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

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