On estimation methods and test for proportional hazards assumptions in survival data

Abstract

This work compared three estimation methods to handle tied survival time data under the semiparametric Cox proportional hazards model framework (the Exact, Breslow and Efron partial likelihood) and also two parametric proportional hazards models (the Exponential and Weibull) which utilized full likelihood estimation method. These methods were described and applied to two datasets, a clinical dataset on breast cancer patients and a dataset on duration of labour before delivery. We also checked for proportional hazards assumptions on some of the covariates used in the analysis. Using Akaike Information Criterion (AIC) for overall model comparison, Efron method had the least AIC value which is an indication of best performance in handling tied observation, whereas Exponential model with highest AIC performed least. On checking the proportionality assumption for the three categorical variables used in the analysis of cancer data, it was observed that the assumption was valid for absence or presence of Lymph Nodes, whereas it was not valid for progesterone receptor and estrogen receptor.

Keywords: Censored data, Proportional hazards model, Akaike Information Criterion, Parametric model, Survivorship function, Partial likelihood