Physical Sciences and Mathematics Commons^™

Model-Robust Bayesian Regression And The Sandwich Estimator, Adam A. Szpiro, Kenneth M. Rice, Thomas Lumley

UW Biostatistics Working Paper Series

PLEASE NOTE THAT AN UPDATED VERSION OF THIS RESEARCH IS AVAILABLE AS WORKING PAPER 338 IN THE UNIVERSITY OF WASHINGTON BIOSTATISTICS WORKING PAPER SERIES (http://www.bepress.com/uwbiostat/paper338).

In applied regression problems there is often sufficient data for accurate estimation, but standard parametric models do not accurately describe the source of the data, so associated uncertainty estimates are not reliable. We describe a simple Bayesian approach to inference in linear regression that recovers least-squares point estimates while providing correct uncertainty bounds by explicitly recognizing that standard modeling assumptions need not be valid. Our model-robust development parallels frequentist estimating equations and leads to intervals …

Estimating Sensitivity And Specificity From A Phase 2 Biomarker Study That Allows For Early Termination, Margaret S. Pepe Phd

UW Biostatistics Working Paper Series

Development of a disease screening biomarker involves several phases. In phase 2 its sensitivity and specificity is compared with established thresholds for minimally acceptable performance. Since we anticipate that most candidate markers will not prove to be useful and availability of specimens and funding is limited, early termination of a study is appropriate if accumulating data indicate that the marker is inadequate. Yet, for markers that complete phase 2, we seek estimates of sensitivity and specificity to proceed with the design of subsequent phase 3 studies.

We suggest early stopping criteria and estimation procedures that adjust for bias caused by …

Bootstrap Confidence Regions For Optimal Operating Conditions In Response Surface Methodology, Roger D. Gibb, I-Li Lu, Walter H. Carter Jr

COBRA Preprint Series

This article concerns the application of bootstrap methodology to construct a likelihood-based confidence region for operating conditions associated with the maximum of a response surface constrained to a specified region. Unlike classical methods based on the stationary point, proper interpretation of this confidence region does not depend on unknown model parameters. In addition, the methodology does not require the assumption of normally distributed errors. The approach is demonstrated for concave-down and saddle system cases in two dimensions. Simulation studies were performed to assess the coverage probability of these regions.

AMS 2000 subj Classification: 62F25, 62F40, 62F30, 62J05.

Key words: Stationary …

Loss-Based Estimation With Evolutionary Algorithms And Cross-Validation, David Shilane, Richard H. Liang, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

Many statistical inference methods rely upon selection procedures to estimate a parameter of the joint distribution of explanatory and outcome data, such as the regression function. Within the general framework for loss-based estimation of Dudoit and van der Laan, this project proposes an evolutionary algorithm (EA) as a procedure for risk optimization. We also analyze the size of the parameter space for polynomial regression under an interaction constraints along with constraints on either the polynomial or variable degree.

Resampling-Based Empirical Bayes Multiple Testing Procedures For Controlling Generalized Tail Probability And Expected Value Error Rates: , Sandrine Dudoit, Houston N. Gilbert, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

This article proposes resampling-based empirical Bayes multiple testing procedures for controlling a broad class of Type I error rates, defined as generalized tail probability (gTP) error rates, gTP(q,g) = Pr(g(V_n,S_n) > q), and generalized expected value (gEV) error rates, gEV(g) = [g(V_n,S_n)], for arbitrary functions g(V_n,S_n) of the numbers of false positives V_n and true positives S_n. Of particular interest are error rates based on the …

A Note On Targeted Maximum Likelihood And Right Censored Data, Mark J. Van Der Laan, Daniel Rubin

U.C. Berkeley Division of Biostatistics Working Paper Series

A popular way to estimate an unknown parameter is with substitution, or evaluating the parameter at a likelihood based fit of the data generating density. In many cases, such estimators have substantial bias and can fail to converge at the parametric rate. van der Laan and Rubin (2006) introduced targeted maximum likelihood learning, removing these shackles from substitution estimators, which were made in full agreement with the locally efficient estimating equation procedures as presented in Robins and Rotnitzsky (1992) and van der Laan and Robins (2003). This note illustrates how targeted maximum likelihood can be applied in right censored data …

Detailed Version: Analyzing Direct Effects In Randomized Trials With Secondary Interventions: An Application To Hiv Prevention Trials, Michael A. Rosenblum, Nicholas P. Jewell, Mark J. Van Der Laan, Stephen Shiboski, Ariane Van Der Straten, Nancy Padian

U.C. Berkeley Division of Biostatistics Working Paper Series

This is the detailed technical report that accompanies the paper “Analyzing Direct Effects in Randomized Trials with Secondary Interventions: An Application to HIV Prevention Trials” (an unpublished, technical report version of which is available online at http://www.bepress.com/ucbbiostat/paper223).

The version here gives full details of the models for the time-dependent analysis, and presents further results in the data analysis section. The Methods for Improving Reproductive Health in Africa (MIRA) trial is a recently completed randomized trial that investigated the effect of diaphragm and lubricant gel use in reducing HIV infection among susceptible women. 5,045 women were randomly assigned to either the …

Optimal Propensity Score Stratification, Jessica A. Myers, Thomas A. Louis

Johns Hopkins University, Dept. of Biostatistics Working Papers

Stratifying on propensity score in observational studies of treatment is a common technique used to control for bias in treatment assignment; however, there have been few studies of the relative efficiency of the various ways of forming those strata. The standard method is to use the quintiles of propensity score to create subclasses, but this choice is not based on any measure of performance either observed or theoretical. In this paper, we investigate the optimal subclassification of propensity scores for estimating treatment effect with respect to mean squared error of the estimate. We consider the optimal formation of subclasses within …

