Comparing cox proportional hazards and accelerated failure time models in survival analysis of HIV adult patients initiated on highly active Anti-Retroviral Therapy

Abstract

The Cox Proportional Hazards model is the most popular technique for analysis of the effects of covariates on survival time. This is so because of its simplicity and no assumptions are made about the nature or shape of the hazard function. Under certain circumstances, Cox Proportional hazards model may not be appropriate. The AFT model is another alternative, this is a class of parametric models that include the Exponential, Weibull, Log-normal, Log-logistic and the Gamma. In this study, Cox PH and AFT models were fitted to data of adult HIV patients initiated on HAART and their results were compared to determine the best model to predict survival on HAART. Regression results of Cox PH and AFT models were compared at univariate and multivariate levels. Proportional Hazards assumption and potential for AFT in the data were tested. Performance among AFT and Cox PH models was assessed using Goodness of fit method. Discrimination among AFT models was done using maximum likelihood and Akaike Information Criteria. Results showed that univariate and multivariate models of the Cox PH and AFT models were similar, but the AFT models provided a better description of the data. The PH assumption did not hold. The Gamma AFT was the best model by both the Goodness of fit and Akaike Information Criteria in predicting patient survival on HAART. Baseline CD4 cell count, WHO stage, Body Mass Index and age were significantly associated with mortality on HAART. The AFT model is a more valuable and realistic alternative to the Cox PH model in situations when the PH assumption does not hold and therefore should be considered as an alternative to the Cox PH in the survival analysis of patients initiated on HAART.