Stitelman Ori M, De Gruttola Victor, van der Laan Mark J
University of California, Berkeley, CA, USA.
Int J Biostat. 2012 Sep 18;8(1):/j/ijb.2012.8.issue-1/1557-4679.1334/1557-4679.1334.xml. doi: 10.1515/1557-4679.1334.
In many randomized controlled trials the outcome of interest is a time to event, and one measures on each subject baseline covariates and time-dependent covariates until the subject either drops-out, the time to event is observed, or the end of study is reached. The goal of such a study is to assess the causal effect of the treatment on the survival curve. We present a targeted maximum likelihood estimator of the causal effect of treatment on survival fully utilizing all the available covariate information, resulting in a double robust locally efficient substitution estimator that will be consistent and asymptotically linear if either the censoring mechanism is consistently estimated, or if the maximum likelihood based estimator is already consistent. In particular, under the independent censoring assumption assumed by current methods, this TMLE is always consistent and asymptotically linear so that it provides valid confidence intervals and tests. Furthermore, we show that when both the censoring mechanism and the initial maximum likelihood based estimator are mis-specified, and thus inconsistent, the TMLE exhibits stability when inverse probability weighted estimators and double robust estimating equation based methods break down The TMLE is used to analyze the Tshepo study, a study designed to evaluate the efficacy, tolerability, and development of drug resistance of six different first-line antiretroviral therapies. Most importantly this paper presents a general algorithm that may be used to create targeted maximum likelihood estimators of a large class of parameters of interest for general longitudinal data structures.
在许多随机对照试验中，感兴趣的结果是事件发生时间，并且要对每个受试者测量基线协变量和随时间变化的协变量，直到受试者退出、观察到事件发生时间或达到研究结束。此类研究的目标是评估治疗对生存曲线的因果效应。我们提出了一种针对治疗对生存的因果效应的靶向最大似然估计器，充分利用所有可用的协变量信息，得到一个双重稳健的局部有效替代估计器，如果截尾机制被一致估计，或者基于最大似然的估计器已经是一致的，那么该估计器将是一致的且渐近线性的。特别是，在当前方法所假设的独立截尾假设下，这种靶向最大似然估计器总是一致的且渐近线性的，从而能提供有效的置信区间和检验。此外，我们表明，当截尾机制和基于初始最大似然的估计器都被错误设定且因此不一致时，在逆概率加权估计器和基于双重稳健估计方程的方法失效的情况下，靶向最大似然估计器表现出稳定性。靶向最大似然估计器被用于分析特绍波研究，该研究旨在评估六种不同一线抗逆转录病毒疗法的疗效、耐受性和耐药性发展情况。最重要的是，本文提出了一种通用算法，可用于为一般纵向数据结构创建一大类感兴趣参数的靶向最大似然估计器。
