Mixture analysis of longitudinal binary data

The dependence of longitudinal binary outcomes on covariates and the covariation observed between them is often modelled by (multivariate) logistic and probit models, respectively, assuming specified association structure or random effects. Alternatively, latent class models may be used that capture the covariation by assuming heterogeneity of the observational units regarding their reaction tendencies while postulating independence within classes. In the presence of a few categorical covariates, the multi-group method of latent class analysis allows one to relate the class sizes and the class-specific response probabilities to these covariates. Wheeze data from the Harvard Six-Cities study on respiratory health are a typical example for such a situation: at four occasions, the wheeze status of 537 children was examined, 187 among them exposed to maternal smoking and 350 not exposed. Thus, there is a single binary covariate (maternal smoking versus no maternal smoking) making easily applicable the multi-group method of latent class analysis. Based on a series of unrestricted and restricted models having up to three classes for the exposed and not-exposed subgroup each, no statistically significant effect of maternal smoking on children's wheeze status could be substantiated. Moreover, it was not possible to show statistically significant difference at all between the two distributions of wheeze patterns collected from exposed and not-exposed children.