%0 Journal Article
%T Power Loss of Stratified Log-Rank Test in Homogeneous Samples
%A Changyong Feng
%A Hongyue Wang
%A Xin M. Tu
%J Journal of Quality and Reliability Engineering
%D 2010
%R 10.1155/2010/942184
%X We study the loss of power of the stratified log-rank test (SLRT) compared to the unstratified log-rank test (ULRT) in the case of a large number of strata with relatively a small number of stratum sizes in terms of the asymptotic distributions of test statistics under local alternatives. The SLRT tends to lose information due to overstratification. It is better to test the homogeneity among strata before using the stratified log-rank test. 1. Introduction It is well known in survival analysis that the (unstratified) log-rank test (ULRT) is the most efficient invariant test under contiguous alternatives in the proportional hazards model [1, 2]. Gill [3] gave a nice proof of this conclusion by using the Cauchy-Schwarz inequality. In multicenter clinical trials with time-to-event as the primary outcome variable, we want to compare the treatment effects of two or more treatment methods. In the example in Section 6, patients were randomized in a ration to two treatment groups. The primary outcome is the time to death from all causes during the study. Individuals from different centers are assumed to be independent. Even if the treatment effect can be assumed to be the same among centers, each center may have some factors which make the baseline hazard functions different from center to center. For this kind of data, the stratified log-rank test (SLRT) can be used to account for the baseline difference. Some previous work has been developed to study the power loss of the log-rank test. Akazawa et al. [4] evaluated through simulation the loss of power of stratified log-rank test due to the the heterogeneity in clinical trials. Generally, the power of the stratified log-rank test decreases due to two reasons: (i) the stratum size may be too small and (ii) the individuals in the same stratum are heterogeneous. The simulation shows that the loss of power is substantial when the stratum size is very small and ¡°the total number of failures and the treatment effect are fixed¡±. From the stratified Cox regression model in survival analysis, we can see that if the stratum size is small, its contribution to the overall test is small with censored data in the stratum. This may decrease the power of the stratified log-rank test. Note the stratified log-rank test is the score test from stratified partial likelihood (see Section 3). In this paper, we consider the case where there is a large number of strata, but each stratum has a relatively small sample size. We assume that patients are homogeneous within each treatment group. For this kind of data, we can construct both
%U http://www.hindawi.com/journals/jqre/2010/942184/