Statistical Theory Commons^™

Bringing Game Theory To Hypothesis Testing: Establishing Finite Sample Bounds On Inference, Karl H. Schlag

COBRA Preprint Series

Small sample properties are of fundamental interest when only limited data is available. Exact inference is limited by constraints imposed by specific nonrandomized tests and of course also by lack of more data. These effects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a fictitious game against nature. We use this method to investigate sequential …

Estimation And Testing For The Effect Of A Genetic Pathway On A Disease Outcome Using Logistic Kernel Machine Regression Via Logistic Mixed Models, Dawei Liu, Debashis Ghosh, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Powerful And Flexible Multilocus Association Test For Quantitative Traits, Lydia Coulter Kwee, Dawei Liu, Xihong Lin, Debashis Ghosh, Michael P. Epstein

Harvard University Biostatistics Working Paper Series

No abstract provided.

Nonparametric Regression Using Local Kernel Estimating Equations For Correlated Failure Time Data, Zhangsheng Yu, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

A Comparison Of Methods For Estimating The Causal Effect Of A Treatment In Randomized Clinical Trials Subject To Noncompliance, Rod Little, Qi Long, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Semiparametric Maximum Likelihood Estimation In Normal Transformation Models For Bivariate Survival Data, Yi Li, Ross L. Prentice, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Accounting For Errors From Predicting Exposures In Environmental Epidemiology And Environmental Statistics, Adam A. Szpiro, Lianne Sheppard, Thomas Lumley

UW Biostatistics Working Paper Series

PLEASE NOTE THAT AN UPDATED VERSION OF THIS RESEARCH IS AVAILABLE AS WORKING PAPER 350 IN THE UNIVERSITY OF WASHINGTON BIOSTATISTICS WORKING PAPER SERIES (http://www.bepress.com/uwbiostat/paper350).

In environmental epidemiology and related problems in environmental statistics, it is typically not practical to directly measure the exposure for each subject. Environmental monitoring is employed with a statistical model to assign exposures to individuals. The result is a form of exposure misspecification that can result in complicated errors in the health effect estimates if the exposure is naively treated as known. The exposure error is neither “classical” nor “Berkson”, so standard regression calibration methods …

Supervised Distance Matrices: Theory And Applications To Genomics, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a new approach to studying the relationship between a very high dimensional random variable and an outcome. Our method is based on a novel concept, the supervised distance matrix, which quantifies pairwise similarity between variables based on their association with the outcome. A supervised distance matrix is derived in two stages. The first stage involves a transformation based on a particular model for association. In particular, one might regress the outcome on each variable and then use the residuals or the influence curve from each regression as a data transformation. In the second stage, a choice of distance …

Confidence Intervals For The Population Mean Tailored To Small Sample Sizes, With Applications To Survey Sampling, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

The validity of standard confidence intervals constructed in survey sampling is based on the central limit theorem. For small sample sizes, the central limit theorem may give a poor approximation, resulting in confidence intervals that are misleading. We discuss this issue and propose methods for constructing confidence intervals for the population mean tailored to small sample sizes.

We present a simple approach for constructing confidence intervals for the population mean based on tail bounds for the sample mean that are correct for all sample sizes. Bernstein's inequality provides one such tail bound. The resulting confidence intervals have guaranteed coverage probability …

Doubly Robust Ecological Inference, Daniel B. Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

The ecological inference problem is a famous longstanding puzzle that arises in many disciplines. The usual formulation in epidemiology is that we would like to quantify an exposure-disease association by obtaining disease rates among the exposed and unexposed, but only have access to exposure rates and disease rates for several regions. The problem is generally intractable, but can be attacked under the assumptions of King's (1997) extended technique if we can correctly specify a model for a certain conditional distribution. We introduce a procedure that it is a valid approach if either this original model is correct or if we …

Properties Of Monotonic Effects On Directed Acyclic Graphs, Tyler J. Vanderweele, James M. Robins

COBRA Preprint Series

Various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations. Counterexamples are provided to show that the results do not hold under less restrictive conditions. Monotonic effects are furthermore used to relate signed edges on a causal directed acyclic graph to qualitative effect modification. The theory is applied to an example concerning the direct effect of smoking on cardiovascular disease controlling for hypercholesterolemia. Monotonicity assumptions are used to construct a test for whether there is a variable that confounds the relationship between the mediator, hypercholesterolemia, and the outcome, cardiovascular disease.

