Identification of biomarker‐by‐treatment interactions in randomized clinical trials with survival outcomes and high‐dimensional spaces

Stratified medicine seeks to identify biomarkers or parsimonious gene signatures distinguishing patients that will benefit most from a targeted treatment. We evaluated 12 approaches in high-dimensional Cox models in randomized clinical trials: penalization of the biomarker main effects and biomarker-by-treatment interactions (full-lasso, three kinds of adaptive lasso, ridge+lasso and group-lasso); dimensionality reduction of the main effect matrix via linear combinations (PCA+lasso (where PCA is principal components analysis) or PLS+lasso (where PLS is partial least squares)); penalization of modified covariates or of the arm-specific biomarker effects (two-I model); gradient boosting; and univariate approach with control of multiple testing. We compared these methods via simulations, evaluating their selection abilities in null and alternative scenarios. We varied the number of biomarkers, of nonnull main effects and true biomarker-by-treatment interactions. We also proposed a novel measure evaluating the interaction strength of the developed gene signatures. In the null scenarios, the group-lasso, two-I model, and gradient boosting performed poorly in the presence of nonnull main effects, and performed well in alternative scenarios with also high interaction strength. The adaptive lasso with grouped weights was too conservative. The modified covariates, PCA+lasso, PLS+lasso, and ridge+lasso performed moderately. The full-lasso and adaptive lassos performed well, with the exception of the full-lasso in the presence of only nonnull main effects. The univariate approach performed poorly in alternative scenarios. We also illustrate the methods using gene expression data from 614 breast cancer patients treated with adjuvant chemotherapy.