A COMPARATIVE ANALYSIS OF COX, WEIBULL, FRAILTY AND EXPONENTIAL SURVIVAL MODELS ON SMALL SAMPLE SIZE DATA FROM A KAPOSI’S SARCOMA STUDY AT QUEEN ELIZABETH CENTRAL HOSPITAL

Abstract

The Cox PH regression model has become the survival model of choice in clinical trials as it is robust to model misspecification compared to other models. However little is known whether Cox is still a robust and better method to use given small sample size. This study compared the performance of Cox, Weibull, Exponential and Frailty models where the sample size is small.The 4 models were fitted to data from an open label, three arm randomised efficacy trial for AIDS related Kaposi‟s sarcoma at QECH with total sample of 90 children aged <16 years. Proportions of baseline characteristics were compared across treatment groups using Pearson Chi-squared tests for categorical and ANOVA for continuous variables. Plots of log-log of survival against log of survival time and global tests were used to test suitability of PH assumption. Selection of the best model fit was based on AIC. Out of ninety patients, 53% were males, average age was 8 years (SD = 2.8years), while 89% were HIV positive. Baseline characteristics did not differ in treatment groups; gender (p=0.56), age (p=0.57) and HIV status (p=0.26). Although results from both global tests and plots of log-log of survival against log of survival time indicated no violation of the PH assumption, exponential model was the best with AIC=174.1. Basing on the exponential model, children treated with Vincristine monotherapy survived evidently poorly compared with those on etoposide (HR=5.8, p=0.04). Given a clinical trial with small sample size, the Exponential parametric models can elicit more precise results compared to the semi-parametric Cox PH model.