The Use of Cox and Piecewise Exponential Models in the Determination of Renal Failure

Abstract

Cox Proportional hazards model has played a great role in epidemiological and clinical researches in examining the influence of covariates on hazard distributions when no specification of the baseline hazard is made. It is a robust model irrespective of the nature of baseline hazard distribution. However, it is less popular when it is of primary
interest to estimate the hazard function. The purpose of this study is to fit and compare piecewise exponential and Cox models using renal failure data. For the piecewise exponential model, the hospital admission duration of the patients was split into various non-overlapping time intervals such that the hazard rates were assumed to be constant within each interval but not necessarily constant across the entire time duration. The results were compared with the standard Cox proportional hazards model. It was found under both models that age of the patients, diagnosis (categorized as chronic or acute), and blood pressure (systolic and diastolic) significantly influenced mortality from renal failure among the patients under study. However, based on AIC, piecewise exponential model showed superiority over Cox proportional hazards model and improved as the length of the intervals increased.