Volume 21 Issue 5 - February 17, 2012 PDF
The simultaneous use of weighted logrank and weighted Kaplan-Meier statistics with clustered right-censored data
Yunchan Chi* and Pei-Fang Su
Department of Statistics, College of Management, National Cheng Kung University
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Clustered right-censored data often arise from tumorigenicity experiments and clinical trials. For example, in an otology study, 78 children with both ears suffering from otitis media are randomly assigned into the treatment group or control group to place ventilating tubes in both ears to reduce the prevalence of middle ear effusion. The goal of such a study was to examine whether postsurgical treatment can extend the lifetimes of tubes. Note a child in each sample is referred to as a cluster and the lifetimes within each cluster may correlate with one another but the lifetimes in the two samples are independent. If the tube is still functional at the end of the study, then its lifetime is greater than the endpoint, and therefore, it is regarded as a right-censored observation. In general, the data observed in this otology study are referred to as two independent samples of clustered right-censored data.

For testing the equality of two survival functions, Jung and Jeong have extended weighted logrank tests (WLR) to such data, while the weighted Kaplan-Meier test (WKM) can be derived based on the work of O’Gorman and Akritas. The weight functions in both classes of tests (WLR and WKM) can be selected to be more sensitive to detect a certain alternative; however, since the exact alternative is unknown, it is difficult to specify the selected weights in advance. Because WLR is rank-based, it is not sensitive to the magnitude of the difference in survival times. Although WKM is constructed to be more sensitive to the magnitude of the difference in survival times, it is not sensitive to late hazard differences. Therefore, in order to combine the advantages of these two classes of tests, this paper developed a class of versatile tests based on simultaneously using WLR and WKM for two independent samples of clustered right-censored data. The comparative results from a simulation study showed that the proposed methods preserve better power across a broad range of alternatives.
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