Comparison of methods for analyzing longitudinal binary outcomes: cognitive status as an example

Longitudinal data generate correlated observations. Ignoring correlation can lead to incorrect estimation of standard errors, resulting in incorrect inferences of parameters. In the example used here, standard logistic regression, a population-averaged (PA) model fit using generalized estimating equations (GEE), and random-intercept models are used to model binary outcomes at baseline, three and six years later. The outcomes indicate cognitive impairment versus no cognitive impairment in a sample of community dwelling elders. The models include both time-invariant (age, gender) and time-varying (time, interactions with time) covariates. The absolute estimates from random-intercept models are larger than those of both standard logistic and GEE models. Compared to the model fit using GEE that accounts for time dependency, standard logistic regression models overestimate standard errors of time-varying covariates (such as time, and time by problems with activities of daily living), and underestimate the standard errors of time-invariant covariates (such as age and gender). The standard errors from the random-intercept model are larger than those from logistic regression and GEE models. The choice of models, GEE or random-intercept, depends on the research question and the nature of the covariates. Population-averaged methods are appropriate when between-subjects effects are of interest, and random-effects are useful when subject-specific effects are important.