Frailty Survival Model Analysis of the National Deceased Donor Kidney Transplant Dataset Using Poisson Variance Structures

In a recent study of transplant outcomes, donor age, cerebrovascular accident as the cause of death (CVA), renal insufficiency (serum creatinine >1.5 mg/dL), and history of hypertension have been identified as donor factors associated with elevated risk of kidney transplant failure. It is of great interest to know whether there remain other unmeasured donor factors associated with elevated risk of graft failure. In this article we study a sample of 6,024 deceased donor kidney transplants performed in 194 centers from 1995 to 2000. In addition to variation among transplant recipients, there are two other random effects: unmeasured donor and unrecorded center factors (data not available at the physician level). These two random effects are crossed, because the two kidneys from the same donor can be transplanted in different centers. Multivariate frailty models are applied to analyze the data. The likelihood functions of both parametric (e.g., with piecewise constant baseline hazard) and semiparametric multivariate frailty models are shown to be proportional to the likelihood functions of a class of mixed Poisson regression models. The penalized quasi-likelihood method is used as the numerical procedure for these mixed Poisson regression models. Thus we are able to estimate and model crossed random-effects structures for survival analysis. Although about 30% of recipient graft survival rate variation due to donor factors is explained by the measured donor characteristics, the remaining variation among donors in graft survival rate is still statistically significant, suggesting that there may be other unmeasured donor factors associated with a reduced graft survival rate. We also find significant variation of graft failure rates among transplant centers due to unrecorded center factors. Therefore, this study suggests that practice patterns at transplant centers and identification of other donor factors may merit further investigation.