Bivariate Survival Data Under Censoring: Simulation Procedure for Group Sequential Boundaries

In clinical trials, ethical considerations dictate that the accumulating data be analyzed for potential early termination due to treatment differences or adverse effects. Group sequential procedures take into account the effect of such interim analyses in univariate cases. When the outcome is correlated bivariate, often the problem is simplified to a univariate situation with corresponding loss of information. We consider the bivariate exponential distribution of Sarkar to develop a parametric methodology for interim analysis of clinical trials. We first present the procedure for testing the hypothesis of no treatment difference assuming complete uncensored data. Secondly, we incorporate three types of censoring schemes into the procedure. Finally, we show how group sequential methods apply to the bivariate censored case. The method is illustrated by simulating two equal samples of size 500 from the bivariate exponential distribution of Sarkar. The samples for the experimental and the control groups were generated having mean failure times for each of the organs of 20 months and 16 months, respectively. Different correlations between the failure times of the organs were also considered. A program in C++ was written to obtain the estimators and standard errors using the Newton Raphson procedure and then we incorporated the group sequential procedures. Numerical results are presented.