Simulation Comparisons of Semi-Parametric Accelerated Failure Time Model With Different Bandwidths

The proportional hazards (PH) model and the accelerated failure time (AFT) model are the most popular models to fit the censoring data. Sometimes, the PH assumption cannot be satisfied, and therefore, the AFT model becomes a useful alternative to the PH model. Comparing with the least square method and the rank estimation method, the profile likelihood method needs less computation time in estimating the parameters and associated variances in the semi-parametric AFT model. The main aim of this thesis is to investigate the impact of the different bandwidths on the estimations in the profile likelihood method. Additionally, we also evaluate its performances according to the different sample sizes and censoring rates. Finally, we make recommendation of its usage in practice. For illustration, we apply the semi-parametric AFT model to the real datasets: methadone maintenance treatment and primary biliary cirrhosis, using the profile likelihood method