Latent class models for longitudinal studies of the elderly with data missing at random

The elderly population in the USA is expected to double in size by the year 2025, making longitudinal health studies of this population of increasing importance. The degree of loss to follow-up in studies of the elderly, which is often because elderly people cannot remain in the study, enter a nursing home or die, make longitudinal studies of this population problematic. We propose a latent class model for analysing multiple longitudinal binary health outcomes with multiple-cause non-response when the data are missing at random and a non-likelihood-based analysis is performed. We extend the estimating equations approach of Robins and co-workers to latent class models by reweighting the multiple binary longitudinal outcomes by the inverse probability of being observed. This results in consistent parameter estimates when the probability of non-response depends on observed outcomes and covariates (missing at random) assuming that the model for non-response is correctly specified. We extend the non-response model so that institutionalization, death and missingness due to failure to locate, refusal or incomplete data each have their own set of non-response probabilities. Robust variance estimates are derived which account for the use of a possibly misspecified covariance matrix, estimation of missing data weights and estimation of latent class measurement parameters. This approach is then applied to a study of lower body function among a subsample of the elderly participating in the 6-year Longitudinal Study of Aging.     

Latent class logistic regression: application to marijuana use and attitudes among high school seniors

Summary.  Analysing the use of marijuana is challenging in part because there is no widely accepted single measure of individual use. Similarly, there is no single response variable that effectively captures attitudes toward its social and moral acceptability. One approach is to view the joint distribution of multiple use and attitude indicators as a mixture of latent classes. Pooling items from the annual 'Monitoring the future' surveys of American high school seniors from 1977 to 2001, we find that marijuana use and attitudes are well summarized by a four-class model. Secular trends in class prevalences over this period reveal major shifts in use and attitudes. Applying a multinomial logistic model to the latent response, we investigate how class membership relates to demographic and life style factors, political beliefs and religiosity over time. Inferences about the parameters of the latent class logistic model are obtained by a combination of maximum likelihood and Bayesian techniques.