Strategies for analyzing multilevel cluster-randomized studies with binary outcomes collected at varying intervals of time.

Frequently, studies are conducted in a real clinic setting. When the outcome of interest is collected longitudinally over a specified period of time, this design can lead to unequally spaced intervals and varying numbers of assessments. In our study, these features were embedded in a randomized, factorial design in which interventions to improve blood pressure control were delivered to both patients and providers. We examine the effect of the intervention and compare methods of estimation of both fixed effects and variance components in the multilevel generalized linear mixed model. Methods of comparison include penalized quasi-likelihood (PQL), adaptive quadrature, and Bayesian Monte Carlo methods. We also investigate the implications of reducing the data and analysis to baseline and final measurements. In the full analysis, the PQL fixed-effects estimates were closest to zero and confidence intervals were generally narrower than those of the other methods. The adaptive quadrature and Bayesian fixed-effects estimates were similar, but the Bayesian credible intervals were consistently wider. Variance component estimation was markedly different across methods, particularly for the patient-level random effects. In the baseline and final measurement analysis, we found that estimates and corresponding confidence intervals for the adaptive quadrature and Bayesian methods were very similar. However, the time effect was diminished and other factors also failed to reach statistical significance, most likely due to decreased power. When analyzing data from this type of design, we recommend using either adaptive quadrature or Bayesian methods to fit a multilevel generalized linear mixed model including all available measurements.