Biostatistics (2002), 3, 3, pp. 407–420 Printed in Great Britain
A generalized mover–stayer model for panel data RICHARD J. COOK, JOHN D. KALBFLEISCH, GRACE Y. YI Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1
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S UMMARY A generalized mover–stayer model is described for conditionally Markov processes under panel observation. Marginally the model represents a mixture of nested continuous-time Markov processes in which sub-models are defined by constraining some transition intensities to zero between two or more states of a full model. A Fisher scoring algorithm is described which facilitates maximum likelihood estimation based only on the first derivatives of the transition probability matrices. The model is fit to data from a smoking prevention study and is shown to provide a significant improvement in fit over a timehomogeneous Markov model. Extensions are developed which facilitate examination of covariate effects on both the transition intensities and the mover–stayer probabilities. Keywords: Latent variables; Marginal likelihood; Markov model; Multi-state process; Time homogeneous intensity.
1. I NTRODUCTION Multi-state stochastic models provide a useful framework for the analysis of data from longitudinal studies when interest lies in dynamic aspects of the process under investigation. When subjects are observed continuously over a period of observation, transitions between states are observed and parametric, nonparametric, and semiparametric methods may be used (Andersen et al., 1993). In contrast, when the subjects are seen at discrete time points, exact transition times are not observed and all that is known is the state occupied at each as