Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Statistics and Econometrics

The aim of this thesis is to provide introduction to different methods for modeling survival data. There are three major approaches for modeling survival data: non- parametric, semi-parametric and parametric approaches. Each approach has its own advantages and disadvantages. This thesis is primarily concerned with parametric approach-also, known as accelerated failure time approach and semi-parametric approach {u2013}also, known as proportional hazard cox approach. An elaborated discussion of the two approaches is presented. This discussion included (for each approach): specification of the model -derivation of the likelihood function {u2013} estimation of parameters using maximum likelihood method- inference and statistical tests about model parameters using likelihood ratio, Wald and score tests. For Parametric approach, two famous types of survival time distributions were handled: Exponential and Weibull distributions.For semi-parametric approach (Cox proportional Hazard approach) two approximating methods for estimating the survival function and other related lifetime indicators from the Cox model estimates were discussed: The Kalbfleisch {u2013} Prentice method and The Breslow method. Also, the Cox model as a special case of counting processes is discussed and two diagnostic measures for assessing the assumption of proportional hazard (Cox {u2013} Snell residuals- Schoenfeld residuals) were also displayed. For the purpose of comparing between different parametric and semi-parametric models, real data example (MUGUS data) was supplied for comparative study between different survival models

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