Combining techniques for screening and evaluating interaction terms on high-dimensional time-to-event data

Molecular data, e.g. arising from microarray technology, is often used for predicting survival probabilities of patients. For multivariate risk prediction models on such high-dimensional data, there are established techniques that combine parameter estimation and variable selection. One big challenge is to incorporate interactions into such prediction models. In this feasibility study, we present building blocks for evaluating and incorporating interactions terms in high-dimensional time-to-event settings, especially for settings in which it is computationally too expensive to check all possible interactions.

We use a boosting technique for estimation of effects and the following building blocks for pre-selecting interactions: (1) resampling, (2) random forests and (3) orthogonalization as a data pre-processing step. In a simulation study, the strategy that uses all building blocks is able to detect true main effects and interactions with high sensitivity in different kinds of scenarios. The main challenge are interactions composed of variables that do not represent main effects, but our findings are also promising in this regard. Results on real world data illustrate that effect sizes of interactions frequently may not be large enough to improve prediction performance, even though the interactions are potentially of biological relevance.

Screening interactions through random forests is feasible and useful, when one is interested in finding relevant two-way interactions. The other building blocks also contribute considerably to an enhanced pre-selection of interactions. We determined the limits of interaction detection in terms of necessary effect sizes. Our study emphasizes the importance of making full use of existing methods in addition to establishing new ones.