This paper considers one-step targeted maximum likelihood estimation method for general competing risks and survival analysis settings where event times take place on the positive real line R+ and are subject to right-censoring. Our interest is overall in the effects of baseline treatment decisions, static, dynamic or stochastic, possibly confounded by pre-treatment covariates. We point out two overall contributions of our work. First, our method can be used to obtain simultaneous inference across all absolute risks in competing risks settings. Second, we present a practical result for achieving inference for the full survival curve, or a full absolute risk curve, across time by targeting over a fine enough grid of points. The one-step procedure is based on a one-dimensional universal least favorable submodel for each cause-specific hazard that can be implemented in recursive steps along a corresponding universal least favorable submodel. We present a theorem for conditions to achieve weak convergence of the estimator for an infinite-dimensional target parameter. Our empirical study demonstrates the use of the methods.
翻译:本文件审议了一般相互竞争的风险和生存分析环境的一次性目标最大可能性估计方法,在这种环境中,事件发生时间是在正正实际线R+上,并受到右检检查。我们的兴趣是,基线处理决定、静态的、动态的或随机的、可能由预处理共变所困扰的、可能由预处理共变引起的基本处理决定的总体影响。我们指出了我们工作的两种总体贡献。首先,我们的方法可用于在相互竞争的风险环境中获得对所有绝对风险的同步推论。第二,我们提出了一个实际结果,通过对足够精细的点网格进行定向,实现整个生存曲线或完全绝对风险曲线的推论。一步骤程序基于一个一维的、最不可取的子模型,用于每种特定原因的危害,在相应的普遍最不优惠的子模型中可以反复执行。我们提出了一种理论,用于使一个无限目标参数的估量参数达到薄弱的趋同。我们的经验研究展示了方法的使用情况。