establish both within and outside the field the practical importance of computer-intensive statistical methods, such as the bootstrap, shrinkage estimation, and local false discovery rates. Besides gaining traction themselves, these methods have stimulated parallel developments in other areas, such as MCMC algorithms for Bayesian calculations.

Teaching

2020-21 Courses

Stanford Advisees

  • Doctoral Dissertation Advisor (AC)
    Fang Cai
  • Undergraduate Major Advisor
    Adam Behrendt

Publications

All Publications

  • The Effect of Ethanol Consumption on Composition and Morphology of Femur Cortical Bone in Wild-Type and ALDH2*2-Homozygous Mice. Calcified tissue international Malkovskiy, A. V., Van Wassenhove, L. D., Goltsev, Y., Osei-Sarfo, K., Chen, C., Efron, B., Gudas, L. J., Mochly-Rosen, D., Rajadas, J. 2020

    Abstract

    ALDH2 inactivating mutation (ALDH2*2) is the most abundant mutation leading to bone morphological aberration. Osteoporosis has long been associated with changes in bone biomaterial in elderly populations. Such changes can be exacerbated with elevated ethanol consumption and in subjects with impaired ethanol metabolism, such as carriers of aldehyde dehydrogenase 2 (ALDH2)-deficient gene, ALDH2*2. So far, little is known about bone compositional changes besides a decrease in mineralization. Raman spectroscopic imaging has been utilized to study the changes in overall composition of C57BL/6 female femur bone sections, as well as in compound spatial distribution. Raman maps of bone sections were analyzed using multilinear regression with these four isolated components, resulting in maps of their relative distribution. A 15-week treatment of both wild-type (WT) and ALDH2*2/*2 mice with 20% ethanol in the drinking water resulted in a significantly lower mineral content (p<0.05) in the bones. There was no significant change in mineral and collagen content due to the mutation alone (p>0.4). Highly localized islets of elongated adipose tissue were observed on most maps. Elevated fat content was found in ALDH2*2 knock-in mice consuming ethanol (p<0.0001) and this effect appeared cumulative. This work conclusively demonstrates that that osteocytes in femurs of older female mice accumulate fat, as has been previously theorized, and that fat accumulation is likely modulated by levels of acetaldehyde, the ethanol metabolite.

    View details for DOI 10.1007/s00223-020-00769-1

    View details for PubMedID 33068139

  • deconvolveR: A G-Modeling Program for Deconvolution and Empirical Bayes Estimation JOURNAL OF STATISTICAL SOFTWARE Narasimhan, B., Efron, B. 2020; 94 (11): 1?20

    View details for DOI 10.18637/jss.v094.i11

    View details for Web of Science ID 000565254900001

  • Derivation and validation of a prognostic score for neonatal mortality in Ethiopia: a case-control study. BMC pediatrics Mediratta, R. P., Amare, A. T., Behl, R., Efron, B., Narasimhan, B., Teklu, A., Shehibo, A., Ayalew, M., Kache, S. 2020; 20 (1): 238

    Abstract

    BACKGROUND: Early warning scores for neonatal mortality have not been designed for low income countries. We developed and validated a score to predict mortality upon admission to a NICU in Ethiopia.METHODS: We conducted a retrospective case-control study at the University of Gondar Hospital, Gondar, Ethiopia. Neonates hospitalized in the NICU between January 1, 2016 to June 31, 2017. Cases were neonates who died and controls were neonates who survived.RESULTS: Univariate logistic regression identified variables associated with mortality. The final model was developed with stepwise logistic regression. We created the Neonatal Mortality Score, which ranged from 0 to 52, from the model's coefficients. Bootstrap analysis internally validated the model. The discrimination and calibration were calculated. In the derivation dataset, there were 207 cases and 605 controls. Variables associated with mortality were admission level of consciousness, admission respiratory distress, gestational age, and birthweight. The AUC for neonatal mortality using these variables in aggregate was 0.88 (95% CI 0.85-0.91). The model achieved excellent discrimination (bias-corrected AUC) under internal validation. Using a cut-off of 12, the sensitivity and specificity of the Neonatal Mortality Score was 81 and 80%, respectively. The AUC for the Neonatal Mortality Score was 0.88 (95% CI 0.85-0.91), with similar bias-corrected AUC. In the validation dataset, there were 124 cases and 122 controls, the final model and the Neonatal Mortality Score had similar discrimination and calibration.CONCLUSIONS: We developed, internally validated, and externally validated a score that predicts neonatal mortality upon NICU admission with excellent discrimination and calibration.

    View details for DOI 10.1186/s12887-020-02107-8

    View details for PubMedID 32434513

  • Prediction, Estimation, and Attribution JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 2020; 115 (530): 636?55

    View details for DOI 10.1080/01621459.2020.1762613

    View details for Web of Science ID 000538423300011

  • The Automatic Construction of Bootstrap Confidence Intervals JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS Efron, B., Narasimhan, B. 2020

    View details for DOI 10.1080/10618600.2020.1714633

    View details for Web of Science ID 000519484100001

  • Letermovir Prophylaxis Decreases Burden of CMV in Patients at High Risk for CMV Disease Following Hematopoietic Cell Transplant. Biology of blood and marrow transplantation : journal of the American Society for Blood and Marrow Transplantation Johnsrud, J. J., Nguyen, I. T., Domingo, W., Narasimhan, B., Efron, B., Brown, J. W. 2020

    Abstract

    Despite effective therapies, CMV continues to have a significant impact on morbidity and mortality in hematopoietic cell transplant recipients. At particular risk are recipients of alternative grafts such as umbilical cord blood (UCB), haploidentical transplants (haplo), or patients conditioned with T-cell depleting regimens such as anti-thymocyte globulin (ATG). With the approval of letermovir, its impact on high risk patients is of particular interest. To evaluate the impact of letermovir prophylaxis at our center we performed a retrospective analysis of 114 high risk patients who received letermovir as prophylaxis (LET PPX) between January 2018 through December 2019, including 30 UCB and 22 haplo recipients, compared to 637 historical controls with comparable risk between January 2013 and December 2019. By D+100, letermovir prophylaxis significantly decreased the incidence of both CMV DNAemia compared to controls (45.37% vs 74.1%; P <.001) and clinically significant CMV infection (12.04% vs 48.82%; P <.001). The impact of LET PPX was even more profound on the incidence of clinically significant CMV infection (CSI) defined as the administration of antiviral therapy either as preemptive therapy for CMV DNAemia or treatment for CMV disease. CSI was significantly lower in haplo recipients on LET PPX compared to controls (13.64% vs 73.33%; P= .02) and UCB recipients on LET PPX compared to controls (3.45% vs 37.5%; P <.001). No patients on LET primary PPX developed CMV disease in any treatment group by D+100, compared to controls (0% vs 5.34%, respectively; P= .006). Patients on LET PPX had fewer hospitalizations involving initiation of anti-CMV therapy compared to controls (0.93% vs 15.23%, respectively). Our analysis of the largest cohort of patients at high risk for CMV reactivation published to date demonstrates that letermovir prophylaxis significantly reduces the number of patients who receive CMV-active antiviral therapy for either DNAemia or disease due to CMV.

    View details for DOI 10.1016/j.bbmt.2020.07.002

    View details for PubMedID 32653623

  • Rejoinder: Bayes, Oracle Bayes, and Empirical Bayes STATISTICAL SCIENCE Efron, B. 2019; 34 (2): 234?35

    View details for DOI 10.1214/19-STS674REJ

    View details for Web of Science ID 000476620700009

  • Bayes, Oracle Bayes and Empirical Bayes STATISTICAL SCIENCE Efron, B. 2019; 34 (2): 177?201

    View details for DOI 10.1214/18-STS674

    View details for Web of Science ID 000476620700001

  • Proteomic analysis of monolayer-integrated proteins on lipid droplets identifies amphipathic interfacial alpha-helical membrane anchors. Proceedings of the National Academy of Sciences of the United States of America Pataki, C. I., Rodrigues, J., Zhang, L., Qian, J., Efron, B., Hastie, T., Elias, J. E., Levitt, M., Kopito, R. R. 2018

    Abstract

    Despite not spanning phospholipid bilayers, monotopic integral proteins (MIPs) play critical roles in organizing biochemical reactions on membrane surfaces. Defining the structural basis by which these proteins are anchored to membranes has been hampered by the paucity of unambiguously identified MIPs and a lack of computational tools that accurately distinguish monolayer-integrating motifs from bilayer-spanning transmembrane domains (TMDs). We used quantitative proteomics and statistical modeling to identify 87 high-confidence candidate MIPs in lipid droplets, including 21 proteins with predicted TMDs that cannot be accommodated in these monolayer-enveloped organelles. Systematic cysteine-scanning mutagenesis showed the predicted TMD of one candidate MIP, DHRS3, to be a partially buried amphipathic alpha-helix in both lipid droplet monolayers and the cytoplasmic leaflet of endoplasmic reticulum membrane bilayers. Coarse-grained molecular dynamics simulations support these observations, suggesting that this helix is most stable at the solvent-membrane interface. The simulations also predicted similar interfacial amphipathic helices when applied to seven additional MIPs from our dataset. Our findings suggest that interfacial helices may be a common motif by which MIPs are integrated into membranes, and provide high-throughput methods to identify and study MIPs.

    View details for PubMedID 30104359

  • CURVATURE AND INFERENCE FOR MAXIMUM LIKELIHOOD ESTIMATES ANNALS OF STATISTICS Efron, B. 2018; 46 (4): 1664?92

    View details for DOI 10.1214/17-AOS1598

    View details for Web of Science ID 000436600900010

  • SPECIAL SECTION IN MEMORY OF STEPHEN E. FIENBERG (1942-2016) AOAS EDITOR-IN-CHIEF 2013-2015 ANNALS OF APPLIED STATISTICS Gneiting, T., Asher, J., Carriquiry, A., Davis, R., Dawid, A., Efron, B., Haberman, S., Kou, S., Newton, M., Paddock, S., Prewitt, K., Raftery, A., Stein, M., Straf, M. 2018; 12 (2): III-X

    View details for DOI 10.1214/17-AOAS122ED

    View details for Web of Science ID 000440054700001

  • Anti-HER2 scFv-directed extracellular vesicle-mediated mRNA-based gene delivery inhibits growth of HER2-positive human breast tumor xenografts by prodrug activation. Molecular cancer therapeutics Wang, J., Forterre, A. V., Zhao, J., Frimannsson, D. O., Delcayre, A., Antes, T. J., Efron, B., Jeffrey, S. S., Pegram, M. D., Matin, A. C. 2018

    Abstract

    This paper deals with specific targeting of the prodrug/enzyme regimen, CNOB/HChrR6, to treat a serious disease namely HER2+ve human breast cancer with minimal off-target toxicity. HChrR6 is an improved bacterial enzyme that converts CNOB into the cytotoxic drug MCHB. Extracellular vesicles (EVs) were used for mRNA-based HchrR6 gene delivery: EVs may cause minimal immune rejection, and mRNA may be superior to DNA for gene delivery. To confine HChrR6 generation and CNOB activation to the cancer, the EVHB chimeric protein was constructed. It contains high affinity anti-HER2 scFv antibody (ML39) and is capable of latching on to EV surface. Cells transfected with EVHB-encoding plasmid generated EVs displaying this protein ("directed EVs"). Transfection of a separate batch of cells with the new plasmid, XPort/HChrR6, generated EVs containing HChrR6 mRNA; incubation with pure EVHB enabled these to target the HER2 receptor, generating "EXO-DEPT" EVs. EXO-DEPT treatment specifically enabled HER2-overexpressing BT474 cells to convert CNOB into MCHB in actinomycin D independent manner, showing successful and specific delivery of HCHrR6 mRNA. EXO-DEPTs --but not undirected EVs-- plus CNOB caused near-complete growth-arrest of orthotopic BT474 xenografts in vivo, demonstrating for the first time EV-mediated delivery of functional exogenous mRNA to tumors. EXO-DEPTs may be generated from patient's own dendritic cells to evade immune rejection, and without plasmids and their potentially harmful genetic material, raising the prospect of clinical use of this regimen. This approach can be employed to treat any disease overexpressing a specific marker.

    View details for PubMedID 29483213

  • Improvement in treatment abandonment in pediatric patients with cancer in Guatemala. Pediatric blood & cancer Alvarez, E., Seppa, M., Rivas, S., Fuentes, L., Valverde, P., Antillón-Klussmann, F., Castellanos, M., Sweet-Cordero, E. A., Messacar, K., Kurap, J., Bustamante, M., Howard, S. C., Efron, B., Luna-Fineman, S. 2017

    Abstract

    Treatment refusal and abandonment are major causes of treatment failure for children with cancer in low- and middle-income countries (LMICs), like Guatemala. This study identified risk factors for and described the intervention that decreased abandonment.This was a retrospective study of Guatemalan children (0-18 years) with cancer treated at the Unidad Nacional de Oncología Pediátrica (UNOP), 2001-2008, using the Pediatric Oncology Network Database. Treatment refusal was a failure to begin treatment and treatment abandonment was a lapse of 4 weeks or longer in treatment. The impact of medicina integral, a multidisciplinary psychosocial intervention team at UNOP was evaluated. Cox proportional hazards analysis identified the effect of demographic and clinical factors on abandonment. Kaplan-Meier analysis estimated the survival.Of 1,789 patients, 21% refused or abandoned treatment. Abandonment decreased from 27% in 2001 to 7% in 2008 following the implementation of medicina integral. Factors associated with increased risk of refusal and abandonment: greater distance to the centre (P < 0.001), younger age (P = 0.017) and earlier year of diagnosis (P < 0.001). Indigenous race/ethnicity (P = 0.002) was associated with increased risk of abandonment alone. Abandonment correlated with decreased overall survival: 0.57 ± 0.02 (survival ± standard error) for those who completed therapy versus 0.06 ± 0.02 for those who abandoned treatment (P < 0.001) at 8.3 years.This study identified distance, age, year of diagnosis and indigenous race/ethnicity as risk factors for abandonment. A multidisciplinary intervention reduced abandonment and can be replicated in other LMICs.

