Abstract

In this thesis, I consider the problem of accounting for model uncertainty in a parametric regression model with focus on the uncertainty involved in selection of the optimal transformation of a continuous predictor in the Cox proportional hazards model (Cox, 1972). I use the minimum AIC approach to select a posteriori the optimal transformation of a continuous predictor. First, I review literature on criteria and methods for selecting the " best-fitting " model based on the results obtained from a sample, in Chapter 1. Then, in Chapter 2, I discuss the general problem of model selection uncertainty on inference and summarize research in this area. Next, I evaluate the impact of the data-dependent model selection approach on type I error rate through simulations. In simulations, I generate data, assuming both linear and non-linear dependence of hazard on a continuous covariate as well as no association. The generated data are then used to estimate a series of models with various functional form, to assess the impact of model selection on type I error and on statistical power. Some of the above methodological problems are then illustrated in the analysis of a real-life dataset including several cardiovascular risk factors.