Discrete Duration Models combining Dynamic and Random Effects. (REVISED, February 2000)

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 the two mentioned variations
simultaneously. The approach is a combination of the dynamic
generalized linear model with dynamic time-varying baseline and
covariate effects and the generalized linear mixed 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 done by an EM-type algorithm. Finally, the
proposed method is applied to data of the Veteran's Administration
Lung Cancer Trial.