    View details for DOI 10.1002/pbc.26560

    View details for PubMedID 28423236

  • Small-Volume Injections: Evaluation of Volume Administration Deviation From Intended Injection Volumes. Anesthesia and analgesia Muffly, M. K., Chen, M. I., Claure, R. E., Drover, D. R., Efron, B., Fitch, W. L., Hammer, G. B. 2017

    Abstract

    In the perioperative period, anesthesiologists and postanesthesia care unit (PACU) nurses routinely prepare and administer small-volume IV injections, yet the accuracy of delivered medication volumes in this setting has not been described. In this ex vivo study, we sought to characterize the degree to which small-volume injections (?0.5 mL) deviated from the intended injection volumes among a group of pediatric anesthesiologists and pediatric postanesthesia care unit (PACU) nurses. We hypothesized that as the intended injection volumes decreased, the deviation from those intended injection volumes would increase.Ten attending pediatric anesthesiologists and 10 pediatric PACU nurses each performed a series of 10 injections into a simulated patient IV setup. Practitioners used separate 1-mL tuberculin syringes with removable 18-gauge needles (Becton-Dickinson & Company, Franklin Lakes, NJ) to aspirate 5 different volumes (0.025 mL, 0.05 mL, 0.1 mL, 0.25 mL, and 0.5 mL) of 0.25 mM Lucifer Yellow (LY) fluorescent dye constituted in saline (Sigma Aldrich, St. Louis, MO) from a rubber-stoppered vial. Each participant then injected the specified volume of LY fluorescent dye via a 3-way stopcock into IV tubing with free-flowing 0.9% sodium chloride (10 mL/min). The injected volume of LY fluorescent dye and 0.9% sodium chloride then drained into a collection vial for laboratory analysis. Microplate fluorescence wavelength detection (Infinite M1000; Tecan, Mannedorf, Switzerland) was used to measure the fluorescence of the collected fluid. Administered injection volumes were calculated based on the fluorescence of the collected fluid using a calibration curve of known LY volumes and associated fluorescence. To determine whether deviation of the administered volumes from the intended injection volumes increased at lower injection volumes, we compared the proportional injection volume error (loge [administered volume/intended volume]) for each of the 5 injection volumes using a linear regression model. Analysis of variance was used to determine whether the absolute log proportional error differed by the intended injection volume. Interindividual and intraindividual deviation from the intended injection volume was also characterized.As the intended injection volumes decreased, the absolute log proportional injection volume error increased (analysis of variance, P < .0018). The exploratory analysis revealed no significant difference in the standard deviations of the log proportional errors for injection volumes between physicians and pediatric PACU nurses; however, the difference in absolute bias was significantly higher for nurses with a 2-sided significance of P = .03.Clinically significant dose variation occurs when injecting volumes ?0.5 mL. Administering small volumes of medications may result in unintended medication administration errors.

    View details for DOI 10.1213/ANE.0000000000001976

    View details for PubMedID 28338490

  • Statistical thinking for 21st century scientists. Science advances Cox, D. R., Efron, B. 2017; 3 (6): e1700768

    Abstract

    Statistical science provides a wide range of concepts and methods for studying situations subject to unexplained variability. Such considerations enter fields ranging from particle physics and astrophysics to genetics, sociology and economics, and beyond; to associated areas of application such as engineering, agriculture, and medicine, in particular in clinical trials. Successful application hinges on absorption of statistical thinking into the subject matter and, hence, depends strongly on the field in question and on the individual investigators. It is the job of theoretical statisticians both to be alive to the challenges of specific applications and, at the same time, to develop methods and concepts that, with good fortune, will be broadly applicable.

    View details for PubMedID 28630933

    View details for PubMedCentralID PMC5470825

  • Effect of Perioperative Gabapentin on Postoperative Pain Resolution and Opioid Cessation in a Mixed Surgical Cohort: A Randomized Clinical Trial. JAMA surgery Hah, J., Mackey, S. C., Schmidt, P., McCue, R., Humphreys, K., Trafton, J., Efron, B., Clay, D., Sharifzadeh, Y., Ruchelli, G., Goodman, S., Huddleston, J., Maloney, W. J., Dirbas, F. M., Shrager, J., Costouros, J., Curtin, C., Carroll, I. 2017

    Abstract

    Guidelines recommend using gabapentin to decrease postoperative pain and opioid use, but significant variation exists in clinical practice.To determine the effect of perioperative gabapentin on remote postoperative time to pain resolution and opioid cessation.A randomized, double-blind, placebo-controlled trial of perioperative gabapentin was conducted at a single-center, tertiary referral teaching hospital. A total of 1805 patients aged 18 to 75 years scheduled for surgery (thoracotomy, video-assisted thoracoscopic surgery, total hip replacement, total knee replacement, mastectomy, breast lumpectomy, hand surgery, carpal tunnel surgery, knee arthroscopy, shoulder arthroplasty, and shoulder arthroscopy) were screened. Participants were enrolled from May 25, 2010, to July 25, 2014, and followed up for 2 years postoperatively. Intention-to-treat analysis was used in evaluation of the findings.Gabapentin, 1200 mg, preoperatively and 600 mg, 3 times a day postoperatively or active placebo (lorazepam, 0.5 mg) preoperatively followed by inactive placebo postoperatively for 72 hours.Primary outcome was time to pain resolution (5 consecutive reports of 0 of 10 possible levels of average pain at the surgical site on the numeric rating scale of pain). Secondary outcomes were time to opioid cessation (5 consecutive reports of no opioid use) and the proportion of participants with continued pain or opioid use at 6 months and 1 year.Of 1805 patients screened for enrollment, 1383 were excluded, including 926 who did not meet inclusion criteria and 273 who declined to participate. Overall, 8% of patients randomized were lost to follow-up. A total of 202 patients were randomized to active placebo and 208 patients were randomized to gabapentin in the intention-to-treat analysis (mean [SD] age, 56.7 [11.7] years; 256 (62.4%) women and 154 (37.6%) men). Baseline characteristics of the groups were similar. Perioperative gabapentin did not affect time to pain cessation (hazard ratio [HR], 1.04; 95% CI, 0.82-1.33; P?=?.73) in the intention-to-treat analysis. However, participants receiving gabapentin had a 24% increase in the rate of opioid cessation after surgery (HR, 1.24; 95% CI, 1.00-1.54; P?=?.05). No significant differences were noted in the number of adverse events as well as the rate of medication discontinuation due to sedation or dizziness (placebo, 42 of 202 [20.8%]; gabapentin, 52 of 208 [25.0%]).Perioperative administration of gabapentin had no effect on postoperative pain resolution, but it had a modest effect on promoting opioid cessation after surgery. The routine use of perioperative gabapentin may be warranted to promote opioid cessation and prevent chronic opioid use. Optimal dosing and timing of perioperative gabapentin in the context of specific operations to decrease opioid use should be addressed in further research.clinicaltrials.gov Identifier: NCT01067144.

    View details for PubMedID 29238824

  • Empirical Bayes deconvolution estimates BIOMETRIKA Efron, B. 2016; 103 (1): 1-20

    View details for DOI 10.1093/biomet/asv068

    View details for Web of Science ID 000371685300001

  • Exploring Value in Congenital Heart Disease: An Evaluation of Inpatient Admissions CONGENITAL HEART DISEASE Shin, A. Y., Hu, Z., Jin, B., Lal, S., Rosenthal, D. N., Efron, B., Sharek, P. J., Sutherland, S. M., Cohen, H. J., McElhinney, D. B., Roth, S. J., Ling, X. B. 2015; 10 (6): E278-E287

    Abstract

    Understanding value provides an important context for improvement. However, most health care models fail to measure value. Our objective was to categorize inpatient encounters within an academic congenital heart program based on clinical outcome and the cost to achieve the outcome (value). We aimed to describe clinical and nonclinical features associated with value.We defined hospital encounters based on outcome per resource utilized. We performed principal component and cluster analysis to classify encounters based on mortality, length of stay, hospital cost and revenue into six classes. We used nearest shrunken centroid to identify discriminant features associated with the cluster-derived classes. These features underwent hierarchical clustering and multivariate analysis to identify features associated with each class.We analyzed all patients admitted to an academic congenital heart program between September 1, 2009, and December 31, 2012.A total of 2658 encounters occurred during the study period. Six classes were categorized by value. Low-performing value classes were associated with greater institutional reward; however, encounters with higher-performing value were associated with a loss in profitability. Encounters that included insertion of a pediatric ventricular assist device (log OR 2.5 [95% CI, 1.78 to 3.43]) and acquisition of a hospital-acquired infection (log OR 1.42 [95% CI, 0.99 to 1.87]) were risk factors for inferior health care value.Among the patients in our study, institutional reward was not associated with value. We describe a framework to target quality improvement and resource management efforts that can benefit patients, institutions, and payers alike.

    View details for DOI 10.1111/chd.12290

    View details for Web of Science ID 000367379300004

  • Allogeneic hematopoietic cell transplantation after failed autologous transplant for lymphoma using TLI and anti-thymocyte globulin conditioning BONE MARROW TRANSPLANTATION Rezvani, A. R., Kanate, A. S., Efron, B., Chhabra, S., Kohrt, H. E., Shizuru, J. A., Laport, G. G., Miklos, D. B., Benjamin, J. E., JOHNSTON, L. J., Arai, S., Weng, W., Negrin, R. S., Strober, S., Lowsky, R. 2015; 50 (10): 1286-1292

    Abstract

    We describe 47 patients with lymphoma and failed prior autologous hematopoietic cell transplantation (HCT) who received TLI-ATG (anti-thymocyte globulin) conditioning followed by allogeneic HCT. Thirty-two patients had non-Hodgkin lymphoma (NHL; diffuse large B-cell lymphoma (n=19), T-cell NHL (n=6), mantle cell lymphoma (n=4) or other B-cell subtypes (n=3)), and 15 had Hodgkin lymphoma. The median follow-up was 4.9 (range, 2.1-11.9) years. The cumulative incidence of grade II-IV acute GvHD at day +100 was 12%, and the cumulative incidence of extensive chronic GvHD at 1 year was 36%. The 3-year cumulative incidences of overall survival (OS), PFS and non-relapse mortality (NRM) were 81%, 44% and 7%, respectively. Fifteen patients died (relapse, n=10; NRM, n=5). Among the 25 patients with relapse after allogeneic HCT, 11 (44%) achieved durable (>1 year) CRs following donor lymphocyte infusion or chemoradiotherapy. The majority of surviving patients (75%; n=24) were able to discontinue all immunosuppression. For patients with relapsed lymphoma after autologous HCT, allogeneic HCT using TLI-ATG conditioning is a well-tolerated, predominantly outpatient therapy with low NRM (7% at 3 years), a low incidence of GvHD, durable disease control and excellent OS (81% at 3 years).

    View details for DOI 10.1038/bmt.2015.149

    View details for PubMedID 26146806

  • Frequentist accuracy of Bayesian estimates JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY Efron, B. 2015; 77 (3): 617-646

    View details for DOI 10.1111/rssb.12080

    View details for Web of Science ID 000354409800003

  • Frequentist accuracy of Bayesian estimates. Journal of the Royal Statistical Society. Series B, Statistical methodology Efron, B. 2015; 77 (3): 617?46

    Abstract

    In the absence of relevant prior experience, popular Bayesian estimation techniques usually begin with some form of "uninformative" prior distribution intended to have minimal inferential influence. Bayes rule will still produce nice-looking estimates and credible intervals, but these lack the logical force attached to experience-based priors and require further justification. This paper concerns the frequentist assessment of Bayes estimates. A simple formula is shown to give the frequentist standard deviation of a Bayesian point estimate. The same simulations required for the point estimate also produce the standard deviation. Exponential family models make the calculations particularly simple, and bring in a connection to the parametric bootstrap.