The Construction And Analysis Of Adaptive Group Sequential Designs, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In order to answer scientific questions of interest one often carries out an ordered sequence of experiments generating the appropriate data over time. The design of each experiment involves making various decisions such as 1) What variables to measure on the randomly sampled experimental unit?, 2) How regularly to monitor the unit, and for how long?, 3) How to randomly assign a treatment or drug-dose to the unit?, among others. That is, the design of each experiment involves selecting a so called treatment mechanism/monitoring mechanism/ missingness/censoring mechanism, where these mechanisms represent a formally defined conditional distribution of one of these …

Empirical Null And False Discovery Rate Inference For Exponential Families, Armin Schwartzman

Harvard University Biostatistics Working Paper Series

No abstract provided.

Marginal Structural Models For Partial Exposure Regimes, Stijn Vansteelandt, Karl Mertens, Carl Suetens, Els Goetghebeur

Harvard University Biostatistics Working Paper Series

Intensive care unit (ICU) patients are ell known to be highly susceptible for nosocomial (i.e. hospital-acquired) infections due to their poor health and many invasive therapeutic treatments. The effects of acquiring such infections in ICU on mortality are however ill understood. Our goal is to quantify these effects using data from the National Surveillance Study of Nosocomial Infections in Intensive Care

Units (Belgium). This is a challenging problem because of the presence of time-dependent confounders (such as exposure to mechanical ventilation)which lie on the causal path from infection to mortality. Standard statistical analyses may be severely misleading in such settings …

Covariate Adjustment For The Intention-To-Treat Parameter With Empirical Efficiency Maximization, Daniel B. Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In randomized experiments, the intention-to-treat parameter is defined as the difference in expected outcomes between groups assigned to treatment and control arms. There is a large literature focusing on how (possibly misspecified) working models can sometimes exploit baseline covariate measurements to gain precision, although covariate adjustment is not strictly necessary. In Rubin and van der Laan (2008), we proposed the technique of empirical efficiency maximization for improving estimation by forming nonstandard fits of such working models. Considering a more realistic randomization scheme than in our original article, we suggest a new class of working models for utilizing covariate information, show …

A Bayesian Approach To Effect Estimation Accounting For Adjustment Uncertainty, Chi Wang, Giovanni Parmigiani, Ciprian Crainiceanu, Francesca Dominici

Johns Hopkins University, Dept. of Biostatistics Working Papers

Adjustment for confounding factors is a common goal in the analysis of both observational and controlled studies. The choice of which confounding factors should be included in the model used to estimate an effect of interest is both critical and uncertain. For this reason it is important to develop methods that estimate an effect, while accounting not only for confounders, but also for the uncertainty about which confounders should be included. In a recent article, Crainiceanu et al. (2008) have identified limitations and potential biases of Bayesian Model Averaging (BMA) (Raftery et al., 1997; Hoeting et al., 1999)when applied to …

Estimation Of Controlled Direct Effects, Sylvie Goetgeluk, Stijn Vansteelandt, Els Goetghebeur

Harvard University Biostatistics Working Paper Series

No abstract provided.

Using Regression Models To Analyze Randomized Trials: Asymptotically Valid Hypothesis Tests Despite Incorrectly Specified Models, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Regression models are often used to test for cause-effect relationships from data collected in randomized trials or experiments. This practice has deservedly come under heavy scrutiny, since commonly used models such as linear and logistic regression will often not capture the actual relationships between variables, and incorrectly specified models potentially lead to incorrect conclusions. In this paper, we focus on hypothesis test of whether the treatment given in a randomized trial has any effect on the mean of the primary outcome, within strata of baseline variables such as age, sex, and health status. Our primary concern is ensuring that such …

Geostatistical Inference Under Preferential Sampling, Peter J. Diggle, Raquel Menezes, Ting-Li Su

Johns Hopkins University, Dept. of Biostatistics Working Papers

Geostatistics involves the fitting of spatially continuous models to spatially discrete data (Chil`es and Delfiner, 1999). Preferential sampling arises when the process that determines the data-locations and the process being modelled are stochastically dependent. Conventional geostatistical methods assume, if only implicitly, that sampling is non-preferential. However, these methods are often used in situations where sampling is likely to be preferential. For example, in mineral exploration samples may be concentrated in areas thought likely to yield high-grade ore. We give a general expression for the likelihood function of preferentially sampled geostatistical data and describe how this can be evaluated approximately using …

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.