  In randomized controlled trials, forest plots are frequently used to
investigate the homogeneity of treatment effect estimates in subgroups.
However, the interpretation of subgroup-specific treatment effect estimates
requires great care due to the smaller sample size of subgroups and the large
number of investigated subgroups. Bayesian shrinkage methods have been proposed
to address these issues, but they often focus on disjoint subgroups while
subgroups displayed in forest plots are overlapping, i.e., each subject appears
in multiple subgroups. In our approach, we first build a flexible Cox model
based on all available observations, including categorical covariates that
identify the subgroups of interest and their interactions with the treatment
group variable. We explore both penalized partial likelihood estimation with a
lasso or ridge penalty for treatment-by-covariate interaction terms, and
Bayesian estimation with a regularized horseshoe prior. One advantage of the
Bayesian approach is the ability to derive credible intervals for shrunken
subgroup-specific estimates. In a second step, the Cox model is marginalized to
obtain treatment effect estimates for all subgroups. We illustrate these
methods using data from a randomized clinical trial in follicular lymphoma and
evaluate their properties in a simulation study. In all simulation scenarios,
the overall mean-squared error is substantially smaller for penalized and
shrinkage estimators compared to the standard subgroup-specific treatment
effect estimator but leads to some bias for heterogeneous subgroups. We
recommend that subgroup-specific estimators, which are typically displayed in
forest plots, are more routinely complemented by treatment effect estimators
based on shrinkage methods. The proposed methods are implemented in the R
package bonsaiforest.