    View details for PubMedID 26089740

    View details for PubMedCentralID PMC4467036

  • Number of Lymph Nodes Removed and Survival after Gastric Cancer Resection: An Analysis from the US Gastric Cancer Collaborative. Journal of the American College of Surgeons Gholami, S., Janson, L., Worhunsky, D. J., Tran, T. B., Squires, M. H., Jin, L. X., Spolverato, G., Votanopoulos, K. I., Schmidt, C., Weber, S. M., Bloomston, M., Cho, C. S., Levine, E. A., Fields, R. C., Pawlik, T. M., Maithel, S. K., Efron, B., Norton, J. A., Poultsides, G. A. 2015; 221 (2): 291?99

    Abstract

    Examination of at least 16 lymph nodes (LNs) has been traditionally recommended during gastric adenocarcinoma resection to optimize staging, but the impact of this strategy on survival is uncertain. Because recent randomized trials have demonstrated a therapeutic benefit from extended lymphadenectomy, we sought to investigate the impact of the number of LNs removed on prognosis after gastric adenocarcinoma resection.We analyzed patients who underwent gastrectomy for gastric adenocarcinoma from 2000 to 2012, at 7 US academic institutions. Patients with M1 disease or R2 resections were excluded. Disease-specific survival (DSS) was calculated using the Kaplan-Meier method and compared using log-rank and Cox regression analyses.Of 742 patients, 257 (35%) had 7 to 15 LNs removed and 485 (65%) had ?16 LNs removed. Disease-specific survival was not significantly longer after removal of ?16 vs 7 to 15 LNs (10-year survival, 55% vs 47%, respectively; p = 0.53) for the entire cohort, but was significantly improved in the subset of patients with stage IA to IIIA (10-year survival, 74% vs 57%, respectively; p = 0.018) or N0-2 disease (72% vs 55%, respectively; p = 0.023). Similarly, for patients who were classified to more likely be "true N0-2," based on frequentist analysis incorporating both the number of positive and of total LNs removed, the hazard ratio for disease-related death (adjusted for T stage, R status, grade, receipt of neoadjuvant and adjuvant therapy, and institution) significantly decreased as the number of LNs removed increased.The number of LNs removed during gastrectomy for adenocarcinoma appears itself to have prognostic implications for long-term survival.

    View details for PubMedID 26206635

  • Outcomes Following Cardiac Catheterization After Congenital Heart Surgery CATHETERIZATION AND CARDIOVASCULAR INTERVENTIONS Siehr, S. L., Martin, M. H., Axelrod, D., Efron, B., Peng, L., Roth, S. J., Perry, S., Shin, A. Y. 2014; 84 (4): 622-628

    Abstract

    Describe outcomes following unplanned cardiac catheterization after congenital heart surgery.Utility of cardiac catheterization following congenital heart surgery is relatively understudied.Retrospective study examining demographics, indications, and outcomes of unplanned cardiac catheterization after congenital heart surgery at a single institution.Between October 2004 and April 2011, 120 patients underwent 150 unplanned postoperative cardiac catheterizations. Median day of catheterization was postoperative day 20 (range 1-269 days). Survival 30 days postcatheterization was 85%; overall survival to hospital discharge was 72%. Indications for catheterization: 63 for hemodynamic evaluation, 46 for likely intervention, and 41 for assessment of surgical repair. Of the 150 hemodynamic/interventional catheterizations, 103 (69%) were associated with a change in clinical management: 59 trans-catheter interventions, 22 re-operations, 11 changes in medication, six changes in surgical plan, and five withdrawals of support. Complications included hemorrhage in two patients, supraventricular tachycardia in two patients, and transient complete heart block requiring cardiopulmonary resuscitation in one patient.Cardiac catheterization following congenital heart surgery may enable important diagnostic and therapeutic changes in clinical and surgical management. Complications were rare.

    View details for DOI 10.1002/ccd.25490

    View details for Web of Science ID 000342826900018

  • Outcomes following cardiac catheterization after congenital heart surgery. Catheterization and cardiovascular interventions Siehr, S. L., Martin, M. H., Axelrod, D., Efron, B., Peng, L., Roth, S. J., Perry, S., Shin, A. Y. 2014; 84 (4): 622-628

    Abstract

    Describe outcomes following unplanned cardiac catheterization after congenital heart surgery.Utility of cardiac catheterization following congenital heart surgery is relatively understudied.Retrospective study examining demographics, indications, and outcomes of unplanned cardiac catheterization after congenital heart surgery at a single institution.Between October 2004 and April 2011, 120 patients underwent 150 unplanned postoperative cardiac catheterizations. Median day of catheterization was postoperative day 20 (range 1-269 days). Survival 30 days postcatheterization was 85%; overall survival to hospital discharge was 72%. Indications for catheterization: 63 for hemodynamic evaluation, 46 for likely intervention, and 41 for assessment of surgical repair. Of the 150 hemodynamic/interventional catheterizations, 103 (69%) were associated with a change in clinical management: 59 trans-catheter interventions, 22 re-operations, 11 changes in medication, six changes in surgical plan, and five withdrawals of support. Complications included hemorrhage in two patients, supraventricular tachycardia in two patients, and transient complete heart block requiring cardiopulmonary resuscitation in one patient.Cardiac catheterization following congenital heart surgery may enable important diagnostic and therapeutic changes in clinical and surgical management. Complications were rare.

    View details for DOI 10.1002/ccd.25490

    View details for PubMedID 24659225

  • Estimation and Accuracy After Model Selection JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 2014; 109 (507): 991-1007

    View details for DOI 10.1080/01621459.2013.823775

    View details for Web of Science ID 000342852100012

  • Two Modeling Strategies for Empirical Bayes Estimation STATISTICAL SCIENCE Efron, B. 2014; 29 (2): 285-301

    View details for DOI 10.1214/13-STS455

    View details for Web of Science ID 000341171400015

  • Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife JOURNAL OF MACHINE LEARNING RESEARCH Wager, S., Hastie, T., Efron, B. 2014; 15: 1625-1651

    View details for Web of Science ID 000344638100001

  • Estimation and Accuracy after Model Selection. Journal of the American Statistical Association Efron, B. 2014; 109 (507): 991?1007

    Abstract

    Classical statistical theory ignores model selection in assessing estimation accuracy. Here we consider bootstrap methods for computing standard errors and confidence intervals that take model selection into account. The methodology involves bagging, also known as bootstrap smoothing, to tame the erratic discontinuities of selection-based estimators. A useful new formula for the accuracy of bagging then provides standard errors for the smoothed estimators. Two examples, nonparametric and parametric, are carried through in detail: a regression model where the choice of degree (linear, quadratic, cubic, ?) is determined by the Cp criterion, and a Lasso-based estimation problem.

    View details for PubMedID 25346558

    View details for PubMedCentralID PMC4207812

  • Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife. Journal of machine learning research : JMLR Wager, S., Hastie, T., Efron, B. 2014; 15 (1): 1625?51

    Abstract

    We study the variability of predictions made by bagged learners and random forests, and show how to estimate standard errors for these methods. Our work builds on variance estimates for bagging proposed by Efron (1992, 2013) that are based on the jackknife and the infinitesimal jackknife (IJ). In practice, bagged predictors are computed using a finite number B of bootstrap replicates, and working with a large B can be computationally expensive. Direct applications of jackknife and IJ estimators to bagging require B = ?(n1.5) bootstrap replicates to converge, where n is the size of the training set. We propose improved versions that only require B = ?(n) replicates. Moreover, we show that the IJ estimator requires 1.7 times less bootstrap replicates than the jackknife to achieve a given accuracy. Finally, we study the sampling distributions of the jackknife and IJ variance estimates themselves. We illustrate our findings with multiple experiments and simulation studies.

    View details for PubMedID 25580094

  • Two modeling strategies for empirical Bayes estimation. Statistical science : a review journal of the Institute of Mathematical Statistics Efron, B. 2014; 29 (2): 285?301

    Abstract

    Empirical Bayes methods use the data from parallel experiments, for instance observations Xk ~ ? (? k , 1) for k = 1, 2, ?, N, to estimate the conditional distributions ? k |Xk . There are two main estimation strategies: modeling on the ? space, called "g-modeling" here, and modeling on the×space, called "f-modeling." The two approaches are de- scribed and compared. A series of computational formulas are developed to assess their frequentist accuracy. Several examples, both contrived and genuine, show the strengths and limitations of the two strategies.

    View details for PubMedID 25324592

  • The Impact of Circadian Misalignment on Athletic Performance in Professional Football Players SLEEP Smith, R. S., Efron, B., Mah, C. D., Malhotra, A. 2013; 36 (12): 1999-2001

    Abstract

    We hypothesized that professional football teams would perform better than anticipated during games occurring close to their circadian peak in performance.We reviewed the past 40 years of evening and daytime professional football games between west coast and east coast United States teams. In order to account for known factors influencing football game outcomes we compared the results to the point spread which addresses all significant differences between opposing teams for sports betting purposes. One sample t-tests, Wilcoxon signed ranked tests, and linear regression were performed. Comparison to day game data was included as a control.Academic medical center.N/A.N/A.The results were strongly in favor of the west coast teams during evening games against east coast teams, with the west coast teams beating the point spread about twice as often (t = 3.95, P < 0.0001) as east coast teams. For similar daytime game match-ups, we observed no such advantage.Sleep and circadian physiology have profound effects on human function including the performance of elite athletes. Professional football players playing close to the circadian peak in performance demonstrate a significant athletic advantage over those who are playing at other times. Application of this knowledge is likely to enhance human performance.

    View details for DOI 10.5665/sleep.3248

    View details for Web of Science ID 000327773300033

    View details for PubMedID 24293776

    View details for PubMedCentralID PMC3825451

  • Mathematics. Bayes' theorem in the 21st century. Science Efron, B. 2013; 340 (6137): 1177-1178

    View details for DOI 10.1126/science.1236536

    View details for PubMedID 23744934

  • Outcomes After Non-Myeloablative Allogeneic Hematopoietic Cell Transplantation with Total Lymphoid Irradiation and Anti-Thymocyte Globulin in Lymphoid Malignancies After Failed Autologous Transplantation BMT Tandem Meetings Kanate, A. S., Efron, B., Chhabra, S., Kohrt, H., Shizuru, J. A., Laport, G. G., Miklos, D. B., Benjamin, J., Johnston, L., Arai, S., Weng, W., Negrin, R., Strober, S., Lowsky, R. ELSEVIER SCIENCE INC. 2013: S154?S155

    View details for Web of Science ID 000314441900082

  • A 250-YEAR ARGUMENT: BELIEF, BEHAVIOR, AND THE BOOTSTRAP BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Efron, B. 2013; 50 (1): 129-146

    View details for Web of Science ID 000326278800004

  • BAYESIAN INFERENCE AND THE PARAMETRIC BOOTSTRAP ANNALS OF APPLIED STATISTICS Efron, B. 2012; 6 (4): 1971-1997

    Abstract

    The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families, and are particularly simple starting from Jeffreys invariant prior. Because of the i.i.d. nature of bootstrap sampling, familiar formulas describe the computational accuracy of the Bayes estimates. Besides computational methods, the theory provides a connection between Bayesian and frequentist analysis. Efficient algorithms for the frequentist accuracy of Bayesian inferences are developed and demonstrated in a model selection example.

    View details for DOI 10.1214/12-AOAS571

    View details for Web of Science ID 000314458400026

    View details for PubMedCentralID PMC3703677

  • Bayesian inference and the parametric bootstrap. The annals of applied statistics Efron, B. 2012; 6 (4): 1971?97

    Abstract

    The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families, and are particularly simple starting from Jeffreys invariant prior. Because of the i.i.d. nature of bootstrap sampling, familiar formulas describe the computational accuracy of the Bayes estimates. Besides computational methods, the theory provides a connection between Bayesian and frequentist analysis. Efficient algorithms for the frequentist accuracy of Bayesian inferences are developed and demonstrated in a model selection example.

    View details for PubMedID 23843930

    View details for PubMedCentralID PMC3703677

  • Tweedie's Formula and Selection Bias JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 2011; 106 (496): 1602-1614

    View details for DOI 10.1198/jasa.2011.tm11181

    View details for Web of Science ID 000299662900030

  • False discovery rates and copy number variation BIOMETRIKA Efron, B., Zhang, N. R. 2011; 98 (2): 251-271

    View details for DOI 10.1093/biomet/asr018

    View details for Web of Science ID 000291063300001

  • THE BOOTSTRAP AND MARKOV-CHAIN MONTE CARLO JOURNAL OF BIOPHARMACEUTICAL STATISTICS Efron, B. 2011; 21 (6): 1052-1062

    Abstract

    This note concerns the use of parametric bootstrap sampling to carry out Bayesian inference calculations. This is only possible in a subset of those problems amenable to Markov-Chain Monte Carlo (MCMC) analysis, but when feasible the bootstrap approach offers both computational and theoretical advantages. The discussion here is in terms of a simple example, with no attempt at a general analysis.

    View details for DOI 10.1080/10543406.2011.607736

    View details for Web of Science ID 000299576100002

    View details for PubMedID 22023675

    View details for PubMedCentralID PMC3203753

  • Tweedie's Formula and Selection Bias. Journal of the American Statistical Association Efron, B. 2011; 106 (496): 1602?14

    Abstract

    We suppose that the statistician observes some large number of estimates z(i), each with its own unobserved expectation parameter ?(i). The largest few of the z(i)'s are likely to substantially overestimate their corresponding ?(i)'s, this being an example of selection bias, or regression to the mean. Tweedie's formula, first reported by Robbins in 1956, offers a simple empirical Bayes approach for correcting selection bias. This paper investigates its merits and limitations. In addition to the methodology, Tweedie's formula raises more general questions concerning empirical Bayes theory, discussed here as "relevance" and "empirical Bayes information." There is a close connection between applications of the formula and James-Stein estimation.

