Can the Unit Size Predict Outcomes? Testing for Informativeness in Three-Level Designs

Multilevel data are frequently encountered in biomedical research, and several statistical methods have been developed to analyze such data. Informativeness of the number of units on certain levels often manifests itself in multilevel data analysis and failure to account for this phenomenon will lead to biased inference. Moreover, utilizing an incorrect marginalization approach will also lead to invalid conclusions. To identify the appropriate marginal distribution to be tested in multilevel designs, we propose a sequential testing procedure to test for informativeness of unit sizes in multilevel structures with three levels. At a given level of the design, a bootstrap method is developed to estimate the null distribution of no informativeness of unit size. Simulation studies confirm the efficacy of our sequential procedure in maintaining an overall Type I error rate. Additionally, we extend our testing procedure to a multilevel regression setting, enhancing its practical applicability. We demonstrate the utility of our proposed methods through the analysis of data from a study on periodontal disease and a study on stress levels of preschoolers.