Survival analysis is used to estimate the timetaken to an event of interest. It has been used in various fields such as engineering, medicine and insurance. The aim of this study is to show how survival analysis is used to analyze data in a particular clinical trial. This is achieved by use of the "Survival" package in R. The methods of hypothesis te3sting, modelling and estimation include; Kaplan Meier, cox model and Hazard method. The results were obtained by running the data through R and plotting the various curves. The coefficients obtained on the cox summary indicate that the variables considered for the study were significant. A conclusion was made that treatment using indinavir (IDV) drug increases the survival time of an individual. This paper is open for more research so as to come up with more functions or methods to analyze survival data.