A note on misspecification in joint modeling of correlated data with informative cluster sizes

Abstract

Clustered data are commonly generated in biomedical, economic, and social science studies. When cluster sizes are correlated with primary outcomes, data are identified as correlated data with “informative cluster sizes”. For such data, standard data analysis methods do not apply because of induced biases. Joint modeling approach has been proposed as one of the strategies to analyze informative cluster size data. However, cluster size model misspecification may affect the reliability of joint modeling approach in statistical inference. This article focuses on the joint modeling approach that combines generalized linear mixed models and cluster size models. It reveals the prodigious impact of cluster size model misspecification on the statistical inferences in joint models and offers solutions to this misspecification problem. A modified information matrix test and a sandwich estimator test are adopted, and their effectiveness as diagnostic tools in detecting cluster size model misspecification is demonstrated. Numerical studies show that the two diagnostic tests are highly favorable, but they might inflate Type I errors when the sample size is small. We also recommend an alternative approach to draw inferences by using frequentist model averaging if there is strong confidence that the suitable model is included in the pool of candidate cluster size models. This article reviews a set of related theorems as well as complements them with comprehensive numerical studies, which together provide a methodological solution to the cluster size model misspecification in joint modeling.