    View details for PubMedID 22505788

  • Correlated z-Values and the Accuracy of Large-Scale Statistical Estimates JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 2010; 105 (491): 1042-1055

    Abstract

    We consider large-scale studies in which there are hundreds or thousands of correlated cases to investigate, each represented by its own normal variate, typically a z-value. A familiar example is provided by a microarray experiment comparing healthy with sick subjects' expression levels for thousands of genes. This paper concerns the accuracy of summary statistics for the collection of normal variates, such as their empirical cdf or a false discovery rate statistic. It seems like we must estimate an N by N correlation matrix, N the number of cases, but our main result shows that this is not necessary: good accuracy approximations can be based on the root mean square correlation over all N · (N - 1)/2 pairs, a quantity often easily estimated. A second result shows that z-values closely follow normal distributions even under non-null conditions, supporting application of the main theorem. Practical application of the theory is illustrated for a large leukemia microarray study.

    View details for DOI 10.1198/jasa.2010.tm09129

    View details for Web of Science ID 000283695300016

    View details for PubMedCentralID PMC2967047

  • The Future of Indirect Evidence STATISTICAL SCIENCE Efron, B., Greenland, S., Gelman, A., Kass, R. E. 2010; 25 (2): 145-171

    View details for DOI 10.1214/09-STS308

    View details for Web of Science ID 000285322300001

  • Imprecision of Creatinine-Based GFR Estimates in Uninephric Kidney Donors CLINICAL JOURNAL OF THE AMERICAN SOCIETY OF NEPHROLOGY Tan, J. C., Ho, B., Busque, S., Blouch, K., Derby, G., Efron, B., Myers, B. D. 2010; 5 (3): 497-502

    Abstract

    To ensure long-term safety of living kidney donors, it is now recommended that they be followed for at least 2 years after donation and that serum creatinine levels be monitored. Such levels are often subjected by clinical laboratories to estimating equations and are reported as estimated GFR (eGFR). The accuracy of such equations in uninephric living donors has yet to be validated. This is especially important in older living donors, who often have senescence-related depression of GFR.We compared urinary creatinine clearance, four-variable Modification of Diet in Renal Disease estimating equation (eGFR), and the recently reported CKD-EPI GFR estimating equation with true GFR measured by the urinary iothalamate clearance (iGFR) in 64 subjects after kidney donation.Creatinine clearance overestimated iGFR. Both creatinine-based estimating equations were poorly correlated with and underestimated iGFR. More than half of kidney donors had eGFR <60 ml/min per 1.73 m(2) after donation, a level that categorized them as having stage 3 chronic kidney disease by our current laboratory reporting, whereas only 25% had iGFR <60 ml/min per 1.73 m(2). This misclassification disproportionately affected older donors age > or =55 years, of whom 80% had eGFR <60 ml/min per 1.73 m(2). Neither significant albuminuria nor hypertension was observed.The current practice of reporting eGFR after donation commonly leads to a misclassification of chronic kidney disease, particularly in older donors. To ensure long-term well-being of living kidney donors, more precise estimates of GFR are required, particularly among older potential donors.

    View details for DOI 10.2215/CJN.05280709

    View details for Web of Science ID 000275325000017

    View details for PubMedID 20110343

    View details for PubMedCentralID PMC2827575

  • The Future of Indirect Evidence. Statistical science : a review journal of the Institute of Mathematical Statistics Efron, B. 2010; 25 (2): 145?57

    Abstract

    Familiar statistical tests and estimates are obtained by the direct observation of cases of interest: a clinical trial of a new drug, for instance, will compare the drug's effects on a relevant set of patients and controls. Sometimes, though, indirect evidence may be temptingly available, perhaps the results of previous trials on closely related drugs. Very roughly speaking, the difference between direct and indirect statistical evidence marks the boundary between frequentist and Bayesian thinking. Twentieth-century statistical practice focused heavily on direct evidence, on the grounds of superior objectivity. Now, however, new scientific devices such as microarrays routinely produce enormous data sets involving thousands of related situations, where indirect evidence seems too important to ignore. Empirical Bayes methodology offers an attractive direct/indirect compromise. There is already some evidence of a shift toward a less rigid standard of statistical objectivity that allows better use of indirect evidence. This article is basically the text of a recent talk featuring some examples from current practice, with a little bit of futuristic speculation.

    View details for PubMedID 21243111

    View details for PubMedCentralID PMC3019763

  • Correlated z-values and the accuracy of large-scale statistical estimates. Journal of the American Statistical Association Efron, B. 2010; 105 (491): 1042?55

    Abstract

    We consider large-scale studies in which there are hundreds or thousands of correlated cases to investigate, each represented by its own normal variate, typically a z-value. A familiar example is provided by a microarray experiment comparing healthy with sick subjects' expression levels for thousands of genes. This paper concerns the accuracy of summary statistics for the collection of normal variates, such as their empirical cdf or a false discovery rate statistic. It seems like we must estimate an N by N correlation matrix, N the number of cases, but our main result shows that this is not necessary: good accuracy approximations can be based on the root mean square correlation over all N · (N - 1)/2 pairs, a quantity often easily estimated. A second result shows that z-values closely follow normal distributions even under non-null conditions, supporting application of the main theorem. Practical application of the theory is illustrated for a large leukemia microarray study.

    View details for PubMedID 21052523

    View details for PubMedCentralID PMC2967047

  • ARE A SET OF MICROARRAYS INDEPENDENT OF EACH OTHER? ANNALS OF APPLIED STATISTICS Efron, B. 2009; 3 (3): 922-942

    Abstract

    Having observed an m x n matrix X whose rows are possibly correlated, we wish to test the hypothesis that the columns are independent of each other. Our motivation comes from microarray studies, where the rows of X record expression levels for m different genes, often highly correlated, while the columns represent n individual microarrays, presumably obtained independently. The presumption of independence underlies all the familiar permutation, cross-validation, and bootstrap methods for microarray analysis, so it is important to know when independence fails. We develop nonparametric and normal-theory testing methods. The row and column correlations of X interact with each other in a way that complicates test procedures, essentially by reducing the accuracy of the relevant estimators.

    View details for DOI 10.1214/09-AOAS236

    View details for Web of Science ID 000271979900003

  • Empirical Bayes Estimates for Large-Scale Prediction Problems JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 2009; 104 (487): 1015-1028

    Abstract

    Classical prediction methods such as Fisher's linear discriminant function were designed for small-scale problems, where the number of predictors N is much smaller than the number of observations n. Modern scientific devices often reverse this situation. A microarray analysis, for example, might include n = 100 subjects measured on N = 10,000 genes, each of which is a potential predictor. This paper proposes an empirical Bayes approach to large-scale prediction, where the optimum Bayes prediction rule is estimated employing the data from all the predictors. Microarray examples are used to illustrate the method. The results show a close connection with the shrunken centroids algorithm of Tibshirani et al. (2002), a frequentist regularization approach to large-scale prediction, and also with false discovery rate theory.

    View details for DOI 10.1198/jasa.2009.tm08523

    View details for Web of Science ID 000270916100016

    View details for PubMedCentralID PMC2844005

  • Empirical Bayes Estimates for Large-Scale Prediction Problems. Journal of the American Statistical Association Efron, B. 2009; 104 (487): 1015?28

    Abstract

    Classical prediction methods such as Fisher's linear discriminant function were designed for small-scale problems, where the number of predictors N is much smaller than the number of observations n. Modern scientific devices often reverse this situation. A microarray analysis, for example, might include n = 100 subjects measured on N = 10,000 genes, each of which is a potential predictor. This paper proposes an empirical Bayes approach to large-scale prediction, where the optimum Bayes prediction rule is estimated employing the data from all the predictors. Microarray examples are used to illustrate the method. The results show a close connection with the shrunken centroids algorithm of Tibshirani et al. (2002), a frequentist regularization approach to large-scale prediction, and also with false discovery rate theory.

    View details for PubMedID 20333278

    View details for PubMedCentralID PMC2844005

  • SIMULTANEOUS INFERENCE: WHEN SHOULD HYPOTHESIS TESTING PROBLEMS BE COMBINED? ANNALS OF APPLIED STATISTICS Efron, B. 2008; 2 (1): 197-223

    View details for DOI 10.1214/07-AOAS141

    View details for Web of Science ID 000261057700015

  • Comment: Microarrays, empirical Bayes and the two-groups model STATISTICAL SCIENCE Benjamini, Y., Cai, T. T., Morris, C. N., Rice, K., Spiegelhalter, D., Efron, B. 2008; 23 (1): 23-47

    View details for DOI 10.1214/07-STS236B

    View details for Web of Science ID 000258011200002

  • Microarrays, empirical Bayes and the two-groups model STATISTICAL SCIENCE Efron, B. 2008; 23 (1): 1-22

    View details for DOI 10.1214/07-STS236

    View details for Web of Science ID 000258011200001

  • Prediction of early progression in recently diagnosed IgA nephropathy NEPHROLOGY DIALYSIS TRANSPLANTATION Lemley, K. V., Lafayette, R. A., Derby, G., Blouch, K. L., Anderson, L., Efron, B., Myers, B. D. 2008; 23 (1): 213-222

    Abstract

    Most studies of prognosis in IgA nephropathy (IgAN) have tried to predict dichotomous outcomes based on a small number of clinical or semi-quantitative histological variables in large numbers of patients.We pursued a quite different approach. We measured GFR annually for 4-5 years in 22 adult patients with recently diagnosed IgAN. Quantitative morphology was performed on the diagnostic biopsy specimens and baseline glomerular filtration dynamics were performed at study entry. An initial set of 30 plausible predictor variables (half demographic or physiological, half structural) was reduced to 22 using phylogenetic trees. Least-angle regression (LARS) was used to predict the rate of GFR change from these variablesThe rate of GFR change ranged from a loss of 41 ml/min/year to a gain of 8.6 ml/min/year. We found an optimum predictor set of five baseline variables: the percentage of glomeruli with global sclerosis, the fractional interstitial area, the serum creatinine, the average tuft volume of non-sclerotic glomeruli and the renal plasma flow.The strong predictive relationship of the three structural variables with the slope of GFR in our subjects suggests that even at the time of their initial diagnosis many patients with IgAN already manifest a 'remnant kidney' phenomenon. The distinctive pathophysiological insights derived from this study suggest some of the advantages of intense quantitative investigations applied to a small number of subjects.

    View details for DOI 10.1093/ndt/gfm560

    View details for Web of Science ID 000253022100034

    View details for PubMedID 17890749

  • Size, power and false discovery rates ANNALS OF STATISTICS Efron, B. 2007; 35 (4): 1351-1377

    View details for DOI 10.1214/009053606000001460

    View details for Web of Science ID 000249568000001

  • ON TESTING THE SIGNIFICANCE OF SETS OF GENES ANNALS OF APPLIED STATISTICS Efron, B., Tibshirani, R. 2007; 1 (1): 107-129

    View details for DOI 10.1214/07-AOAS101

    View details for Web of Science ID 000261050400006

  • Correlation and large-scale simultaneous significance testing JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 2007; 102 (477): 93-103

    View details for DOI 10.1198/016214506000001211

    View details for Web of Science ID 000244361000010

  • Minimum volume confidence regions for a multivariate normal mean vector JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY Efron, B. 2006; 68: 655-670

    View details for Web of Science ID 000239928500005

  • Signature patterns of gene expression in mouse atherosclerosis and their correlation to human coronary disease PHYSIOLOGICAL GENOMICS Tabibiazar, R., Wagner, R. A., Ashley, E. A., King, J. Y., Ferrara, R., Spin, J. M., Sanan, D. A., Narasimhan, B., Tibshirani, R., Tsao, P. S., Efron, B., Quertermous, T. 2005; 22 (2): 213-226

    Abstract

    The propensity for developing atherosclerosis is dependent on underlying genetic risk and varies as a function of age and exposure to environmental risk factors. Employing three mouse models with different disease susceptibility, two diets, and a longitudinal experimental design, it was possible to manipulate each of these factors to focus analysis on genes most likely to have a specific disease-related function. To identify differences in longitudinal gene expression patterns of atherosclerosis, we have developed and employed a statistical algorithm that relies on generalized regression and permutation analysis. Comprehensive annotation of the array with ontology and pathway terms has allowed rigorous identification of molecular and biological processes that underlie disease pathophysiology. The repertoire of atherosclerosis-related immunomodulatory genes has been extended, and additional fundamental pathways have been identified. This highly disease-specific group of mouse genes was combined with an extensive human coronary artery data set to identify a shared group of genes differentially regulated among atherosclerotic tissues from different species and different vascular beds. A small core subset of these differentially regulated genes was sufficient to accurately classify various stages of the disease in mouse. The same gene subset was also found to accurately classify human coronary lesion severity. In addition, this classifier gene set was able to distinguish with high accuracy atherectomy specimens from native coronary artery disease vs. those collected from in-stent restenosis lesions, thus identifying molecular differences between these two processes. These studies significantly focus efforts aimed at identifying central gene regulatory pathways that mediate atherosclerotic disease, and the identification of classification gene sets offers unique insights into potential diagnostic and therapeutic strategies in atherosclerotic disease.

