Identification of multivariate responders and non-responders by using Bayesian growth curve latent class models

We propose a multivariate growth curve mixture model that groups subjects on the basis of multiple symptoms measured repeatedly over time. Our model synthesizes features of two models. First, we follow Roy and Lin in relating the multiple symptoms at each time point to a single latent variable. Second, we use the growth mixture model of Muthen and Shedden to group subjects on the basis of distinctive longitudinal profiles of this latent variable. The mean growth curve for the latent variable in each class defines that class's features. For example, a class of 'responders' would have a decline in the latent symptom summary variable over time. A Bayesian approach to estimation is employed where the methods of Elliott and co-workers are extended to estimate simultaneously the posterior distributions of the parameters from the latent variable and growth curve mixture portions of the model. We apply our model to data from a randomized clinical trial evaluating the efficacy of bacillus Calmette-Guerin in treating symptoms of interstitial cystitis. In contrast with conventional approaches using a single subjective global response assessment, we use the multivariate symptom data to identify a class of subjects where treatment demonstrates effectiveness. Simulations are used to confirm identifiability results and to evaluate the performance of our algorithm.