A semivarying joint model for longitudinal binary and continuous outcomes. Issue 1 (25th November 2015) - Kürüm, Esra; Hughes, John; Li, Runze
Abstract: Semivarying models extend varying coefficient models by allowing some regression coefficients to be constant with respect to the underlying covariate(s). In this paper we develop a semivarying joint modelling framework for estimating the time‐varying association between two intensively measured longitudinal responses: a continuous one and a binary one. To overcome the major challenge of jointly modelling these responses, namely, the lack of a natural multivariate distribution we introduce a Gaussian latent variable underlying the binary response. We then decompose the model into two components: a marginal model for the continuous response and a conditional model for the binary response given the continuous response. We develop a two‐stage estimation procedure and discuss the asymptotic normality of the resulting estimators. We assess the finite‐sample performance of our procedure using a simulation study, and we illustrate our method by analyzing binary and continuous responses from the Women's Interagency HIV Study. The Canadian Journal of Statistics 44: 44–57; 2016 © 2015 Statistical Society of Canada