  The idea of "stratified medicine" is an important driver of methodological
research on the identification of predictive biomarkers. Most methods proposed
so far for this purpose have been developed for the use on randomized data
only. However, especially for rare cancers, data from clinical registries or
observational studies might be the only available data source. For such data,
methods for an unbiased estimation of the average treatment effect are well
established. Research on confounder adjustment when investigating the
heterogeneity of treatment effects and the variables responsible for this is
usually restricted to regression modelling. In this paper, we demonstrate how
the predMOB, a tree-based method that specifically searches for predictive
factors, can be combined with common strategies for confounder adjustment
(covariate adjustment, matching, Inverse Probability of Treatment Weighting
(IPTW)). In an extensive simulation study, we show that covariate adjustment
allows the correct identification of predictive factors in the presence of
confounding whereas IPTW fails in situations in which the true predictive
factor is not completely independent of the confounding mechanism. A
combination of both, covariate adjustment and IPTW performs as well as
covariate adjustment alone, but might be more robust in complex settings. An
application to the German Breast Cancer Study Group (GBSG) Trial 2 illustrates
these conclusions.
