  An important task in drug development is to identify patients, which respond
better or worse to an experimental treatment. Identifying predictive
covariates, which influence the treatment effect and can be used to define
subgroups of patients, is a key aspect of this task. Analyses of treatment
effect heterogeneity are however known to be challenging, since the number of
possible covariates or subgroups is often large, while samples sizes in earlier
phases of drug development are often small. In addition, distinguishing
predictive covariates from prognostic covariates, which influence the response
independent of the given treatment, can often be difficult. While many
approaches for these types of problems have been proposed, most of them focus
on the two-arm clinical trial setting, where patients are given either the
treatment or a control. In this paper we consider parallel groups dose-finding
trials, in which patients are administered different doses of the same
treatment. To investigate treatment effect heterogeneity in this setting we
propose a Bayesian hierarchical dose-response model with covariate effects on
dose-response parameters. We make use of shrinkage priors to prevent
overfitting, which can easily occur, when the number of considered covariates
is large and sample sizes are small. We compare several such priors in
simulations and also investigate dependent modeling of prognostic and
predictive effects to better distinguish these two types of effects. We
illustrate the use of our proposed approach using a Phase II dose-finding trial
and show how it can be used to identify predictive covariates and subgroups of
patients with increased treatment effects.
