Physical Sciences and Mathematics Commons^™

Statistical Inference For The Mean Outcome Under A Possibly Non-Unique Optimal Treatment Strategy, Alexander R. Luedtke, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We consider challenges that arise in the estimation of the value of an optimal individualized treatment strategy defined as the treatment rule that maximizes the population mean outcome, where the candidate treatment rules are restricted to depend on baseline covariates. We prove a necessary and sufficient condition for the pathwise differentiability of the optimal value, a key condition needed to develop a regular asymptotically linear (RAL) estimator of this parameter. The stated condition is slightly more general than the previous condition implied in the literature. We then describe an approach to obtain root-n rate confidence intervals for the optimal value …

Online Targeted Learning, Mark J. Van Der Laan, Samuel D. Lendle

U.C. Berkeley Division of Biostatistics Working Paper Series

We consider the case that the data comes in sequentially and can be viewed as sample of independent and identically distributed observations from a fixed data generating distribution. The goal is to estimate a particular path wise target parameter of this data generating distribution that is known to be an element of a particular semi-parametric statistical model. We want our estimator to be asymptotically efficient, but we also want that our estimator can be calculated by updating the current estimator based on the new block of data without having to revisit the past data, so that it is computationally much …

Targeted Learning Of An Optimal Dynamic Treatment, And Statistical Inference For Its Mean Outcome, Mark J. Van Der Laan, Alexander R. Luedtke

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose we observe n independent and identically distributed observations of a time-dependent random variable consisting of baseline covariates, initial treatment and censoring indicator, intermediate covariates, subsequent treatment and censoring indicator, and a final outcome. For example, this could be data generated by a sequentially randomized controlled trial, where subjects are sequentially randomized to a first line and second line treatment, possibly assigned in response to an intermediate biomarker, and are subject to right-censoring. In this article we consider estimation of an optimal dynamic multiple time-point treatment rule defined as the rule that maximizes the mean outcome under the dynamic treatment, …

A Novel Targeted Learning Method For Quantitative Trait Loci Mapping, Hui Wang, Zhongyang Zhang, Sherri Rose, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We present a novel semiparametric method for quantitative trait loci (QTL) mapping in experimental crosses. Conventional genetic mapping methods typically assume parametric models with Gaussian errors and obtain parameter estimates through maximum likelihood estimation. In contrast with univariate regression and interval mapping methods, our model requires fewer assumptions and also accommodates various machine learning algorithms. Estimation is performed with targeted maximum likelihood learning methods. We demonstrate our semiparametric targeted learning approach in a simulation study and a well-studied barley dataset.

Entering The Era Of Data Science: Targeted Learning And The Integration Of Statistics And Computational Data Analysis, Mark J. Van Der Laan, Richard J.C.M. Starmans

U.C. Berkeley Division of Biostatistics Working Paper Series

This outlook article will appear in Advances in Statistics and it reviews the research of Dr. van der Laan's group on Targeted Learning, a subfield of statistics that is concerned with the construction of data adaptive estimators of user-supplied target parameters of the probability distribution of the data and corresponding confidence intervals, aiming to only rely on realistic statistical assumptions. Targeted Learning fully utilizes the state of the art in machine learning tools, while still preserving the important identity of statistics as a field that is concerned with both accurate estimation of the true target parameter value and assessment of …

Super-Learning Of An Optimal Dynamic Treatment Rule, Alexander R. Luedtke, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We consider the estimation of an optimal dynamic two time-point treatment rule defined as the rule that maximizes the mean outcome under the dynamic treatment, where the candidate rules are restricted to depend only on a user-supplied subset of the baseline and intermediate covariates. This estimation problem is addressed in a statistical model for the data distribution that is nonparametric, beyond possible knowledge about the treatment and censoring mechanisms. We propose data adaptive estimators of this optimal dynamic regime which are defined by sequential loss-based learning under both the blip function and weighted classification frameworks. Rather than \textit{a priori} selecting …

Targeted Learning Of The Mean Outcome Under An Optimal Dynamic Treatment Rule, Mark J. Van Der Laan, Alexander R. Luedtke

U.C. Berkeley Division of Biostatistics Working Paper Series

We consider estimation of and inference for the mean outcome under the optimal dynamic two time-point treatment rule defined as the rule that maximizes the mean outcome under the dynamic treatment, where the candidate rules are restricted to depend only on a user-supplied subset of the baseline and intermediate covariates. This estimation problem is addressed in a statistical model for the data distribution that is nonparametric beyond possible knowledge about the treatment and censoring mechanism. This contrasts from the current literature that relies on parametric assumptions. We establish that the mean of the counterfactual outcome under the optimal dynamic treatment …

Deductive Derivation And Computerization Of Compatible Semiparametric Efficient Estimation, Constantine E. Frangakis, Tianchen Qian, Zhenke Wu, Ivan Diaz

U.C. Berkeley Division of Biostatistics Working Paper Series

Researchers often seek robust inference for a parameter through semiparametric estimation. Efficient semiparametric estimation currently requires theoretical derivation of the efficient influence function (EIF), which can be a challenging and time-consuming task. If this task can be computerized, it can save dramatic human effort, which can be transferred, for example, to the design of new studies. Although the EIF is, in principle, a derivative, simple numerical differentiation to calculate the EIF by a computer masks the EIF's functional dependence on the parameter of interest. For this reason, the standard approach to obtaining the EIF has been the theoretical construction of …

Targeted Covariate-Adjusted Response-Adaptive Lasso-Based Randomized Controlled Trials, Antoine Chambaz, Wenjing Zheng, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We present a new covariate-adjusted response-adaptive randomized controlled trial design and inferential procedure built on top of it. The procedure is targeted in the sense that (i) the sequence of randomization schemes is group-sequentially determined by targeting a user-specified optimal randomization design based on accruing data and, (ii) our estimator of the user-specified parameter of interest, seen as the value of a functional evaluated at the true, unknown distribution of the data, is targeted toward it by following the paradigm of targeted minimum loss estimation. We focus for clarity on the case that the parameter of interest is the marginal …

Sieve Plateau Variance Estimators: A New Approach To Confidence Interval Estimation For Dependent Data, Molly M. Davies, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose we have a data set of n-observations where the extent of dependence between them is poorly understood. We assume we have an estimator that is squareroot-consistent for a particular estimand, and the dependence structure is weak enough so that the standardized estimator is asymptotically normally distributed. Our goal is to estimate the asymptotic variance of the standardized estimator so that we can construct a Wald-type confidence interval for the estimate. In this paper we present an approach that allows us to learn this asymptotic variance from a sequence of influence function based candidate variance estimators. We focus on time …

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. …