Semiparametric methods to contrast gap time survival functions: Application to repeat kidney transplantation

Times between successive events (i.e., gap times) are of great importance in survival analysis. Although many methods exist for estimating covariate effects on gap times, very few existing methods allow for comparisons between gap times themselves. Motivated by the comparison of primary and repeat transplantation, our interest is specifically in contrasting the gap time survival functions and their integration (restricted mean gap time). Two major challenges in gap time analysis are non-identifiability of the marginal distributions and the existence of dependent censoring (for all but the first gap time). We use Cox regression to estimate the (conditional) survival distributions of each gap time (given the previous gap times). Combining fitted survival functions based on those models, along with multiple imputation applied to censored gap times, we then contrast the first and second gap times with respect to average survival and restricted mean lifetime. Large-sample properties are derived, with simulation studies carried out to evaluate finite-sample performance. We apply the proposed methods to kidney transplant data obtained from a national organ transplant registry. Mean 10-year graft survival of the primary transplant is significantly greater than that of the repeat transplant, by 3.9 months (p=0.023), a result that may lack clinical importance.