Testing for and adjusting for dependent censoring in survival analysis.

In survival analysis, it is very common to have censored data in which the occurrence times of the event of interest are not completely observed for some subjects under study. Censoring can occur for different reasons, but it is generally assumed that the censoring time is independent of the survival time. In some cases, however, this assumption may not hold. However, many statistical methods for analyzing survival data have been developed on the basis of the assumption of independent censoring. The assumption of independent censoring cannot be tested when only right censored data are available. In this paper, we propose a method for testing the assumption of independent censoring, which involves further following-up of a randomly selected subset of lost-to-follow-up censored subjects until the prearranged time. This further following-up provides additional information for testing the independence assumption. On the basis of the method suggested here, a log rank test statistic for two samples is derived by way of the multivariate counting process and multiplicative intensity model proposed by Gill (1980) and Aalen (1978). The asymptotic properties of the log rank statistic are derived using the result of Andersen et al. (1982). In addition, it is shown that the log rank statistic is equivalent to the score statistic in the time-dependent Cox model. Furthermore, an adjusted estimator of the survivor function is given with an asymptotic variance estimator for the dependent censoring model. Finally, results are reported of a simulation study for calculating the power under proportional hazards alternatives. In summary, this research provides a method for testing the assumption of independent censoring, and provides a method for adjusting the survivor function estimate if the independence assumption is violated.PhDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105230/1/9116233.pdfDescription of 9116233.pdf : Restricted to UM users only