Assessment of bimodal hazard functions by spline regression techniques

Longer follow-up for various kinds of cancer, particularly breast cancer, has made it possible the observation of complex forms of the hazard function of occurrence of metastasis and death. In several studies a bimodal hazard function was obtained, with a possible interpretation in the context of tumor dormancy. The shape of the hazard function is usually estimated by spline regression functions. In the case of breast cancer, no general agreement is obtained on the presence of a complex behavior. This may depend on the properties of the smoothing function adopted. Through simulations of a bimodal hazard function, the eff ectiveness of the piecewise exponential model in the correct identi cation of the shape has been evaluated, using di fferent types of regression models: the cubic splines with and without constraints of linearity in the tails and the P-splines of degree 0 and second order penalty.