Rosenblum Michael, van der Laan Mark J
Johns Hopkins University, MD, USA.
Int J Biostat. 2010 Apr 1;6(1):Article 13. doi: 10.2202/1557-4679.1138.
Models, such as logistic regression and Poisson regression models, are often used to estimate treatment effects in randomized trials. These models leverage information in variables collected before randomization, in order to obtain more precise estimates of treatment effects. However, there is the danger that model misspecification will lead to bias. We show that certain easy to compute, model-based estimators are asymptotically unbiased even when the working model used is arbitrarily misspecified. Furthermore, these estimators are locally efficient. As a special case of our main result, we consider a simple Poisson working model containing only main terms; in this case, we prove the maximum likelihood estimate of the coefficient corresponding to the treatment variable is an asymptotically unbiased estimator of the marginal log rate ratio, even when the working model is arbitrarily misspecified. This is the log-linear analog of ANCOVA for linear models. Our results demonstrate one application of targeted maximum likelihood estimation.
诸如逻辑回归和泊松回归模型等模型，常用于估计随机试验中的治疗效果。这些模型利用随机化之前收集的变量中的信息，以便获得更精确的治疗效果估计值。然而，存在模型设定错误会导致偏差的风险。我们表明，某些易于计算的基于模型的估计量即使在使用的工作模型被任意误设的情况下，渐近无偏。此外，这些估计量是局部有效的。作为我们主要结果的一个特殊情况，我们考虑一个仅包含主项的简单泊松工作模型；在这种情况下，我们证明即使工作模型被任意误设，与治疗变量对应的系数的最大似然估计也是边际对数率比的渐近无偏估计量。这是线性模型中协方差分析的对数线性类似物。我们的结果展示了靶向最大似然估计的一个应用。
