Accounting for established predictors with the multistep elastic net

Multivariable models for prediction or estimating associations with an outcome are rarely built in isolation. Instead, they are based upon a mixture of covariates that have been evaluated in earlier studies (e.g. age, sex, or common biomarkers) and covariates that were collected specifically for the current study (e.g. a panel of novel biomarkers or other hypothesized risk factors). For that context, we present the multi-step elastic net (MSN), which considers penalized regression with variables that can be qualitatively grouped based upon their degree of prior research support: established predictors vs. unestablished predictors. The MSN chooses between uniform penalization of all predictors (the standard elastic net) and weaker penalization of the established predictors in a cross-validated framework, and includes the option to impose zero penalty on the established predictors. In simulation studies that reflect the motivating context, we show the comparability or superiority of the MSN over the standard elastic net, the Integrative LASSO with Penalty Factors, the sparse group lasso, and the group lasso, and we investigate the importance of not penalizing the established predictors at all. We demonstrate the MSN to update a prediction model for pediatric ECMO patient mortality.