Comparative Analysis of the Cox Semi-parametric and Weibull Parametric Models on Colorectal Cancer Data

Abstract

The survival and hazard functions are key concepts in survival analysis for describing the distribution of event times. The survival function gives, for every time, the probability of surviving (or not experiencing the event). The hazard function gives the potential that the event will occur, per time unit, given that an individual has survived up to the specified time. While these are often of direct interest, many other quantities of interest (e.g., median survival) may subsequently be estimated from knowing either the hazard or survival function. This research was a five-year retrospective study on data from a record of colorectal cancer patients that received treatments from 2013 to 2017 in Radiotherapy Department of Usmanu Danfodiyo University Teaching Hospital, Sokoto, being it one of the cancer registries in Nigeria. 9 covariates were selected to fit colorectal cancer data using Cox and Weibull Regression Models. From the result it is concluded that the predictor variables could significantly predict the survival of colorectal cancer patients using Cox. Also the result of the Weibull Proportional Hazard Model shows that the model is adequate enough to predict the survival of the colorectal patients. The A. I. C result shows that, according to our colorectal cancer data, the semi-parametric Cox regression model performed better than the parametric Weibull proportional hazards model. However, in the present study, the Cox model provided an efficient and a better fit to the study data than Weibull model.