Multiple Model Evaluation Absent The Gold Standard Via Model Combination, Edwin J. Iversen, Jr., Giovanni Parmigiani, Sining Chen

Johns Hopkins University, Dept. of Biostatistics Working Papers

We describe a method for evaluating an ensemble of predictive models given a sample of observations comprising the model predictions and the outcome event measured with error. Our formulation allows us to simultaneously estimate measurement error parameters, true outcome — aka the gold standard — and a relative weighting of the predictive scores. We describe conditions necessary to estimate the gold standard and for these estimates to be calibrated and detail how our approach is related to, but distinct from, standard model combination techniques. We apply our approach to data from a study to evaluate a collection of BRCA1/BRCA2 gene …

Analyzing Direct Effects In Randomized Trials With Secondary Interventions , Michael Rosenblum, Nicholas P. Jewell, Mark J. Van Der Laan, Stephen Shiboski, Ariane Van Der Straten, Nancy Padian

U.C. Berkeley Division of Biostatistics Working Paper Series

The Methods for Improving Reproductive Health in Africa (MIRA) trial is a recently completed randomized trial that investigated the effect of diaphragm and lubricant gel use in reducing HIV infection among susceptible women. 5,045 women were randomly assigned to either the active treatment arm or not. Additionally, all subjects in both arms received intensive condom counselling and provision, the "gold standard" HIV prevention barrier method. There was much lower reported condom use in the intervention arm than in the control arm, making it difficult to answer important public health questions based solely on the intention-to-treat analysis. We adapt an analysis …

Comparing Trends In Cancer Rates Across Overlapping Regions, Yi Li, Ram C. Tiwari

Harvard University Biostatistics Working Paper Series

No abstract provided.

Correcting Instrumental Variables Estimators For Systematic Measurement Error, Stijn Vansteelandt, Manoochehr Babanezhad, Els Goetghebeur

Harvard University Biostatistics Working Paper Series

No abstract provided.

Empirical Efficiency Maximization, Daniel B. Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

It has long been recognized that covariate adjustment can increase precision, even when it is not strictly necessary. The phenomenon is particularly emphasized in clinical trials, whether using continuous, categorical, or censored time-to-event outcomes. Adjustment is often straightforward when a discrete covariate partitions the sample into a handful of strata, but becomes more involved when modern studies collect copious amounts of baseline information on each subject.

The dilemma helped motivate locally efficient estimation for coarsened data structures, as surveyed in the books of van der Laan and Robins (2003) and Tsiatis (2006). Here one fits a relatively small working model …

Assessment Of A Cgh-Based Genetic Instability, David A. Engler, Yiping Shen, J F. Gusella, Rebecca A. Betensky

Harvard University Biostatistics Working Paper Series

No abstract provided.

Survival Analysis With Large Dimensional Covariates: An Application In Microarray Studies, David A. Engler, Yi Li

Harvard University Biostatistics Working Paper Series

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time …

Super Learner, Mark J. Van Der Laan, Eric C. Polley, Alan E. Hubbard

U.C. Berkeley Division of Biostatistics Working Paper Series

Previous articles (van der Laan and Dudoit (2003); van der Laan et al. (2006); Sinisi et al. (2007)) advertised and theoretically validated the use of cross-validation to select among many candidate estimators to compute a so called super learner which outperforms any of the given candidate estimators. The theoretical basis was provided for this super learner based on oracle results for the cross-validation selector (e.g., van der Laan and Dudoit (2003); van der Laan et al. (2006)) and in Sinisi et al. (2007). In addition, these papers contained a practical demonstration of the adaptivity of this so called super learner …

Evaluating The Roc Performance Of Markers For Future Events, Margaret Pepe, Yingye Zheng, Yuying Jin

UW Biostatistics Working Paper Series

Receiver operating characteristic (ROC) curves play a central role in the evaluation of biomarkers and tests for disease diagnosis. Predictors for event time outcomes can also be evaluated with ROC curves, but the time lag between marker measurement and event time must be acknowledged. We discuss different definitions of time-dependent ROC curves in the context of real applications. Several approaches have been proposed for estimation. We contrast retrospective versus prospective methods in regards to assumptions and flexibility, including their capacities to incorporate censored data, competing risks and different sampling schemes. Applications to two datasets are presented.

Review Of The Maximum Likelihood Functions For Right Censored Data. A New Elementary Derivation., Stefano Patti, Elia Biganzoli, Patrizia Boracchi

COBRA Preprint Series

Censoring is a well known feature recurrent in the analysis of lifetime data, occurring in the model when exact lifetimes can be collected for only a representative portion of the surveyed individuals. If lifetimes are known only to exceed some given values, it is referred to as right censoring. In this paper we propose a systematization and a new derivation of the likelihood function for right censored sampling schemes; calculations are reported and assumptions are carefully stated. The sampling schemes considered (Type I, II and Random Censoring) give rise to the same ML function. Only the knowledge of elementary probability …

Covariate Adjustment In Randomized Trials With Binary Outcomes: Targeted Maximum Likelihood Estimation, Kelly L. Moore, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Covariate adjustment using linear models for continuous outcomes in randomized trials has been shown to increase efficiency and power over the unadjusted method in estimating the marginal effect of treatment. However, for binary outcomes, investigators generally rely on the unadjusted estimate as the literature indicates that covariate-adjusted estimates based on logistic regression models are less efficient. The crucial step that has been missing when adjusting for covariates is that one must integrate/average the adjusted estimate over those covariates in order to obtain the marginal effect. We apply the method of targeted maximum likelihood estimation (MLE), as presented in van der …

Conservative Estimation Of Optimal Multiple Testing Procedures, James E. Signorovitch

Harvard University Biostatistics Working Paper Series

No abstract provided.