Statistical Theory Commons^™

Targeted Maximum Likelihood Estimation Using Exponential Families, Iván Díaz, Michael Rosenblum

Johns Hopkins University, Dept. of Biostatistics Working Papers

Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We investigate the use of exponential families to define the parametric submodel. This implementation of TMLE gives a general approach for estimating any smooth parameter in the nonparametric model. A computational advantage of this approach is that each iteration of TMLE involves estimation of a parameter in an exponential family, which is a convex optimization problem for which software implementing reliable and computationally efficient methods exists. We illustrate …

Adaptive Pair-Matching In The Search Trial And Estimation Of The Intervention Effect, Laura Balzer, Maya L. Petersen, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In randomized trials, pair-matching is an intuitive design strategy to protect study validity and to potentially increase study power. In a common design, candidate units are identified, and their baseline characteristics used to create the best n/2 matched pairs. Within the resulting pairs, the intervention is randomized, and the outcomes measured at the end of follow-up. We consider this design to be adaptive, because the construction of the matched pairs depends on the baseline covariates of all candidate units. As consequence, the observed data cannot be considered as n/2 independent, identically distributed (i.i.d.) pairs of units, as current practice assumes. …

Meta-Analysis Of Social-Personality Psychological Research, Blair T. Johnson, Alice H. Eagly

CHIP Documents

This publication provides a contemporary treatment of the subject of meta-analysis in relation to social-personality psychology. Meta-analysis literally refers to the statistical pooling of the results of independent studies on a given subject, although in practice it refers as well to other steps of research synthesis, including defining the question under investigation, gathering all available research reports, coding of information about the studies and their effects, and interpretation/dissemination of results. Discussed as well are the hallmarks of high-quality meta-analyses.

Adapting Data Adaptive Methods For Small, But High Dimensional Omic Data: Applications To Gwas/Ewas And More, Sara Kherad Pajouh, Alan E. Hubbard, Martyn T. Smith

U.C. Berkeley Division of Biostatistics Working Paper Series

Exploratory analysis of high dimensional "omics" data has received much attention since the explosion of high-throughput technology allows simultaneous screening of tens of thousands of characteristics (genomics, metabolomics, proteomics, adducts, etc., etc.). Part of this trend has been an increase in the dimension of exposure data in studies of environmental exposure and associated biomarkers. Though some of the general approaches, such as GWAS, are transferable, what has received less focus is 1) how to derive estimation of independent associations in the context of many competing causes, without resorting to a misspecified model, and 2) how to derive accurate small-sample inference …

Testing The Relative Performance Of Data Adaptive Prediction Algorithms: A Generalized Test Of Conditional Risk Differences, Benjamin A. Goldstein, Eric Polley, Farren Briggs, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In statistical medicine comparing the predictability or fit of two models can help to determine whether a set of prognostic variables contains additional information about medical outcomes, or whether one of two different model fits (perhaps based on different algorithms, or different set of variables) should be preferred for clinical use. Clinical medicine has tended to rely on comparisons of clinical metrics like C-statistics and more recently reclassification. Such metrics rely on the outcome being categorical and utilize a specific and often obscure loss function. In classical statistics one can use likelihood ratio tests and information based criterion if the …

Statistical Inference For Data Adaptive Target Parameters, Mark J. Van Der Laan, Alan E. Hubbard, Sara Kherad Pajouh

U.C. Berkeley Division of Biostatistics Working Paper Series

Consider one observes n i.i.d. copies of a random variable with a probability distribution that is known to be an element of a particular statistical model. In order to define our statistical target we partition the sample in V equal size sub-samples, and use this partitioning to define V splits in estimation-sample (one of the V subsamples) and corresponding complementary parameter-generating sample that is used to generate a target parameter. For each of the V parameter-generating samples, we apply an algorithm that maps the sample in a target parameter mapping which represent the statistical target parameter generated by that parameter-generating …

Balancing Score Adjusted Targeted Minimum Loss-Based Estimation, Samuel D. Lendle, Bruce Fireman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Adjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment specific mean with …

Optimal Tests Of Treatment Effects For The Overall Population And Two Subpopulations In Randomized Trials, Using Sparse Linear Programming, Michael Rosenblum, Han Liu, En-Hsu Yen

Johns Hopkins University, Dept. of Biostatistics Working Papers

We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at baseline. The goal is to simultaneously learn which subpopulations benefit from an experimental treatment, while providing strong control of the familywise Type I error rate. We formalize this as a multiple testing problem and show it is computationally infeasible to solve using existing techniques. Our solution involves a novel approach, in which we first transform the original multiple testing problem into a large, sparse linear …

