Case‐only trees and random forests for exploring genotype‐specific treatment effects in randomized clinical trials with dichotomous end points

Discovering gene–treatment interactions in clinical trials is of rising interest in the era of precision medicine. Non‐parametric statistical learning methods such as trees and random forests are useful tools for building prediction rules. We introduce trees and random forests to the recently proposed case‐only approach for discovering gene–treatment interactions and estimating marker‐specific treatment effects for a dichotomous trial's end points. The motivational example is a case–control genetic association study in the prostate cancer prevention trial, which tested the hypothesis whether finasteride can prevent prostate cancer. We compare this novel approach with the interaction tree method previously proposed. Because of the modelling simplicity—directly targeting at interaction—and the statistical efficiency of the case‐only approach, case‐only trees and random forests yield more accurate prediction of heterogeneous treatment effects and a better measure of variable importance, relative to the interaction tree method which uses data from both cases and controls. Application of the proposed case‐only trees and random forests to the prostate cancer prevention trial study yielded a discovery of genotypes that may influence the prevention effect of finasteride.