    View details for DOI 10.1152/physiolgenomics.00001.2005

    View details for Web of Science ID 000230987900011

    View details for PubMedID 15870398

  • Impact of HIV-1 subtype and antiretroviral therapy on protease and reverse transcriptase genotype: Results of a global collaboration PLOS MEDICINE Kantor, R., Katzenstein, D. A., Efron, B., CARVALHO, A. P., Wynhoven, B., Cane, P., Clarke, J., Sirivichayakul, S., Soares, M. A., Snoeck, J., Pillay, C., Rudich, H., Rodrigues, R., Holguin, A., Ariyoshi, K., Bouzas, M. B., Cahn, P., Sugiura, W., Soriano, V., Brigido, L. F., Grossman, Z., Morris, L., Vandamme, A. M., Tanuri, A., Phanuphak, P., WEBER, J. N., Pillay, D., Harrigan, P. R., Camacho, R., Schapiro, J. M., Shafer, R. W. 2005; 2 (4): 325-337

    Abstract

    The genetic differences among HIV-1 subtypes may be critical to clinical management and drug resistance surveillance as antiretroviral treatment is expanded to regions of the world where diverse non-subtype-B viruses predominate.To assess the impact of HIV-1 subtype and antiretroviral treatment on the distribution of mutations in protease and reverse transcriptase, a binomial response model using subtype and treatment as explanatory variables was used to analyze a large compiled dataset of non-subtype-B HIV-1 sequences. Non-subtype-B sequences from 3,686 persons with well characterized antiretroviral treatment histories were analyzed in comparison to subtype B sequences from 4,769 persons. The non-subtype-B sequences included 461 with subtype A, 1,185 with C, 331 with D, 245 with F, 293 with G, 513 with CRF01_AE, and 618 with CRF02_AG. Each of the 55 known subtype B drug-resistance mutations occurred in at least one non-B isolate, and 44 (80%) of these mutations were significantly associated with antiretroviral treatment in at least one non-B subtype. Conversely, of 67 mutations found to be associated with antiretroviral therapy in at least one non-B subtype, 61 were also associated with antiretroviral therapy in subtype B isolates.Global surveillance and genotypic assessment of drug resistance should focus primarily on the known subtype B drug-resistance mutations.

    View details for DOI 10.1371/journal.pmed.0020112

    View details for PubMedID 15839752

  • Mouse strain-specific differences in vascular wall gene expression and their relationship to vascular disease ARTERIOSCLEROSIS THROMBOSIS AND VASCULAR BIOLOGY Tabibiazar, R., Wagner, R. A., Spin, J. M., Ashley, E. A., Narasimhan, B., Rubin, E. M., Efron, B., Tsao, P. S., Tibshirani, R., Quertermous, T. 2005; 25 (2): 302-308

    Abstract

    Different strains of inbred mice exhibit different susceptibility to the development of atherosclerosis. The C3H/HeJ and C57Bl/6 mice have been used in several studies aimed at understanding the genetic basis of atherosclerosis. Under controlled environmental conditions, variations in susceptibility to atherosclerosis reflect differences in genetic makeup, and these differences must be reflected in gene expression patterns that are temporally related to the development of disease. In this study, we sought to identify the genetic pathways that are differentially activated in the aortas of these mice.We performed genome-wide transcriptional profiling of aortas from C3H/HeJ and C57Bl/6 mice. Differences in gene expression were identified at baseline as well as during normal aging and longitudinal exposure to high-fat diet. The significance of these genes to the development of atherosclerosis was evaluated by observing their temporal pattern of expression in the well-studied apolipoprotein E model of atherosclerosis.Gene expression differences between the 2 strains suggest that aortas of C57Bl/6 mice have a higher genetic propensity to develop inflammation in response to appropriate atherogenic stimuli. This study expands the repertoire of factors in known disease-related signaling pathways and identifies novel candidate genes for future study. To gain insights into the molecular pathways that are differentially activated in strains of mice with varied susceptibility to atherosclerosis, we performed comprehensive transcriptional profiling of their vascular wall. Genes identified through these studies expand the repertoire of factors in disease-related signaling pathways and identify novel candidate genes in atherosclerosis.

    View details for DOI 10.1161/011.ATV.0000151372.86863.a5

    View details for Web of Science ID 000226594000009

    View details for PubMedID 15550693

  • The 'miss rate' for the analysis of gene expression data BIOSTATISTICS Taylor, J., Tibshirani, R., Efron, B. 2005; 6 (1): 111-117

    Abstract

    Multiple testing issues are important in gene expression studies, where typically thousands of genes are compared over two or more experimental conditions. The false discovery rate has become a popular measure in this setting. Here we discuss a complementary measure, the 'miss rate', and show how to estimate it in practice.

    View details for DOI 10.1093/biostatistics/kxh021

    View details for Web of Science ID 000226346300009

    View details for PubMedID 15618531

  • The estimation of prediction error: Covariance penalties and cross-validation JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 2004; 99 (467): 619-632

    View details for DOI 10.1198/016214504000000692

    View details for Web of Science ID 000223857500009

  • Least angle regression ANNALS OF STATISTICS Efron, B., Hastie, T., Johnstone, I., Tibshirani, R. 2004; 32 (2): 407-451

    View details for Web of Science ID 000221411000001

  • Large-scale simultaneous hypothesis testing: The choice of a null hypothesis JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 2004; 99 (465): 96-104

    View details for DOI 10.1198/016214504000000089

    View details for Web of Science ID 000220638200010

  • Transcriptional adaptation of Mycobacterium tuberculosis within macrophages: Insights into the phagosomal environment JOURNAL OF EXPERIMENTAL MEDICINE Schnappinger, D., Ehrt, S., Voskuil, M. I., Liu, Y., Mangan, J. A., Monahan, I. M., Dolganov, G., Efron, B., Butcher, P. D., Nathan, C., Schoolnik, G. K. 2003; 198 (5): 693-704

    Abstract

    Little is known about the biochemical environment in phagosomes harboring an infectious agent. To assess the state of this organelle we captured the transcriptional responses of Mycobacterium tuberculosis (MTB) in macrophages from wild-type and nitric oxide (NO) synthase 2-deficient mice before and after immunologic activation. The intraphagosomal transcriptome was compared with the transcriptome of MTB in standard broth culture and during growth in diverse conditions designed to simulate features of the phagosomal environment. Genes expressed differentially as a consequence of intraphagosomal residence included an interferon gamma- and NO-induced response that intensifies an iron-scavenging program, converts the microbe from aerobic to anaerobic respiration, and induces a dormancy regulon. Induction of genes involved in the activation and beta-oxidation of fatty acids indicated that fatty acids furnish carbon and energy. Induction of sigmaE-dependent, sodium dodecyl sulfate-regulated genes and genes involved in mycolic acid modification pointed to damage and repair of the cell envelope. Sentinel genes within the intraphagosomal transcriptome were induced similarly by MTB in the lungs of mice. The microbial transcriptome thus served as a bioprobe of the MTB phagosomal environment, showing it to be nitrosative, oxidative, functionally hypoxic, carbohydrate poor, and capable of perturbing the pathogen's cell envelope.

    View details for Web of Science ID 000185155500002

    View details for PubMedID 12953091

    View details for PubMedCentralID PMC2194186

  • Second thoughts on the bootstrap STATISTICAL SCIENCE Efron, B. 2003; 18 (2): 135-140

    View details for Web of Science ID 000185861100002

  • Recent trends in National Institutes of Health funding of surgical research 122nd Annual Meeting of the American-Surgical-Association Rangel, S. J., Efron, B., Moss, R. L. LIPPINCOTT WILLIAMS & WILKINS. 2002: 277?87

    Abstract

    To compare the amount of National Institutes of Health (NIH) funding provided to departments of surgery with that provided to other major clinical departments, to examine the relationship between peer-review activity and funding success, and to compare trends in participation in the peer-review process between surgeons and representatives from other clinical departments.Surgical research has made enormous contributions to human health. This work is fundamentally dependent on fair and unbiased distribution of extramural research funds from the NIH. To date, no published report has examined the relative distribution of extramural support between departments of surgery and other major clinical departments.Data regarding funding trends and peer-review activity were obtained from the NIH and compared between departments of surgery and four nonsurgical departments (medicine, psychiatry, pediatrics, neurology). Award data were examined during 1996 to 2001. Participation trends were examined during 1998 to 2000.Success rates of surgical proposals were significantly lower than nonsurgical proposals. Differentials in success rates were greatest for proposals assigned to the National Cancer Institute, although relative underfunding for surgical research spanned all major institutes. Awards for surgical grants averaged 5% to 27% less than nonsurgical grants). Surgeons exhibited 35% to 65% less peer-review activity relative to nonsurgeons when normalized to grant submission activity. Overall, surgeons participated on sections where they made up a relatively smaller proportion of total review members compared to nonsurgeons.Surgical grant proposals are less likely to be funded and carry significantly smaller awards compared to nonsurgical proposals. Relatively fewer surgeons participate in the review process, and those who do are more likely to be in the minority within study sections. Multiple strategies are needed to address these trends and level the playing field for surgical research.

    View details for DOI 10.1097/01.SLA.0000026721.64592.F4

    View details for Web of Science ID 000177741500004

    View details for PubMedID 12192314

  • Smoothers and the C-p, generalized maximum likelihood, and extended exponential criteria: A geometric approach JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Kou, S. C., Efron, B. 2002; 97 (459): 766-782

    View details for DOI 10.1198/016214502388618582

    View details for Web of Science ID 000178018500019

  • Empirical Bayes methods and false discovery rates for microarrays GENETIC EPIDEMIOLOGY Efron, B., Tibshirani, R. 2002; 23 (1): 70-86

    Abstract

    In a classic two-sample problem, one might use Wilcoxon's statistic to test for a difference between treatment and control subjects. The analogous microarray experiment yields thousands of Wilcoxon statistics, one for each gene on the array, and confronts the statistician with a difficult simultaneous inference situation. We will discuss two inferential approaches to this problem: an empirical Bayes method that requires very little a priori Bayesian modeling, and the frequentist method of "false discovery rates" proposed by Benjamini and Hochberg in 1995. It turns out that the two methods are closely related and can be used together to produce sensible simultaneous inferences.

    View details for DOI 10.1002/gepi.01124

    View details for Web of Science ID 000176697800006

    View details for PubMedID 12112249

  • Pre-validation and inference in microarrays. Statistical applications in genetics and molecular biology Tibshirani, R. J., Efron, B. 2002; 1: Article1-?

    Abstract

    In microarray studies, an important problem is to compare a predictor of disease outcome derived from gene expression levels to standard clinical predictors. Comparing them on the same dataset that was used to derive the microarray predictor can lead to results strongly biased in favor of the microarray predictor. We propose a new technique called "pre-validation'' for making a fairer comparison between the two sets of predictors. We study the method analytically and explore its application in a recent study on breast cancer.

    View details for PubMedID 16646777

  • The two-way proportional hazards model JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY Efron, B. 2002; 64: 899-909

    View details for Web of Science ID 000179221100017

  • Empirical Bayes analysis of a microarray experiment 160th Annual Meeting of the American-Statistical-Association Efron, B., Tibshirani, R., Storey, J. D., Tusher, V. AMER STATISTICAL ASSOC. 2001: 1151?60

    View details for Web of Science ID 000172728000002

  • Infectious complications among 620 consecutive heart transplant patients at Stanford University Medical Center 10th International Symposium on Infections in the Immunocompromised Montoya, J. G., Giraldo, L. F., Efron, B., Stinson, E. B., Gamberg, P., Hung, S., Giannetti, N., Miller, J., Remington, J. S. OXFORD UNIV PRESS INC. 2001: 629?40

    Abstract

    A total of 1073 infectious episodes (IEs) that occurred in 620 consecutive heart transplantation patients at Stanford Medical Center between 16 December 1980 and 30 June 1996 were reviewed. Infectious complications were a major cause of morbidity and mortality, second only to rejection as the cause of early deaths and the most common cause of late deaths. Of the IEs, 468 (43.6%) were caused by bacteria, 447 (41.7%) by viruses, 109 (10.2%) by fungi, 43 (4.0%) by Pneumocystis carinii, and 6 (0.6%) by protozoa. The largest number of IEs occurred in the lungs (301 [28.1%]). A significant reduction in the incidence of IEs and a delay in presentation after transplantation were observed; these were most likely related to the introduction of new chemoprophylactic regimens during the study period and prevention of significant disease caused by cytomegalovirus.

    View details for Web of Science ID 000170271200007

    View details for PubMedID 11486285

  • Infectious complications among 620 consecutive heart transplant patients at Stanford University Medical Center 10th International Symposium on Infection in the Immunocompromised Host Montoya, J. G., Giraldo, L. F., Efron, B., Stinson, E. B., Gamberg, P., Hunt, S., Giannetti, N., Miller, J., Remington, J. S. CELL PRESS. 2001: 629?U6

    View details for Web of Science ID 000170271400014

  • A meta-analysis of peritoneal drainage versus laparotomy for perforated necrotizing enterocolitis 31st Annual Meeting of the Section-on-Surgery of the American-Academy-of-Pediatrics Moss, R. L., Dimmitt, R. A., Henry, M. C., Geraghty, N., Efron, B. W B SAUNDERS CO-ELSEVIER INC. 2001: 1210?13

    Abstract

    Both primary peritoneal drainage (PPD) and laparotomy (LAP) are used widely for treatment of perforated necrotizing enterocolitis (NEC). Published reports include only anecdotes and small series. The authors used techniques of meta-analysis to determine which treatment is most effective.The authors identified published studies reporting surgical treatment of NEC from January 1, 1978 to December 31, 1999; there were 10 studies (n = 475). The authors were contacted and all available raw patient data for use in meta-analysis (n = 190) were obtained. The authors used logistic regression to determine the relative survival rate after PPD and LAP, controlling for the effect of gestational age and institution.The combined probability of survival in the 10 published studies did not show an advantage for PPD (55%) or LAP (67%; P =.27). When the authors corrected for the effect of birth weight on survival rate, they still did not observe a difference (P =.67). A marked bias in treatment assignment was found with smaller babies undergoing PPD than LAP (931 g versus 1,615 g, respectively; P =.0004). Analysis of raw data showed an even greater bias in treatment assignment. The authors found increased survival rate for LAP versus PPD (62.3% v 35.6%; P =.0009). However, a logistic regression model could not overcome the bias in assignment of patients with a much higher expected mortality rate to PPD.Using currently available data, it is not possible to determine whether PPD or LAP is superior. Bias in treatment assignment precludes conclusions regarding comparative survival. Only a randomized trial will determine which operation is best for the treatment of perforated NEC.

