Abstract
Survival analysis also called time to event analysis aims at making inferences on the life time
or the time elapsed between the recruitment of subjects or the onset of observations, until the
occurrence of some event of interest. Methods used in general statistical analysis, in particular in
regression analysis, are not directly applicable to survival data due to censoring and truncation.
This study reviewed nonparametric, semi-parametric, and briefly parametric methods used in
classical survival analysis, namely the Kaplan-Meier estimation, the Nelson-Aalen estimation, and
the Cox proportional hazards regression model. Furthermore, the study applied the theory of
counting processes and martingales to model the hazard function conditional to covariates using
relative risk model and the Aalen additive risk model.
This study used data collected at Kigali University Teaching Hospital on 933 diabetic patients
admitted or visited the hospital during the period from the 1st January 2008 to the 31st December
2013. The results revealed that the hazard of death from diabetes, for this data, is higher in
male patients as compared to female patients; it is higher in older patients compared to relatively
younger ones; it is also higher in rural compared to urban patients. Patients treated using placebo
had a better survival outcome than those on conventional diabetes medications. Probably, they
were much healthier than those on the other three medications. Patients with normal weight,
overweight, and obesity were found to have a higher hazard of death from diabetes compared to
underweight patients. Patients with type II diabetes had a higher hazard of death as compared
to those with type I diabetes. Finally, patients with moderately high to high blood pressure had
a higher hazard of death compared to patients with low or normal blood pressure. These results
were not found in a single model, but are a summary of findings obtained in several models used...
M.Sc. (Mathematical Statistics)