Random coefficient models for binary longitudinal responses with attrition

We extend the approach introduced by Aitkin and Alfo (1998, Statistics and Computing, 4, pp. 289-307) to the general framework of random coefficient models and propose a class of conditional models to deal with binary longitudinal responses, including unknown sources of heterogeneity in the regression parameters as well as serial dependence of Markovian form. Furthermore, we discuss the extension of the proposed approach to the analysis of informative drop-outs, which represent a central problem in longitudinal studies, and define, as suggested by Follmann and Wu (1995, Biometrics, 51, pp. 151-168), a conditional specification of the full shared parameter model for the primary response and the missingness indicator. The model is applied to a dataset from a methadone maintenance treatment programme held in Sydney in 1986 and previously analysed by Chan et al. (1998, Australian & New Zealand Journal of Statistics, 40, pp. 1-10). All of the proposed models are estimated by means of an EM algorithm for nonparametric maximum likelihood, without assuming any specific parametric distribution for the random coefficients and for the drop-out process. A small scale simulation work is described to explore the behaviour of the extended approach in a number of different situations where informative drop-outs are present.