    View details for DOI 10.1053/jpsu.2001.25764

    View details for PubMedID 11479858

  • Statistical modeling: The two cultures - Comments and rejoinders STATISTICAL SCIENCE Cox, D. R., Efron, B., Hoadley, B., Parzen, E., Breiman, L. 2001; 16 (3): 216-231

    View details for Web of Science ID 000172846900002

  • Selection criteria for scatterplot smoothers ANNALS OF STATISTICS Efron, B. 2001; 29 (2): 470-504

    View details for Web of Science ID 000171342800006

  • The bootstrap and modern statistics JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 2000; 95 (452): 1293-1296

    View details for Web of Science ID 000165470300035

  • HIV-1 genotypic resistance patterns predict response to saquinavir-ritonavir therapy in patients in whom previous protease inhibitor therapy had failed ANNALS OF INTERNAL MEDICINE Zolopa, A. R., Shafer, R. W., Warford, A., Montoya, J. G., Hsu, P., KATZENSTEIN, D., Merigan, T. C., Efron, B. 1999; 131 (11): 813-?

    Abstract

    Tests for resistance to HIV drugs are available for clinical use; however, their predictive value has not been fully assessed.To determine HIV-1 genotypic predictors of a virologic response to saquinavir-ritonavir therapy in patients in whom at least one previous protease inhibitor-containing regimen had failed and to compare the predictive value of baseline genotype with that of standard clinical evaluation.Retrospective clinical cohort study.University-based HIV clinic.54 HIV-1-infected adults treated with saquinavir-ritonavir who had experienced virologic failure while receiving a protease inhibitor-containing regimen for at least 3 months.HIV-1 reverse transcriptase and protease gene sequences, CD4 cell counts, clinical characteristics, detailed antiretroviral treatment history, and plasma HIV-1 RNA levels at baseline and at three follow-up time points (median, 4, 12, and 26 weeks). Virologic failure was defined as a plasma HIV RNA level greater than 1000 copies/mL.In 22 patients (41%), a plasma HIV-1 RNA level less than 500 copies/mL was achieved by week 12; in 15 patients (28%), this response was maintained through week 26. Clinical characteristics predicting a poorer response included a diagnosis of AIDS, lower CD4 cell count, and higher plasma HIV RNA level (P<0.03). Number of previous nucleoside reverse transcriptase inhibitors, previous protease inhibitor therapy, and duration of previous protease inhibitor therapy were predictors of poorer response (P<0.01). Multivariate regression models revealed that protease mutations present at the initiation of saquinavir-ritonavir therapy were the strongest predictors of virologic response. A model of clinical features explained up to 45% of the variation in virologic outcomes by week 12, whereas the explained variance was 71% when genotypic predictors were included.In patients in whom protease inhibitor-containing antiretroviral therapy fails, HIV-1 genotype is predictive of virologic response to subsequent therapy. This predictive capacity adds to that of standard clinical evaluation.

    View details for PubMedID 10610625

  • Nonparametric methods for doubly truncated data JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B., Petrosian, V. 1999; 94 (447): 824-834

    View details for Web of Science ID 000082756400025

  • Clinical resistance patterns and responses to two sequential protease inhibitor regimens in saquinavir and reverse transcriptase inhibitor-experienced persons 5th Conference on Retroviruses and Opportunistic Infections Lawrence, J., Schapiro, J., Winters, M., Montoya, J., Zolopa, A., Pesano, R., Efron, B., Winslow, D., Merigan, T. C. UNIV CHICAGO PRESS. 1999: 1356?64

    Abstract

    The efficacy of sequential protease inhibitor therapy was studied in 16 human immunodeficiency virus (HIV) 1-infected persons in whom saquinavir with multiple nucleoside reverse transcriptase (RT) inhibitors (NRTI) had failed. Nelfinavir plus two NRTIs (new or continued) resulted in minimal (0.59 log RNA copies/mL) and transient (8 weeks) suppression of plasma HIV RNA levels. Rapid failure was surprisingly associated with baseline presence of protease gene mutation L90M (P=.04) in the absence of D30N and with RT mutations D67N (P<.01), K70R/S (P=.02), and K219Q/W/R/E (P<.01). Ten patients were subsequently switched to indinavir plus nevirapine and 2 NRTIs, resulting in a median 1.62 log reduction in plasma HIV RNA, with 3 patients maintaining 400 copies/mL for 24 weeks. These results suggest that nelfinavir may have limited utility after saquinavir failure, particularly without potent concomitant therapy. Combining an NRTI with a new protease inhibitor for rescue may improve response.

    View details for Web of Science ID 000080561100007

    View details for PubMedID 10228055

  • Resistance mutations to zidovudine and saquinavir in patients receiving zidovudine plus saquinavir or zidovudine and zalcitabine plus saquinavir in AIDS Clinical Trials Group 229 JOURNAL OF INFECTIOUS DISEASES Schapiro, J. M., Lawrence, J., Speck, R., Winters, M. A., Efron, B., COOMBS, R. W., Collier, A. C., Merigan, T. C. 1999; 179 (1): 249-253

    Abstract

    The relationships among treatment regimens, plasma human immunodeficiency virus (HIV) RNA levels, and resistance mutations to saquinavir (codons 48 and 90) and zidovudine (codon 215) were examined in a cohort of 144 patients from the AIDS Clinical Trials Group 229 study. After 24-40 weeks of therapy, no patients who had received the two-drug combination (zidovudine plus saquinavir) had only codon 48 mutations, 45.8% had only codon 90 mutations, and 8.3% had both codon 48 and 90 mutations. Mutations developed by patients who had received the three-drug combination (zidovudine and zalcitabine plus saquinavir) were codon 48 alone in 1.4%, codon 90 alone in 33.3%, and both codons 48 and 90 in 4.2%. The difference between the groups showed a trend toward reduced mutations with three versus two drugs but did not reach significance (P=.11, two-sided chi2). Higher baseline HIV RNA levels correlated with the development of protease mutations. Mutations at codon 215 were present in 82% of all patients at baseline and in 87% after therapy.

    View details for Web of Science ID 000077725000035

    View details for PubMedID 9841849

  • The problem of regions ANNALS OF STATISTICS Efron, B., Tibshirani, R. 1998; 26 (5): 1687-1718

    View details for Web of Science ID 000079135700002

  • R.A. Fisher in the 21st century - Invited paper presented at the 1996 R.A. Fisher lecture STATISTICAL SCIENCE Efron, B. 1998; 13 (2): 95-114

    View details for Web of Science ID 000074917200001

  • Risk for retinitis in patients with AIDS can be assessed by quantitation of threshold levels of cytomegalovirus DNA burden in blood JOURNAL OF INFECTIOUS DISEASES Rasmussen, L., Zipeto, D., Wolitz, R. A., Dowling, A., Efron, B., Merigan, T. C. 1997; 176 (5): 1146-1155

    Abstract

    Cytomegalovirus (CMV) retinitis in patients infected with human immunodeficiency virus (HIV) is a significant clinical problem. Seventy-five patients with CD4 T cell counts <100/mm3 were monitored prospectively every 2 months for CMV DNA burden. The target for DNA amplification was a 162-bp fragment from the CMV immediate early gene. CMV DNA burden, at levels of > or =320 in white blood cells or > or =32 in plasma (P = .001), particularly when sustained (P = .005 and .008, respectively), distinguished patients who developed retinitis from those who remained free of disease. Progression to retinitis was not consistently accompanied by increases in CMV burden, indicating that quantitation of CMV burden beyond threshold levels is not necessary to predict risk for development of retinitis. Virus isolation from WBC, but not urine, was also significantly associated with risk for retinitis (P = .001).

    View details for Web of Science ID A1997YD80900004

    View details for PubMedID 9359712

  • A predictive morphometric model for the obstructive sleep apnea syndrome ANNALS OF INTERNAL MEDICINE Kushida, C. A., Efron, B., Guilleminault, C. 1997; 127 (8): 581-?

    Abstract

    Mathematical formulas have been used to clinically predict whether patients will develop the obstructive sleep apnea syndrome (OSAS). However, these models do not take into account the disproportionate craniofacial anatomy that accompanies OSAS independently of obesity.To determine the accuracy of a morphometric model, which combines measurements of the oral cavity with body mass index and neck circumference, in predicting whether a patient has OSAS.6-month prospective study.University-based tertiary referral sleep clinic and research center.300 consecutive patients evaluated for sleep disorders for the first time.Body mass index, neck circumference, and oral cavity measurements were obtained, and a model value was calculated for each patient. Polysomnography was used to determine the number of abnormal respiratory events that occurred during sleep. Sleep apnea was defined as more than five episodes of apnea or hypopnea per hour of sleep.The morphometric model had a sensitivity of 97.6% (95% CI, 95% to 98.9%), a specificity of 100% (CI 92% to 100%), a positive predictive value of 100% (CI, 98.5% to 100%), and a negative predictive value of 88.5% (CI, 77% to 95%). No significant discrepancies were revealed in tests of intermeasurer and test-retest reliability.The morphometric model provides a rapid, accurate, and reproducible method for predicting whether patients in an ambulatory setting have OSAS. The model may be clinically useful as a screening tool for OSAS rather than as a replacement for polysomnography.

    View details for PubMedID 9341055

  • Effect of therapeutic immunization with recombinant gp160 HIV-1 vaccine on HIV-1 proviral DNA and plasma RNA: Relationship to cellular immune responses JOURNAL OF ACQUIRED IMMUNE DEFICIENCY SYNDROMES Kundu, S. K., KATZENSTEIN, D., Valentine, F. T., Spino, C., Efron, B., Merigan, T. C. 1997; 15 (4): 269-274

    Abstract

    Therapeutic vaccination has been proposed as a strategy to augment immune mechanisms to control viral replication and slow clinical progression of HIV infection to disease. Following recombinant gp160 (r-gp160) immunization in three clinical trials, plasma HIV-1 RNA and cellular proviral DNA were assessed by quantitative polymerase chain reaction (PCR) in 76 HIV-seropositive subjects with CD4+ T cell counts > or = 300/mm3. Immunization increased HIV-specific cellular immune responses (e.g., cytotoxic T lymphocyte [CTL] activities, lymphocyte proliferative responses); however, there were no significant effects of immunization or cellular immune responses on measures of plasma RNA or cellular DNA viral load.

    View details for Web of Science ID A1997YA52500004

    View details for PubMedID 9292585

  • Improvements on cross-validation: The .632+ bootstrap method JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B., Tibshirani, R. 1997; 92 (438): 548-560

    View details for Web of Science ID A1997XE29600020

  • The length heuristic for simultaneous hypothesis tests BIOMETRIKA Efron, B. 1997; 84 (1): 143-157

    View details for Web of Science ID A1997WT08200012

  • Circadian rhythms and enhanced athletic performance in the National Football League SLEEP Smith, R. S., Guilleminault, C., Efron, B. 1997; 20 (5): 362-365

    Abstract

    Circadian rhythms produce daily changes in critical elements of athletic performance. We explored the significance of performing at different circadian times in the National Football League (NFL) over the last 25 seasons. West Coast (WC) NFL teams should have a circadian advantage over East Coast (EC) teams during Monday Night Football (MNF) games because WC teams are essentially playing closer to the proposed peak athletic performance time of day. Retrospective data analysis was applied to all games involving WC versus EC teams playing on MNF with start times of 9:00 p.m. Eastern Standard Time (EST) from the 1970-1994 seasons. Logistic regression analysis of win-loss records relative to point spreads and home-field advantage was examined. West Coast teams win more often (p < 0.01) and by more points per game than EC teams. West Coast teams are performing significantly (p < 0.01) better than is predicted by the Las Vegas odds (the point spread). This apparent advantage enhances home-field advantage for WC teams and essentially eliminates the beneficial effects of home-field advantage for EC teams during MNF games. These results support the presence of an enhancement of athletic performance at certain circadian times of the day.

