Modelling correlated binary variables: an application to lower urinary tract symptoms

We present a semiparametric model for time evolving vectors of correlated binary variables. We introduce continuous latent variables which are discretized to obtain the sampling model. We assume that the distribution of the latent variables is an infinite mixture of distributions with weights that vary across some covariate space and with mean and covariance matrix being component specific. This distribution includes also an auto‐regressive term that captures the time evolution of the latent variables and therefore of the binary observations. The method proposed is motivated by the study of lower urinary tract symptoms observed at subsequent attendance visits. In particular, we evaluate the temporal dependence among the symptoms controlling for the presence of urinary tract infection. The results show that the most recurrent symptoms are stress incontinence and voiding, which are also the most related with presence of pyuria, the best biomarker of infections. Furthermore, we observe that the correlation between symptoms changes over time. The pair of symptoms which appear to be the most correlated are pain and voiding.