ASSESSMENT OF FLEXIBLE TECHNIQUES FOR MODELING THE HAZARD FUNCTION IN THE ANALYSIS OF SURVIVAL DATA

In survival analysis the shape of hazard function is essential to explore the time course of a disease, as it provides information useful to support or generate biological hypotheses. When long follow-up is available, the shape of hazard function may be complex. Multiple peaks patterns observed in several data sets for various kinds of tumor, for example breast cancer, have found an interpretation in the context of tumor dormancy theory. To model such possibly complex patterns sufficiently flexible techniques are required. This thesis work compares in the homogenous case the performance of several smoothers in the piecewise exponential model. Regression splines with two different choices for knots location, P-splines, smoothing splines and wavelets (PEW model) have been used in smoothing both a unimodal and a bimodal hazard shape. Simulations have evidenced a generally better performance of penalized splines, in particular the smoothing splines, with respect to regression splines. The not completely satisfying performance of wavelets due to bias at later times deserves further investigation. Of particular clinical interest is the modeling of the hazard function accounting for possibly non-linear, interaction and time-dependent effects of prognostic factors. Neural network extension of piecewise exponential model (PEANN) has been implemented in R and compared with tensor splines, on a data set of 2233 breast cancer patients. Neural networks can represent a practical solution especially in an exploratory context.