    View details for PubMedID 9381059

  • Using specially designed exponential families for density estimation ANNALS OF STATISTICS Efron, B., Tibshirani, R. 1996; 24 (6): 2431-2461

    View details for Web of Science ID A1996WK45900006

  • Bootstrap confidence intervals STATISTICAL SCIENCE DiCiccio, T. J., Efron, B. 1996; 11 (3): 189-212

    View details for Web of Science ID A1996WC62900002

  • Bootstrap confidence levels for phylogenetic trees PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Efron, B., Halloran, E., Holmes, S. 1996; 93 (14): 7085-7090

    Abstract

    Evolutionary trees are often estimated from DNA or RNA sequence data. How much confidence should we have in the estimated trees? In 1985, Felsenstein [Felsenstein, J. (1985) Evolution 39, 783-791] suggested the use of the bootstrap to answer this question. Felsenstein's method, which in concept is a straightforward application of the bootstrap, is widely used, but has been criticized as biased in the genetics literature. This paper concerns the use of the bootstrap in the tree problem. We show that Felsenstein's method is not biased, but that it can be corrected to better agree with standard ideas of confidence levels and hypothesis testing. These corrections can be made by using the more elaborate bootstrap method presented here, at the expense of considerably more computation.

    View details for Web of Science ID A1996UW79200046

    View details for PubMedID 8692949

  • The effect of high-dose saquinavir on viral load and CD4(+) T-cell counts in HIV-infected patients ANNALS OF INTERNAL MEDICINE Schapiro, J. M., Winters, M. A., Stewart, F., Efron, B., Norris, J., Kozal, M. J., Merigan, T. C. 1996; 124 (12): 1039-1050

    Abstract

    To evaluate the efficacy and safety of high-dose therapy with the human immunodeficiency virus (HIV) protease inhibitor saquinavir and to establish the duration of the effect of this therapy.Open-label study.Clinical research referral center.40 adults with human immunodeficiency virus type 1 (HIV-1) infection and CD4+ T-cell counts of 200 to 500 cells/mm3.Monotherapy with 3600 mg or 7200 mg of saquinavir per day, in six divided doses, for 24 weeks.Patients were monitored for adverse events and were evaluated monthly for CD4+ T-cell count, HIV-1 viral load (as measured by reverse transcriptase polymerase chain reaction [PCR] for plasma HIV RNA levels), immune-complex-disassociated p24 antigen levels, peripheral blood mononuclear cell viral DNA levels (as measured by PCR), and resistance mutations to saquinavir. Quantitative peripheral blood mononuclear cell cultures were also done every 2 months.The low-dose saquinavir regimen (3600 mg/d) resulted in a maximal mean decrease in plasma HIV RNA levels of 1.06 log RNA copies/mL of plasma and a mean maximal increase in CD4 counts of 72 cells/mm3. At week 24, the plasma HIV RNA level remained 0.48 log RNA copies/mL of plasma lower than baseline (P < 0.001) and the CD4 count remained 31 cells/mm3 higher than baseline (P = 0.165). The high-dose saquinavir regimen (7200 mg/d) produced a mean maximal decrease in the plasma HIV RNA level of 1.34 log RNA copies/mL of plasma and a mean maximal increase in CD4 count of 121 cells/mm3. At week 24, the plasma HIV RNA level remained 0.85 log RNA copies/mL of plasma lower than baseline (P < 0.001) and the CD4 count remained 82 cells/mm3 higher than baseline (P = 0.002). The high-dose regimen produced a greater reduction in plasma HIV RNA level (P = 0.08), a greater reduction in peripheral blood mononuclear cell cultures (P = 0.008), and a greater increase in CD4 count (P = 0.002) than did the low-dose regimen. Higher plasma drug concentrations in individual patients correlated with greater reductions in plasma HIV RNA levels over the two doses. Nine patients receiving the low-dose regimen and four patients receiving the high-dose regimen developed key saquinavir resistance mutations. Adverse reactions, most commonly gastrointestinal problems and elevated serum aminotransferase levels, were more common in patients receiving the high-dose regimen, but most adverse events were mild and all were reversible.Saquinavir is a potent antiviral agent that has a favorable toxicity profile at high doses. Higher doses produce a greater and more durable suppression of viral load and elevation in CD4+ T-cell counts and may delay the development of resistance mutations. Therapy with high-dose saquinavir alone or in combination with other antiretroviral agents should be investigated further.

    View details for Web of Science ID A1996UQ65800003

    View details for PubMedID 8633817

  • Empirical Bayes methods for combining likelihoods JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1996; 91 (434): 538-550

    View details for Web of Science ID A1996UP55200019

  • TESTING ISOTROPY VERSUS CLUSTERING OF GAMMA-RAY BURSTS ASTROPHYSICAL JOURNAL Efron, B., Petrosian, V. 1995; 449 (1): 216-223

    View details for Web of Science ID A1995RM55500024

  • ON THE CORRELATION OF ANGULAR POSITION WITH TIME OF OCCURRENCE OF GAMMA-RAY BURSTS ASTROPHYSICAL JOURNAL Petrosian, V., Efron, B. 1995; 441 (1): L37-L38

    View details for Web of Science ID A1995QJ10300010

  • DIDANOSINE RESISTANCE IN HIV-INFECTED PATIENTS SWITCHED FROM ZIDOVUDINE TO DIDANOSINE MONOTHERAPY ANNALS OF INTERNAL MEDICINE Kozal, M. J., Kroodsma, K., Winters, M. A., Shafer, R. W., Efron, B., Katzenstein, D. A., Merigan, T. C. 1994; 121 (4): 263-268

    Abstract

    To determine the frequency and pattern of development of specific drug resistance mutations for human immunodeficiency virus (HIV) reverse transcriptase in patients switched from zidovudine to didanosine therapy and to examine the relation of the didanosine resistance mutation at codon 74 of the HIV reverse-transcriptase gene to CD4+ T-cell changes and virus burden.Retrospective analysis of all patients enrolled at Stanford University in protocols where patients were switched from zidovudine to didanosine monotherapy.A university hospital.64 patients infected with HIV who were switched from zidovudine to didanosine monotherapy. Patients had the acquired immunodeficiency syndrome (AIDS), AIDS-related complex, or were asymptomatic (mean [+/- SD] starting CD4+ T-cell count of 129 +/- 88 cells/mm3).Serial serum specimens were tested for the didanosine resistance mutation at codon 74 of the HIV reverse-transcriptase gene and for a zidovudine resistance mutation at codon 215 using selective polymerase chain reactions (PCR). Serum HIV RNA levels were determined by quantitative PCR. CD4+ T-cell counts were determined at serial time points.By 24 weeks of didanosine therapy, the proportion of patients with the didanosine resistance mutation at codon 74 increased from 0% to 56% (36 of 64). In contrast, the proportion of patients with the zidovudine resistance mutation at codon 215 decreased from 84% at the start to 59% after 24 weeks of didanosine therapy (a 25% decrease, 95% lower CI, 15%; P < 0.0001). Patients who developed the codon 74 mutation had a greater decrease in CD4+ T cells after the development of the mutation than did patients without the mutation (P < 0.001). In addition, after 24 weeks of didanosine, patients who developed the codon 74 mutation had a greater serum HIV RNA burden than patients who remained wild type (did not have the mutation) at codon 74 (225,000 compared with 82,400 HIV RNA copies/mL serum; P = 0.01).Among patients infected with HIV who had advanced disease and were switched from zidovudine to didanosine therapy, more than one half developed the didanosine resistance mutation at codon 74 by 24 weeks of didanosine therapy. Patients who developed the codon 74 mutation had a greater decline in CD4+ T cells after the development of the mutation and had a greater serum virus burden than did patients without the codon 74 mutation.

    View details for Web of Science ID A1994PB10200005

    View details for PubMedID 7518658

  • MISSING DATA, IMPUTATION, AND THE BOOTSTRAP - REJOINDER JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1994; 89 (426): 478-479

    View details for Web of Science ID A1994NN15500018

  • SURVIVAL ANALYSIS OF THE GAMMA-RAY BURST DATA JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B., Petrosian, V. 1994; 89 (426): 452-462

    View details for Web of Science ID A1994NN15500015

  • MISSING DATA, IMPUTATION, AND THE BOOTSTRAP JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1994; 89 (426): 463-475

    View details for Web of Science ID A1994NN15500016

  • BAYES AND LIKELIHOOD CALCULATIONS FROM CONFIDENCE-INTERVALS BIOMETRIKA Efron, B. 1993; 80 (1): 3-26

    View details for Web of Science ID A1993KZ19500001

  • A SIMPLE TEST OF INDEPENDENCE FOR TRUNCATED DATA WITH APPLICATIONS TO REDSHIFT SURVEYS ASTROPHYSICAL JOURNAL Efron, B., Petrosian, V. 1992; 399 (2): 345-352

    View details for Web of Science ID A1992JV80600002

  • MORE ACCURATE CONFIDENCE-INTERVALS IN EXPONENTIAL-FAMILIES BIOMETRIKA DICICCIO, T., Efron, B. 1992; 79 (2): 231-245

    View details for Web of Science ID A1992JD28900002

  • POISSON OVERDISPERSION ESTIMATES BASED ON THE METHOD OF ASYMMETRIC MAXIMUM-LIKELIHOOD JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1992; 87 (417): 98-107

    View details for Web of Science ID A1992HF27600013

  • JACKKNIFE-AFTER-BOOTSTRAP STANDARD ERRORS AND INFLUENCE FUNCTIONS JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL Efron, B. 1992; 54 (1): 83-127

    View details for Web of Science ID A1992HB29200003

  • STATISTICAL-DATA ANALYSIS IN THE COMPUTER-AGE SCIENCE Efron, B., Tibshirani, R. 1991; 253 (5018): 390-395

    Abstract

    Most of our familiar statistical methods, such as hypothesis testing, linear regression, analysis of variance, and maximum likelihood estimation, were designed to be implemented on mechanical calculators. Modern electronic computation has encouraged a host of new statistical methods that require fewer distributional assumptions than their predecessors and can be applied to more complicated statistical estimators. These methods allow the scientist to explore and describe data and draw valid statistical inferences without the usual concerns for mathematical tractability. This is possible because traditional methods of mathematical analysis are replaced by specially constructed computer algorithms. Mathematics has not disappeared from statistical theory. It is the main method for deciding which algorithms are correct and efficient tools for automating statistical inference.

    View details for Web of Science ID A1991FY28800027

    View details for PubMedID 17746394

  • COMPLIANCE AS AN EXPLANATORY VARIABLE IN CLINICAL-TRIALS - REJOINDER JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B., Feldman, D. 1991; 86 (413): 25-26

    View details for Web of Science ID A1991FD71200006

  • COMPLIANCE AS AN EXPLANATORY VARIABLE IN CLINICAL-TRIALS JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B., Feldman, D. 1991; 86 (413): 9-17

    View details for Web of Science ID A1991FD71200002

  • REGRESSION PERCENTILES USING ASYMMETRIC SQUARED ERROR LOSS STATISTICA SINICA Efron, B. 1991; 1 (1): 93-125

    View details for Web of Science ID A1991FP63000006

  • AN ANCILLARITY PARADOX WHICH APPEARS IN MULTIPLE LINEAR-REGRESSION - DISCUSSION ANNALS OF STATISTICS Efron, B. 1990; 18 (2): 502-503

    View details for Web of Science ID A1990DP71200005

  • FISHERS INFORMATION IN TERMS OF THE HAZARD RATE ANNALS OF STATISTICS Efron, B., Johnstone, I. M. 1990; 18 (1): 38-62

    View details for Web of Science ID A1990DA37500002

  • MORE EFFICIENT BOOTSTRAP COMPUTATIONS JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1990; 85 (409): 79-89

    View details for Web of Science ID A1990CV05700010

  • COMPUTER-INTENSIVE STATISTICAL-INFERENCE - A CITATION CLASSIC COMMENTARY ON BOOTSTRAP METHODS - ANOTHER LOOK AT THE JACKKNIFE BY EFRON,B. CURRENT CONTENTS/PHYSICAL CHEMICAL & EARTH SCIENCES Efron, B. 1989: 16-16

    View details for Web of Science ID A1989AM72600001

  • PROGNOSTIC INDICATORS OF LAPAROTOMY FINDINGS IN CLINICAL STAGE-I-II SUPRADIAPHRAGMATIC HODGKINS-DISEASE JOURNAL OF CLINICAL ONCOLOGY LEIBENHAUT, M. H., Hoppe, R. T., Efron, B., Halpern, J., Nelsen, T., Rosenberg, S. A. 1989; 7 (1): 81-91

    Abstract

    Between July 1968 and July 1986, 915 patients with clinical stage (CS) I and II Hodgkin's disease limited to sites above the diaphragm underwent laparotomy and splenectomy at Stanford University. Fifteen percent were CS I, of whom 76% had cervical/supraclavicular disease, 13% axillary disease, and 9% mediastinal presentations. CS I patients were more likely to be male, were significantly older, and were significantly less likely to have nodular sclerosis (NS) histology than CS II patients. Twenty percent of CS I patients and 30% of CS II patients were pathologically upstaged. No CS I patients were upstaged to pathological stage (PS) IV. Univariate and multivariate analyses of presenting clinical characteristics were performed to predict staging laparotomy findings. CS I women, CS I patients with mediastinal-only disease, and CS I men with either lymphocyte predominance or interfollicular histologies were at low risk for having disease below the diaphragm (5%) or requiring chemotherapy (0%). CS II women who were less than 27 years old and had only two or three sites of disease were also at low risk for upstaging (9%) or requiring chemotherapy (2%). Mixed cellularity histology and male gender were associated with increased risk for subdiaphragmatic disease and require laparotomy; the presence of systemic symptoms was not correlated with laparotomy findings. These results confirm the importance of performing staging laparotomy for the majority of patients who present with supradiaphragmatic Hodgkin's disease if treatment programs are based on the presence and extent of subdiaphragmatic disease. Selected subgroups are at low risk for subdiaphragmatic disease and might be spared laparotomy if they are treated with mantle, paraaortic, and splenic irradiation.

