Proportional Hazard Survival Models For Assessing Association Between Risk Factors And Early Death Of HIV/TB Co-Infected Patients

Abstract

Survival analysis has proven to be a major breakthrough in the analysis of time to event. The methodologies surrounding the concept of Survival Analysis seems laudable to most researchers especially in the medical, engineering, agricultural and actuarial field. Kaplan-Meier method which is applicable for estimating the survival function, log-rank test used for comparing the equality of two or more survival distributions, and the Cox proportional hazard model for inspecting the covariate effects on the hazard function are the most common analysis being applied because of their easy interpretation and high applicability. The popularity of other Proportional Hazard apart from Cox PH models is questionable though they also provide some competitive advantage. This particular thesis present the fundamental concept of the non-parametric method which is the Kaplan-Meier and Log-rank test, the semi parametric method involving the Cox proportional analysis and the Parametric Proportional Hazard models which are Exponential, Weibull and the Gompertz proportional model. The paper applied survival methods to HIV/TB co-infected patients data from the Korle Bu teaching Hospital. The main objective is to become familiar with the risk factors associated to early death of TB and HIV/AIDS co-infected patients. The proportionality assumptions assessed and some model diagnostics were made with some graphical presentations. The proportionality assumption was satisfied and the models were compared by the AIC values. Weibull proportional hazard model recorded the lowest AIC value making it a better model to fit the data set. The thesis considered the variables Age of patient, Marital status, Initial weight of patients, Category of tuberculosis suffered and the CD4 cell count. The variable Initial weight and CD4 cell count was significant at 0.05 significant level. We suggest that proportionality assumption should be assessed and other less popular PH models should be considered to provide the best fitted models and hence a better prediction.