A SEQUENTIAL APPROACH FOR CLUSTEREDSURVIVAL DATA IN FAMILY STUDIES BASEDON A WEIGHTED LOG-RANK STATISTIC

摘要

In this paper, we propose an extension of the weighted log-rank statistic proposedby Gangnon and Kosorok (2004) to the analysis of correlated survival data in thecontext of a sequential family design. The proposed test statistic is a nonparametricweighted log rank statistic where the weight is a function of the intra-class familialcorrelation. This intra-class familial correlation is estimated in an initial step, prior thestart of the sequential design, using a gamma frailty model. The sequential procedurestarts with an initial sample size and continues until a weight function is completelyspent, following the idea of Shen and Cai (2003). This weight function is updatedat each interim analysis, based on the number of events observed previously. Earlystopping boundaries for futility are also defined. This work is developed in the contextof genetic association studies where the goal is to test a newly discovered gene ona time-to-event disease outcome (e.g. time to cancer). The sequential procedure thenallows to stop the study when enough information has been gathered either to reject thenull hypothesis of no gene effect or to accept the null hypothesis (futility stopping).Our simulations demonstrate the good properties of our approach in finite samplesboth in terms of size and power of the test statistic. Our real application to a studyof familial colorectal cancer also confirms the interest of this method by allowing anearly stopping of the study. Finally, a discussion on the pros and cons of this approachas well as further extensions is provided.