    View details for Web of Science ID A1989R711000012

    View details for PubMedID 2909669

  • APPLICATION OF THE BOOTSTRAP STATISTICAL-METHOD TO THE TAU-DECAY-MODE PROBLEM PHYSICAL REVIEW D Hayes, K. G., PERL, M. L., Efron, B. 1989; 39 (1): 274-279

    View details for Web of Science ID A1989R659600022

  • 3 EXAMPLES OF COMPUTER-INTENSIVE STATISTICAL-INFERENCE SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES A Efron, B. 1988; 50: 338-362

    View details for Web of Science ID A1988U787800003

  • THEORETICAL COMPARISON OF BOOTSTRAP CONFIDENCE-INTERVALS - DISCUSSION ANNALS OF STATISTICS Efron, B. 1988; 16 (3): 969-972

    View details for Web of Science ID A1988Q161700007

  • COMPUTER-INTENSIVE METHODS IN STATISTICAL REGRESSION SIAM REVIEW Efron, B. 1988; 30 (3): 421-449

    View details for Web of Science ID A1988Q013300004

  • BOOTSTRAP CONFIDENCE-INTERVALS - GOOD OR BAD PSYCHOLOGICAL BULLETIN Efron, B. 1988; 104 (2): 293-296

    View details for Web of Science ID A1988P931200010

  • LOGISTIC-REGRESSION, SURVIVAL ANALYSIS, AND THE KAPLAN-MEIER CURVE JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1988; 83 (402): 414-425

    View details for Web of Science ID A1988P159900015

  • DID SHAKESPEARE WRITE A NEWLY-DISCOVERED POEM BIOMETRIKA Thisted, R., Efron, B. 1987; 74 (3): 445-455

    View details for Web of Science ID A1987J985100001

  • EMPIRICAL BAYES CONFIDENCE-INTERVALS BASED ON BOOTSTRAP SAMPLES - COMMENT JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1987; 82 (399): 754-754

    View details for Web of Science ID A1987K240900008

  • BETTER BOOTSTRAP CONFIDENCE-INTERVALS JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1987; 82 (397): 171-185

    View details for Web of Science ID A1987G462600027

  • JACKKNIFE, BOOTSTRAP AND OTHER RESAMPLING METHODS IN REGRESSION-ANALYSIS - DISCUSSION ANNALS OF STATISTICS Efron, B. 1986; 14 (4): 1301-1304

    View details for Web of Science ID A1986F899900004

  • DOUBLE EXPONENTIAL-FAMILIES AND THEIR USE IN GENERALIZED LINEAR-REGRESSION JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1986; 81 (395): 709-721

    View details for Web of Science ID A1986D958800020

  • HOW BIASED IS THE APPARENT ERROR RATE OF A PREDICTION RULE JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1986; 81 (394): 461-470

    View details for Web of Science ID A1986C648000023

  • TESTING FOR INDEPENDENCE IN A 2-WAY TABLE - NEW INTERPRETATIONS OF THE CHI-SQUARE STATISTIC - REJOINDER ANNALS OF STATISTICS Diaconis, P., Efron, B. 1985; 13 (3): 905-913

    View details for Web of Science ID A1985AST9500012

  • BOOTSTRAP CONFIDENCE-INTERVALS FOR A CLASS OF PARAMETRIC PROBLEMS BIOMETRIKA Efron, B. 1985; 72 (1): 45-58

    View details for Web of Science ID A1985AEB8600006

  • TESTING FOR INDEPENDENCE IN A 2-WAY TABLE - NEW INTERPRETATIONS OF THE CHI-SQUARE STATISTIC ANNALS OF STATISTICS Diaconis, P., Efron, B. 1985; 13 (3): 845-874

    View details for Web of Science ID A1985AST9500001

  • COMPARING NON-NESTED LINEAR-MODELS JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1984; 79 (388): 791-803

    View details for Web of Science ID A1984TW42600005

  • ESTIMATING THE ERROR RATE OF A PREDICTION RULE - IMPROVEMENT ON CROSS-VALIDATION JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1983; 78 (382): 316-331

    View details for Web of Science ID A1983QU74700021

  • COMPUTER-INTENSIVE METHODS IN STATISTICS SCIENTIFIC AMERICAN Diaconis, P., Efron, B. 1983; 248 (5): 116-?

    View details for Web of Science ID A1983QL31500013

  • TRANSFORMATION THEORY - HOW NORMAL IS A FAMILY OF DISTRIBUTIONS ANNALS OF STATISTICS Efron, B. 1982; 10 (2): 323-339

    View details for Web of Science ID A1982NV35500001

  • MAXIMUM-LIKELIHOOD AND DECISION-THEORY ANNALS OF STATISTICS Efron, B. 1982; 10 (2): 340-356

    View details for Web of Science ID A1982NV35500002

  • CENSORED-DATA AND THE BOOTSTRAP JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1981; 76 (374): 312-319

    View details for Web of Science ID A1981LT69100018

  • THE JACKKNIFE ESTIMATE OF VARIANCE ANNALS OF STATISTICS Efron, B., Stein, C. 1981; 9 (3): 586-596

    View details for Web of Science ID A1981LT24600012

  • NONPARAMETRIC ESTIMATES OF STANDARD ERROR - THE JACKKNIFE, THE BOOTSTRAP AND OTHER METHODS BIOMETRIKA Efron, B. 1981; 68 (3): 589-599

    View details for Web of Science ID A1981MR77800002

  • MINIMUM CHI-SQUARE, NOT MAXIMUM-LIKELIHOOD ANNALS OF STATISTICS Berkson, J., Efron, B., Ghosh, J. K., Lecam, L., Pfanzagl, J., Rao, C. R. 1980; 8 (3): 457-487

    View details for Web of Science ID A1980JW75600001

  • COMPUTERS AND THE THEORY OF STATISTICS - THINKING THE UNTHINKABLE SIAM REVIEW Efron, B. 1979; 21 (4): 460-480

    View details for Web of Science ID A1979HR75400002

  • HOW BROAD IS CLASS OF NORMAL SCALE MIXTURES ANNALS OF STATISTICS Efron, B., Olshen, R. A. 1978; 6 (5): 1159-1164

    View details for Web of Science ID A1978FM78400014

  • ASSESSING ACCURACY OF MAXIMUM LIKELIHOOD ESTIMATOR - OBSERVED VERSUS EXPECTED FISHER INFORMATION BIOMETRIKA Efron, B., Hinkley, D. V. 1978; 65 (3): 457-482

    View details for Web of Science ID A1978GA54900001

  • GEOMETRY OF EXPONENTIAL FAMILIES ANNALS OF STATISTICS Efron, B. 1978; 6 (2): 362-376

    View details for Web of Science ID A1978EQ63300008

  • REGRESSION AND ANOVA WITH ZERO-ONE DATA - MEASURES OF RESIDUAL VARIATION JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1978; 73 (361): 113-121

    View details for Web of Science ID A1978ET15700024

  • CONTROVERSIES IN FOUNDATIONS OF STATISTICS AMERICAN MATHEMATICAL MONTHLY Efron, B. 1978; 85 (4): 231-246

    View details for Web of Science ID A1978FA50900003

  • RADIATION-INDUCED INHIBITION OF COMPENSATORY RENAL GROWTH IN WEANLING MOUSE KIDNEY RADIOLOGY Donaldson, S. S., MOSKOWITZ, P. S., CANTY, E. L., Efron, B. 1978; 128 (2): 491-495

    Abstract

    Weanling mice were given 500, 1,000, 1,500, or 2,000 rads single-fraction renal irradiation immediately following unilateral nephrectomy and sacrificed 3 days or 3, 6, 12, or 24 weeks later. Inhibition of compensatory renal growth was related to both radiation dose and time following treatment; it was transient following 500 and 1,000 rads but persisted following 1,500 and 2,000 rads. Renal growth was inhibited more than body growth. These studies indicate that the weanling mouse kidney is more sensitive to radiation-induced inhibition of compensatory renal growth than adult mice or other rodents.

    View details for Web of Science ID A1978FH28200041

    View details for PubMedID 663265

  • STEINS PARADOX IN STATISTICS SCIENTIFIC AMERICAN Efron, B., Morris, C. 1977; 236 (5): 119-127

    View details for Web of Science ID A1977DD55500008

  • EFFICIENCY OF COXS LIKELIHOOD FUNCTION FOR CENSORED DATA JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1977; 72 (359): 557-565

    View details for Web of Science ID A1977DR95700011

  • ESTIMATING NUMBER OF UNSEEN SPECIES - HOW MANY WORDS DID SHAKESPEARE KNOW BIOMETRIKA Efron, B., Thisted, R. 1976; 63 (3): 435-447

    View details for Web of Science ID A1976CP66700003

  • NECESSARY ANALYSIS AND ADAPTIVE INFERENCE - COMMENT JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1976; 71 (353): 111-112

    View details for Web of Science ID A1976BJ18600018

  • FAMILIES OF MINIMAX ESTIMATORS OF MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION ANNALS OF STATISTICS Efron, B., Morris, C. 1976; 4 (1): 11-21

    View details for Web of Science ID A1976BD53100002

  • MULTIVARIATE EMPIRICAL BAYES AND ESTIMATION OF COVARIANCE MATRICES ANNALS OF STATISTICS Efron, B., Morris, C. 1976; 4 (1): 22-32

    View details for Web of Science ID A1976BD53100003

  • REREADING FISHER,RA ANNALS OF STATISTICS Savage, L. J., Efron, B., EISENHART, C., FINETTI, B. D., Fraser, D. A., Godambe, V. P., Good, I. J., KEMPTHORNE, O., Stigler, S. M. 1976; 4 (3): 441-500

    View details for Web of Science ID A1976BU00800001

  • DATA-ANALYSIS USING STEINS ESTIMATOR AND ITS GENERALIZATIONS JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B., Morris, C. 1975; 70 (350): 311-319

    View details for Web of Science ID A1975AH43000007

  • POSSIBLE PROGNOSTIC USEFULNESS OF ASSESSING SERUM-PROTEINS AND CHOLESTEROL IN MALIGNANCY CANCER Chao, F. C., Efron, B., Wolf, P. 1975; 35 (4): 1223-1229

    Abstract

    Serial measurement of serum proteins, albumin, and cholesterol levels was used in attempt to assess the course and prognosis in cancer patients. This assessment is based on the fact that their declines followed first order kinetics and that these patients usually died when their levels were lower than half the initial levels. Two categories of cancer patients were identified: those in whom the initial measurements of serum albumin or cholersterol, taken soon after diagnosis, were declining (Group I), and those who showed such a decline as they entered an advanced or terminal phase (Group II). Group I included cancer of the stomach, kidney, lung (adenocarcinoma and squamous cell carcinoma), oral cavity, large intestine, breast (40%), bladder, ovary (70%), pancreas, and prostate; leukemia (acute myeloid and lymphocytic); and Hodgkin's disease (60%), all of which accounted for approximately 90% of the major causes of cancer deaths. Group II included Hodgkin's disease (40%), and cancer of the ovary (30%) and breast (60%), all of which accounted for 10% of the major causes of cancer deaths.

    View details for Web of Science ID A1975W165600027

    View details for PubMedID 1167805

  • DEFINING CURVATURE OF A STATISTICAL PROBLEM (WITH APPLICATIONS TO 2ND ORDER EFFICIENCY) ANNALS OF STATISTICS Efron, B. 1975; 3 (6): 1189-1217

    View details for Web of Science ID A1975AX73200001

  • EFFICIENCY OF LOGISTIC REGRESSION COMPARED TO NORMAL DISCRIMINANT-ANALYSIS JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B. 1975; 70 (352): 892-898

    View details for Web of Science ID A1975AY20700021

  • BIASED VERSUS UNBIASED ESTIMATION ADVANCES IN MATHEMATICS Efron, B. 1975; 16 (3): 259-277

    View details for Web of Science ID A1975AH94800001

  • STEINS ESTIMATION RULE AND ITS COMPETITORS - EMPIRICAL BAYES APPROACH JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Efron, B., Morris, C. 1973; 68 (341): 117-130

    View details for Web of Science ID A1973P259500025

  • FORCING A SEQUENTIAL EXPERIMENT TO BE BALANCED NATIONAL CANCER INSTITUTE MONOGRAPHS Efron, B. 1973: 571-572

    View details for Web of Science ID A1973Q863600103

  • COMBINING POSSIBLY RELATED ESTIMATION PROBLEMS JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL Efron, B., Morris, C. 1973; 35 (3): 379-421

    View details for Web of Science ID A1973S223100001

  • EMPIRICAL BAYES ON VECTOR OBSERVATIONS - EXTENSION OF STEINS METHOD BIOMETRIKA Efron, B., Morris, C. 1972; 59 (2): 335-347

    View details for Web of Science ID A1972N270900010

Footer Links:

Stanford Medicine Resources: