Analyzing survival curves at a fixed point in time for paired and clustered right-censored data

In clinical trials, information about certain time points may be of interest in making decisions about treatment effectiveness. Therefore, rather than comparing entire survival curves, researchers may wish to focus the comparison on fixed time points with potential clinical utility. For two independent samples of right-censored data, Klein et al. (2007) compared survival probabilities at a fixed time point by studying a number of tests based on transformations of the KaplanMeier estimators of the survival function. To compare the survival probabilities at a fixed time point for paired right-censored data or clustered right-censored data, however, their approach requires modification. In this paper, we extend the statistics to accommodate possible within-pair and within-cluster correlation. We use simulation studies to present comparative results. Finally, we illustrate the implementation of these methods using two real data sets.