Bayesian analysis of differential effects in multi-group regression methods. (June 2021) - Quintero, Adrian; Verbeke, Geert; Bruyneel, Luk; Lesaffre, Emmanuel
In regression analysis, the data sample is often composed of diverse sub-populations such as ethnicities and geographical regions. In multiple application areas, it is important to identify the groups where each covariate has a positive, negative or null impact on the response. If the number of sub-populations is small, a full interaction model may be fit with group-specific covariate effects. However, if the number of groups is very large, for example, hospitals or other clustering units, such a model is not identifiable. Therefore, we propose a prior distribution which combines the information across sub-populations with a similar covariate effect. This Bayesian analysis of differential effects (BADE) classifies the group-specific covariate effects as positive, negative or null. Besides allowing the analysis of differential effects for many sub-populations, the proposed approach improves substantially the identification of important interactions in cases with few groups. This is illustrated via simulations. The procedure is motivated on, and applied to, a large study related to patients' satisfaction with hospitals, where we show that classifying group-specific covariate effects based on methods such as mixed-effects models may be strongly misleading.