Parametric models to assess tracking of categorical high-risk sexual behaviour for HIV infection

Prevalence and tracking (within-individual correlation) of high-risk behaviour measured in longitudinal studies provide a complementary description of how behaviour is maintained over time. Without tracking, when population prevalences are approximately constant over time, the steadiness of the aggregate pattern is likely to mask the dynamic changes of the response occurring on an individual level. In this paper, a parametric model is proposed for the estimation of these features when the observed response is a time-stationary categorical measurement. The model extends the standard Dirichlet-multinomial model in the spirit of Prentice (1986, JASA) by allowing both negative and positive correlation among repeated categorical measurements. In addition, both the marginal category probabilities and the tracking can be modelled as a function of individual-level covariates. Details regarding likelihood based estimation and inference are provided and illustrated with data from the Multicenter AIDS Cohort Study (MACS).