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Full-Text Articles in Physical Sciences and Mathematics
Tmle For Marginal Structural Models Based On An Instrument, Boriska Toth, Mark J. Van Der Laan
Tmle For Marginal Structural Models Based On An Instrument, Boriska Toth, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
We consider estimation of a causal effect of a possibly continuous treatment when treatment assignment is potentially subject to unmeasured confounding, but an instrumental variable is available. Our focus is on estimating heterogeneous treatment effects, so that the treatment effect can be a function of an arbitrary subset of the observed covariates. One setting where this framework is especially useful is with clinical outcomes. Allowing the causal dose-response curve to depend on a subset of the covariates, we define our parameter of interest to be the projection of the true dose-response curve onto a user-supplied working marginal structural model. We …
A Generally Efficient Targeted Minimum Loss Based Estimator, Mark J. Van Der Laan
A Generally Efficient Targeted Minimum Loss Based Estimator, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Suppose we observe n independent and identically distributed observations of a finite dimensional bounded random variable. This article is concerned with the construction of an efficient targeted minimum loss-based estimator (TMLE) of a pathwise differentiable target parameter based on a realistic statistical model.
The canonical gradient of the target parameter at a particular data distribution will depend on the data distribution through an infinite dimensional nuisance parameter which can be defined as the minimizer of the expectation of a loss function (e.g., log-likelihood loss). For many models and target parameters the nuisance parameter can be split up in two components, …
Super-Learning Of An Optimal Dynamic Treatment Rule, Alexander R. Luedtke, Mark J. Van Der Laan
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
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 …
Targeted Learning Of An Optimal Dynamic Treatment, And Statistical Inference For Its Mean Outcome, Mark J. Van Der Laan
Targeted Learning Of An Optimal Dynamic Treatment, And Statistical Inference For Its Mean Outcome, Mark J. Van Der Laan
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, …
Causal Inference For Networks, Mark J. Van Der Laan
Causal Inference For Networks, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
Suppose that we observe a population of causally connected units according to a network. On each unit we observe a set of potentially connected units that contains the true connections, and a longitudinal data structure, which includes time-dependent exposure or treatment, time-dependent covariates, a final outcome of interest. The target quantity of interest is defined as the mean outcome for this group of units if the exposures of the units would be probabilistically assigned according to a known specified mechanism, where the latter is called a stochastic intervention. Causal effects of interest are defined as contrasts of the mean of …
Adaptive Matching In Randomized Trials And Observational Studies, Mark J. Van Der Laan, Laura Balzer, Maya L. Petersen
Adaptive Matching In Randomized Trials And Observational Studies, Mark J. Van Der Laan, Laura Balzer, Maya L. Petersen
U.C. Berkeley Division of Biostatistics Working Paper Series
In many randomized and observational studies the allocation of treatment among a sample of n independent and identically distributed units is a function of the covariates of all sampled units. As a result, the treatment labels among the units are possibly dependent, complicating estimation and posing challenges for statistical inference. For example, cluster randomized trials frequently sample communities from some target population, construct matched pairs of communities from those included in the sample based on some metric of similarity in baseline community characteristics, and then randomly allocate a treatment and a control intervention within each matched pair. In this case, …
Model Checking Techniques For Regression Models In Cancer Screening, Debashis Ghosh
Model Checking Techniques For Regression Models In Cancer Screening, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
There has been much work on developing statistical procedures for associating tumor size with the probability of detecting a metastasis. Recently, Ghosh (2004) developed a unified statistical framework in which equivalences with censored data structures and models for tumor size and metastasis were examined. Based on this framework, we consider model checking techniques for semiparametric regression models in this paper. The procedures are for checking the additive hazards model. Goodness of fit methods are described for assessing functional form of covariates as well as the additive hazards assumption. The finite-sample properties of the methods are assessed using simulation studies.