Smoothing Hazard Functions and Time-Varying Effects in Discrete Duration and Competing Risks Models

State space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modelling and smooth estimation of hazard functions and time-varying effects in a flexible way. Full Bayesian or posterior mean estimation, using numerical integration techniques or Monte Carlo methods, can become computationally rather demanding or even infeasible for higher dimensions and larger data sets. Therefore, based on previous work on filtering and smoothing for multicategorical time series and longitudinal data, our approach uses posterior mode estimation. Thus we have to maximize posterior densities or, equivalently, a penalized likelihood, which enforces smoothness of hazard functions and time-varying effects by a roughness penalty. Dropping the Bayesian smoothness prior and adopting a nonparametric viewpoint, one might also start directly from maximizing this penalized likelihood. We show how Fisher scoring smoothing iterations can be carried out efficiently by iteratively applying linear Kalman filtering and smoothing to a working model. This algorithm can be combined with an EM-type procedure to estimate unknown smoothing- or hyperparameters. The methods are applied to a larger set of unemployment duration data with one and, in a further analysis, multiple terminating events from the German socio-economic panel GSOEP

Estimating Time-Varying Effects of Prognostic Factors for Stomach Cancer Patients within a Dynamic Grouped Cox Model

We describe the identification of prognostic factors in the framework of a completely resected stomach cancer survival-study. For the analysis the dynamic grouped Cox-Model was used allowing for time-varying covariate effects. Therefore the hazard rate might be non-proportional. As estimation concept we applied the posterior mode, computed by iteratively weighted Kalman filtering and smoothing steps. The medical study and questions are described, the statistical method is illustrated, the results are given and interpreted and the method is discussed