A Class of Weighted Log-Rank Tests for Survival Data When the Event is Rare
针对随访研究中事件发生率低的情况，提出对Gp加权对数秩统计量的简单修改，使其在罕见事件下仍有效，并通过模拟证明其效率优于原方法。
In many epidemiological and medical follow-up studies, a majority of study subjects do not experience the event of interest during the follow-up period. An important example is the ongoing prostate, lung, colorectal, and ovarian cancer Screening trial of the National Cancer Institute. In such a situation, the widely used Gp family of weighted log-rank statistics essentially reduces to the special case of the (unweighted) log-rank statistics. We propose a simple modification to the Gp family that adapts to survival data with rare events, a concept that we formulate in terms of a small number of events at the study endpoint relative to the sample size. The usual asymptotic properties, including convergence in distribution of the standardized statistics to the standard normal, are obtained under the rare event formulation. Semiparametric transformation models forming sequences of contiguous alternatives are considered and, for each p, a specific such model is identified so that the corresponding modified Gp statistic is asymptotically efficient. Simulation studies show that the proposed statistics do behave differently from the original Gp statistics when the event rate during the study period is low and the former could lead to a substantial efficiency gain over the latter. Extensions to the Gp γ family and to the regression problem are also given.