Discrete duration models combining dynamic and random effects.

Survival data may include two different sources of variation, namely variation over time and variation over units. If both of these variations are present, neglecting one of them can cause serious bias in the estimations. Here we present an approach for discrete duration data that includes both time-varying and unit-specific effects to model these two variations simultaneously. The approach is a combination of a dynamic survival model with dynamic time-varying baseline and covariate effects and a frailty model measuring unobserved heterogeneity with random effects varying independently over units. Estimation is based on posterior modes, i.e., we maximize the joint posterior distribution of the unknown parameters to avoid numerical integration and simulation techniques, that are necessary in a full Bayesian analysis. Estimation of unknown hyperparameters is achieved by an EM-type algorithm. Finally, the proposed method is applied to data of the Veteran's Administration Lung Cancer Trial.