Wang Xiaofei, Bai Fangfang, Pang Herbert, George Stephen L
a Department of Biostatistics and Bioinformatics, Duke University , Durham , NC , USA.
b School of Statistics, University of International Business and Economics , Beijing , China.
J Biopharm Stat. 2019;29(4):592-605. doi: 10.1080/10543406.2019.1633659. Epub 2019 Jul 9.
For time-to-event outcomes, the Kaplan-Meier estimator is commonly used to estimate survival functions of treatment groups and to compute marginal treatment effects, such as the difference in survival rates between treatments at a landmark time. The derived estimates of the marginal treatment effect are uniformly consistent under general conditions when data are from randomized clinical trials. For data from observational studies, however, these statistical quantities are often biased due to treatment-selection bias. Propensity score-based methods estimate the survival function by adjusting for the disparity of propensity scores between treatment groups. Unfortunately, misspecification of the regression model can lead to biased estimates. Using an empirical likelihood (EL) method in which the moments of the covariate distribution of treatment groups are constrained to equality, we obtain consistent estimates of the survival functions and the marginal treatment effect. Equating moments of the covariate distribution between treatment groups simulate the covariate distribution that would have been obtained if the patients had been randomized to these treatment groups. We establish the consistency and the asymptotic limiting distribution of the proposed EL estimators. We demonstrate that the proposed estimator is robust to model misspecification. Simulation is used to study the finite sample properties of the proposed estimator. The proposed estimator is applied to a lung cancer observational study to compare two surgical procedures in treating early-stage lung cancer patients.
对于事件发生时间结局,常用Kaplan-Meier估计量来估计治疗组的生存函数,并计算边际治疗效果,比如在某个标志性时间点治疗之间生存率的差异。当数据来自随机临床试验时,在一般条件下,边际治疗效果的导出估计量是一致的。然而,对于来自观察性研究的数据,由于治疗选择偏倚,这些统计量往往存在偏差。基于倾向评分的方法通过调整治疗组之间倾向评分的差异来估计生存函数。不幸的是,回归模型的错误设定会导致有偏差的估计。使用一种经验似然(EL)方法,其中治疗组协变量分布的矩被约束为相等,我们得到了生存函数和边际治疗效果的一致估计。使治疗组之间协变量分布的矩相等,模拟了如果患者被随机分配到这些治疗组本应得到的协变量分布。我们建立了所提出的EL估计量的一致性和渐近极限分布。我们证明所提出的估计量对模型错误设定具有稳健性。通过模拟研究所提出估计量的有限样本性质。将所提出的估计量应用于一项肺癌观察性研究,以比较两种治疗早期肺癌患者的手术方法。