Semiparametric Estimation Of Parametric Hazard Rates

Abstract

The best known methods for estimating hazard rate functions in survival analysis models are either purely parametric or purely nonparametric. The parametric ones are sometimes too biased while the nonparametric ones are sometimes too variable. There should therefore be scope for methods that somehow try to combine parametric and nonparametric features. In the present paper three semiparametric approaches to hazard rate estimation are presented. The first idea uses a dynamic local likelihood approach to fit the locally most suitable member in a given parametric class of hazard rates. Thus the parametric hazard rate estimate at time s inserts a parameter estimate that also depends on s. The second idea is to write the true hazard as a product of an initial parametric estimate times a correction factor, and then estimate this factor nonparametrically using orthogonal expansions. Finally the third idea is Bayesian in flavour and builds a larger nonparametric hazard process prior around a given parametric hazard model. The hazard estimate in this case is the posterior expectation. Properties of the resulting estimators are discussed.