Estimating Effects On Rare Outcomes: Knowledge Is Power, Laura B. Balzer, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Many of the secondary outcomes in observational studies and randomized trials are rare. Methods for estimating causal effects and associations with rare outcomes, however, are limited, and this represents a missed opportunity for investigation. In this article, we construct a new targeted minimum loss-based estimator (TMLE) for the effect of an exposure or treatment on a rare outcome. We focus on the causal risk difference and statistical models incorporating bounds on the conditional risk of the outcome, given the exposure and covariates. By construction, the proposed estimator constrains the predicted outcomes to respect this model knowledge. Theoretically, this bounding provides …

Adaptive Randomization Designs, Jenna Colavincenzo

Statistics

Adaptive design methodologies use prior information to develop a clinical trial design. The goal of an adaptive design is to maintain the integrity and validity of the study while giving the researcher flexibility in identifying the optimal treatment. An example of an adaptive design can be seen in a basic pharmaceutical trial. There are three phases of the overall trial to compare treatments and experimenters use the information from the previous phase to make changes to the subsequent phase before it begins.

Adaptive design methods have been in practice since the 1970s, but have become increasingly complex ever since. One …

Development Of A Bayesian Joint Logistic Model To Better Study The Association Between Haplotypes And Disease, Anthony M. D'Amelio Jr

Dissertations and Theses (Open Access)

In 2011, there will be an estimated 1,596,670 new cancer cases and 571,950 cancer-related deaths in the US. With the ever-increasing applications of cancer genetics in epidemiology, there is great potential to identify genetic risk factors that would help identify individuals with increased genetic susceptibility to cancer, which could be used to develop interventions or targeted therapies that could hopefully reduce cancer risk and mortality.

In this dissertation, I propose to develop a new statistical method to evaluate the role of haplotypes in cancer susceptibility and development. This model will be flexible enough to handle not only haplotypes of any …

Estimation Of A Non-Parametric Variable Importance Measure Of A Continuous Exposure, Chambaz Antoine, Pierre Neuvial, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We define a new measure of variable importance of an exposure on a continuous outcome, accounting for potential confounders. The exposure features a reference level x0 with positive mass and a continuum of other levels. For the purpose of estimating it, we fully develop the semi-parametric estimation methodology called targeted minimum loss estimation methodology (TMLE) [van der Laan & Rubin, 2006; van der Laan & Rose, 2011]. We cover the whole spectrum of its theoretical study (convergence of the iterative procedure which is at the core of the TMLE methodology; consistency and asymptotic normality of the estimator), practical implementation, simulation …

A Regularization Corrected Score Method For Nonlinear Regression Models With Covariate Error, David M. Zucker, Malka Gorfine, Yi Li, Donna Spiegelman

Harvard University Biostatistics Working Paper Series

No abstract provided.

Effectively Selecting A Target Population For A Future Comparative Study, Lihui Zhao, Lu Tian, Tianxi Cai, Brian Claggett, L. J. Wei

Harvard University Biostatistics Working Paper Series

When comparing a new treatment with a control in a randomized clinical study, the treatment effect is generally assessed by evaluating a summary measure over a specific study population. The success of the trial heavily depends on the choice of such a population. In this paper, we show a systematic, effective way to identify a promising population, for which the new treatment is expected to have a desired benefit, using the data from a current study involving similar comparator treatments. Specifically, with the existing data we first create a parametric scoring system using multiple covariates to estimate subject-specific treatment differences. …

On The Covariate-Adjusted Estimation For An Overall Treatment Difference With Data From A Randomized Comparative Clinical Trial, Lu Tian, Tianxi Cai, Lihui Zhao, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Estimation And Testing In Targeted Group Sequential Covariate-Adjusted Randomized Clinical Trials, Antoine Chambaz, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

This article is devoted to the construction and asymptotic study of adaptive group sequential covariate-adjusted randomized clinical trials analyzed through the prism of the semiparametric methodology of targeted maximum likelihood estimation (TMLE). We show how to build, as the data accrue group-sequentially, a sampling design which targets a user-supplied optimal design. We also show how to carry out a sound TMLE statistical inference based on such an adaptive sampling scheme (therefore extending some results known in the i.i.d setting only so far), and how group-sequential testing applies on top of it. The procedure is robust (i.e., consistent even if the …

