A Reanalysis of the Stanford Heart Transplant Data

Abstract

This article represents analyses of survival of patients in the Stanford Heart Transplantation Program. We model survival time as a function of patient covariates and transplant status, and compare the results obtained using various parametric representations for survival time, including the Weibull, lognormal, and piecewise exponential distributions. Pretransplant and posttransplant survival are considered separately, and the effect of transplantation on survival is examined by comparison of the separate hazard functions. Comparisons are made with previous analyses. Using the piecewise exponential models, we estimate a generally declining hazard before transplant; after transplant the hazard increases for about 60 days, then declines. The presence of heavy censoring before and after transplant means that many of the other parametric models with differing shapes for the hazard all give equally adequate fits to the data. Inferences about the effect of covariates are also relatively insensitive to the exact choice of parametric model, although important exceptions can occur if the parametric model is clearly contradicted by the data. Using a variety of models, we do find large differences in predicted survival of transplanted and nontransplanted patients as a function of patient age and calendar time of transplant. The variability in these estimated differences is correspondingly large, mainly due to a lack of information about the long-term survival of the nontransplanted group. As a result, analysis of these data leaves unresolved the issue of the effect of transplant on survival.

Key Words:

• Survival analyses
• Heart transplant
• Hazard models
• Weibull
• Piecewise exponential