  Subgroup analysis is a frequently used tool for evaluating heterogeneity of
treatment effect and heterogeneity in treatment harm across observed baseline
patient characteristics. While treatment efficacy and adverse event measures
are often reported separately for each subgroup, analyzing their
within-subgroup joint distribution is critical for better informed patient
decision-making. In this paper, we describe Bayesian models for performing a
subgroup analysis to compare the joint occurrence of a primary endpoint and an
adverse event between two treatment arms. Our approaches emphasize estimation
of heterogeneity in this joint distribution across subgroups, and our
approaches directly accommodate subgroups with small numbers of observed
primary and adverse event combinations. In addition, we describe several ways
in which our models may be used to generate interpretable summary measures of
benefit-risk tradeoffs for each subgroup. The methods described here are
illustrated throughout using a large cardiovascular trial (N = 9,361)
investigating the efficacy of an intervention for reducing systolic blood
pressure to a lower-than-usual target.
