Latent trajectory modelling of multivariate binary data

Latent trajectory analysis is a form of latent class analysis, where the manifest variables are longitudinal measurements of a single outcome. The latent classes may correspond to either constant increasing or decreasing levels of the outcome over time and describe different severity or course of a disease. Extension to multiple outcomes at each time point allows more accurate determination of classes, with classes based on combination of the outcomes, however requiring models which account for both correlation between outcomes and periods. Three models are described for multiple binary outcomes, observed at each time point: a latent class model where all outcomes are considered independent at all time points, a model incorporating random effects for subject only and one incorporating random effects for subject and period. The methods are applied to data on asthma and allergy symptoms in infants, with symptoms recorded at four time points, and it is shown that the incorporation of subject and period heterogeneity results in lower estimates of the number of latent classes.