Modelling graft survival after kidney transplantation using semi-parametric and parametric survival models
Achilonu, Okechinyere Juliet
This study presents survival modelling and evaluation of risk factors of graft survival in the context of kidney transplant data generated in South Africa. Beyond the Kaplan-Meier estimator, the Cox proportional hazard (PH) model is the standard method used in identifying risk factors of graft survival after kidney transplant. The Cox PH model depends on the proportional hazard assumption, which is rarely met. Assessing and accounting for this assumption is necessary before using this model. When the PH assumption is not valid, modi cation of the Cox PH model could o er more insight into parameter estimates and the e ect of time-varying predictors at di erent time points. This study aims to identify the survival model that will e ectively describe the study data by employing the Cox PH and parametric accelerated failure time (AFT) models. To identify the risk factors that mediate graft survival after kidney transplant, secondary data involving 751 adults that received a single kidney transplant in Charlotte Maxeke Johannesburg Academic Hospital between 1984 and 2004 was analysed. The graft survival of these patients was analysed in three phases (overall, short-term and long-term) based on the follow-up times. The Cox PH and AFT models were employed to determine the signi cant risk factors. The purposeful method of variable selection based on the Cox PH model was used for model building. The performance of each model was assessed using the Cox-Snell residuals and the Akaike Information Criterion. The t of the appropriate model was evaluated using deviance residuals and the delta-beta statistics. In order to further assess how appropriately the best model t the study data for each time period, we simulated a right-censored survival data based on the model parameter-estimates. Overall, the PH assumption was violated in this study. By extending the standard Cox PH model, the resulting models out-performed the standard Cox PH model. The evaluation methods suggest that the Weibull model is the most appropriate in describing the overall graft survival, while the log-normal model is more reasonable in describing short-and long-term graft survival. Generally, the AFT models out-performed the standard Cox regression model in all the analyses. The simulation study resulted in parameter estimates comparable with the estimates from the real data. Factors that signi cantly in uenced graft survival are recipient age, donor type, diabetes, delayed graft function, ethnicity, no surgical complications, and interaction between recipient age and diabetes. Statistical inferences made from the appropriate survival model could impact on clinical practices with regards to kidney transplant in South Africa. Finally, limitations of the study are discussed in the context of further studies.
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in ful lment of the requirements for the degree of Master of Science in Statistics November, 2017
Achilonu, Okechinyere Juliet (2017) Modelling graft survival after kidney transplantation using semi-parametric and parametric survival models, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/24024>