{'fraction_non_alphanumeric': 0.02265705458290422, 'fraction_numerical': 0.0, 'mean_word_length': 5.412541254125412, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Rank-based p-values for sparse high-dimensional risk prediction models fitted by componentwise boosting

There are many techniques for fitting sparse risk prediction models to highdimensional data, e.g., allowing to predict a clinical endpoint by automatically determining a small set of informative covariates from gene expression measurements. Techniques for regularized estimation, such as componentwise boosting, provide sparse estimates for linear predictors. Many estimated parameters will be equal to zero, resulting in good prediction performance and a short list of informative genes. However, typically no p-values for single genes will be available, which is a downside compared to univariate test-based approaches. We address this by presenting an approach for obtaining p-values for componentwise likelihood-based boosting. The latter technique performs a large number of model fitting steps, where in each step one covariate is selected based on a score statistic. For quantifying uncertainty, we propose to consider the ranking based on the score statistic for all covariates in each step. Comparing the median rank of a covariate across boosting steps to a null distribution, obtained from data with permuted response, provides a p-value that takes the multivariable structure into account. In a simulation study, these rank-based p-values for multivariable models are seen to provide competitive performance concerning identification of informative covariates. In contrast to univariate p-values, the actual Type I error rates are close to the nominal level in most settings. In an application to time-to-event data with gene expression measurements from patients with diffuse large-B-cell lymphoma, the proposed p-values are seen to provide valuable complementary information to the fitted model. This combines the advantages of multivariable risk prediction techniques and univariate approaches for quantifying uncertainty.