Estimation of the Base Hazard Function by Bootstrapping

This thesis examines the techniques in estimating the base hazard function by bootstrapping. The base hazard function is a crucial part of survival analysis. It is used to construct an estimate of the proportional hazard model for every individual. As in many methods for analysing survival data, this thesis utilizes the nonparametric model of Kaplan Meier, the Cox proportional hazard regression of the parametric model and the data validation by bootstrapping. The Cox proportional hazard regression is used to model failure time data in censored data. Bootstrapping schemes validate the models based on Efron’s technique and the data samples are generated using S-Plus programme randomizer. v Assessment of this method is investigated by performing simulation study on generated data. Two simulation studies are carried out to confirm the suitability of the models. Graph obtained from the results indicated that bootstrapping provides an alternative method in constructing estimation for base hazard function. This method is good alternative for a distribution-free approach with a minimal set of data

Semiparametric binary model for clustered survival data

This paper considers a method to analyze semiparametric binary models for clustered survival data when the responses are correlated. We extend parametric generalized estimating equation (GEE) to semiparametric GEE by introducing smoothing spline into the model. A backfitting algorithm is used in the derivation of the estimating equation for the parametric and nonparametric components of a semiparametric binary covariate model. The properties of the estimates for both are evaluated using simulation studies. We investigated the effects of the strength of cluster correlation and censoring rates on properties of the parameters estimate. The effect of the number of clusters and cluster size are also discussed. Results show that the GEE-SS are consistent and efficient for parametric component and nonparametric component of semiparametric binary covariates