Wang Mei-Cheng, Huang Chiung-Yu
Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, 615 N. Wolfe Street, Baltimore, Maryland 21205, U.S.A.
Division of Biostatistics and Bioinformatics, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University, 550 N. Broadway, Baltimore, Maryland 21205, U.S.A.
Biometrika. 2014 Sep 1;101(3):553-566. doi: 10.1093/biomet/asu016.
This paper proposes a unified framework to characterize the rate function of a recurrent event process through shape and size parameters. In contrast to the intensity function, which is the event occurrence rate conditional on the event history, the rate function is the occurrence rate unconditional on the event history, and thus it can be interpreted as a population-averaged count of events in unit time. In this paper, shape and size parameters are introduced and used to characterize the association between the rate function (·) and a random variable . Measures of association between and (·) are defined via shape- and size-based coefficients. Rate-independence of and (·) is studied through tests of shape-independence and size-independence, where the shape-and size-based test statistics can be used separately or in combination. These tests can be applied when is a covariable possibly correlated with the recurrent event process through (·) or, in the one-sample setting, when is the censoring time at which the observation of (·) is terminated. The proposed tests are shape- and size-based, so when a null hypothesis is rejected, the test results can serve to distinguish the source of violation.
本文提出了一个统一框架，通过形状和大小参数来刻画复发事件过程的速率函数。与强度函数（即基于事件历史的事件发生率）不同，速率函数是不依赖于事件历史的发生率，因此它可以被解释为单位时间内事件的总体平均计数。在本文中，引入了形状和大小参数，并用于刻画速率函数（·）与一个随机变量之间的关联。通过基于形状和大小的系数来定义与（·）之间的关联度量。通过形状独立性和大小独立性检验来研究与（·）的速率独立性，其中基于形状和大小的检验统计量可以单独使用或组合使用。当是一个可能通过（·）与复发事件过程相关的协变量时，或者在单样本设置中，当是终止对（·）观察的删失时间时，这些检验都可以应用。所提出的检验是基于形状和大小的，因此当原假设被拒绝时，检验结果可以用于区分违规的来源。