Minimum Description Length Measures Of Evidence For Enrichment, Zhenyu Yang, David R. Bickel

COBRA Preprint Series

In order to functionally interpret differentially expressed genes or other discovered features, researchers seek to detect enrichment in the form of overrepresentation of discovered features associated with a biological process. Most enrichment methods treat the p-value as the measure of evidence using a statistical test such as the binomial test, Fisher's exact test or the hypergeometric test. However, the p-value is not interpretable as a measure of evidence apart from adjustments in light of the sample size. As a measure of evidence supporting one hypothesis over the other, the Bayes factor (BF) overcomes this drawback of the p-value but lacks …

Landmark Prediction Of Survival, Layla Parast, Tianxi Cai

Harvard University Biostatistics Working Paper Series

No abstract provided.

Stratifying Subjects For Treatment Selection With Censored Event Time Data From A Comparative Study, Lihui Zhao, Tianxi Cai, Lu Tian, Hajime Uno, Scott D. Solomon, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Principled Sure Independence Screening For Cox Models With Ultra-High-Dimensional Covariates, Sihai Dave Zhao, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Estimating Causal Effects In Trials Involving Multi-Treatment Arms Subject To Non-Compliance: A Bayesian Frame-Work, Qi Long, Roderick J. Little, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Super Learner In Prediction, Eric C. Polley, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Super learning is a general loss based learning method that has been proposed and analyzed theoretically in van der Laan et al. (2007). In this article we consider super learning for prediction. The super learner is a prediction method designed to find the optimal combination of a collection of prediction algorithms. The super learner algorithm finds the combination of algorithms minimizing the cross-validated risk. The super learner framework is built on the theory of cross-validation and allows for a general class of prediction algorithms to be considered for the ensemble. Due to the previously established oracle results for the cross-validation …

Assessing Noninferiority In A Three-Arm Trial Using The Bayesian Approach, Pulak Ghosh, Farouk S. Nathoo, Mithat Gonen, Ram C. Tiwari

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm clinical trial is usually recommended for non-inferiority trials by the Food and Drug Administration (FDA). The three-arm trial consists of a placebo, a reference, and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with …

Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations, Lu Wang, Andrea Rotnitzky, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Likelihood Ratio Testing For Admixture Models With Application To Genetic Linkage Analysis, Chong-Zhi Di, Kung-Yee Liang

Johns Hopkins University, Dept. of Biostatistics Working Papers

We consider likelihood ratio tests (LRT) and their modifications for homogeneity in admixture models. The admixture model is a special case of two component mixture model, where one component is indexed by an unknown parameter while the parameter value for the other component is known. It has been widely used in genetic linkage analysis under heterogeneity, in which the kernel distribution is binomial. For such models, it is long recognized that testing for homogeneity is nonstandard and the LRT statistic does not converge to a conventional 2 distribution. In this paper, we investigate the asymptotic behavior of the LRT for …

Graphical Procedures For Evaluating Overall And Subject-Specific Incremental Values From New Predictors With Censored Event Time Data, Hajime Uno, Tianxi Cai, Lu Tian, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Readings In Targeted Maximum Likelihood Estimation, Mark J. Van Der Laan, Sherri Rose, Susan Gruber

U.C. Berkeley Division of Biostatistics Working Paper Series

This is a compilation of current and past work on targeted maximum likelihood estimation. It features the original targeted maximum likelihood learning paper as well as chapters on super (machine) learning using cross validation, randomized controlled trials, realistic individualized treatment rules in observational studies, biomarker discovery, case-control studies, and time-to-event outcomes with censored data, among others. We hope this collection is helpful to the interested reader and stimulates additional research in this important area.

Causal Inference For Nested Case-Control Studies Using Targeted Maximum Likelihood Estimation, Sherri Rose, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

A nested case-control study is conducted within a well-defined cohort arising out of a population of interest. This design is often used in epidemiology to reduce the costs associated with collecting data on the full cohort; however, the case control sample within the cohort is a biased sample. Methods for analyzing case-control studies have largely focused on logistic regression models that provide conditional and not marginal causal estimates of the odds ratio. We previously developed a Case-Control Weighted Targeted Maximum Likelihood Estimation (TMLE) procedure for case-control study designs, which relies on the prevalence probability q0. We propose the use of …

Comparing Risk Scoring Systems Beyond The Roc Paradigm In Survival Analysis, Hajime Uno, Lu Tian, Tianxi Cai, Isaac S. Kohane, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Marginalized Frailty Models For Multivariate Survival Data, Megan Othus, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.