Bayesian multilevel multivariate logistic regression for superiority decision-making under observable treatment heterogeneity

TL;DR

This paper introduces a Bayesian multilevel multivariate logistic regression model designed to accurately analyze complex datasets with hierarchical structures and multiple correlated outcomes, improving inference and decision-making in heterogeneous populations.

Contribution

The paper presents a novel Bayesian multilevel multivariate logistic regression approach that accounts for hierarchical data and heterogeneity, providing more accurate and insightful analysis than existing methods.

Findings

Multilevel modeling controls Type I error rates effectively.

The proposed model outperforms single-level models in power with more clusters.

Model facilitates interpretation through posterior success probabilities.

Abstract

In medical, social, and behavioral research we often encounter datasets with a multilevel structure and multiple correlated dependent variables. These data are frequently collected from a study population that distinguishes several subpopulations with different (i.e., heterogeneous) effects of an intervention. Despite the frequent occurrence of such data, methods to analyze them are less common and researchers often resort to either ignoring the multilevel and/or heterogeneous structure, analyzing only a single dependent variable, or a combination of these. These analysis strategies are suboptimal: Ignoring multilevel structures inflates Type I error rates, while neglecting the multivariate or heterogeneous structure masks detailed insights. To analyze such data comprehensively, the current paper presents a novel Bayesian multilevel multivariate logistic regression model. The clustered structure of multilevel data is taken into account, such that posterior inferences can be made with accurate error rates. Further, the model shares information between different subpopulations in the estimation of average and conditional average multivariate treatment effects. To facilitate interpretation, multivariate logistic regression parameters are transformed to posterior success probabilities and differences between them. A numerical evaluation compared our framework to less comprehensive alternatives and highlighted the need to model the multilevel structure: Treatment comparisons based on the multilevel model had targeted Type I error rates, while single-level alternatives resulted in inflated Type I errors. Further, the multilevel model was more powerful than a single-level model when the number of clusters was higher. ...