Abstract Genetic profiles of cancer patients are expected to vary with tumour progression. Therefore, it may be desirable to incorporate interactions between tumour stage and high-dimensional omics variables in prognostic models. These interactions may be confounded with other clinical risk factors. We present a novel interaction model for colorectal cancer prognosis based on 20,000+ omics variables, the tumour stage, and a small set of clinical risk factors. The model consists of a regression tree, fitted with only tumour stage and clinical risk factors, and omics-based regressions in the leaf nodes. To stabilize estimation of the node-specific omics effects, we develop a fusion-type penalized likelihood estimator, for which we derive shrinkage limits and computationally efficient tuning of hyperparameters. We show the benefit of the fused estimator in simulations. The colorectal cancer application reveals that FusedTree obtains good model fit compared to competitors and hence benefits from the incorporation of interaction effects. Furthermore, we develop a post hoc test suggesting that the overall omics effect does not further improve prognosis for subgroups of colorectal cancer patients.
Goedhart et al. (Fri,) studied this question.