Integrating Complex Selection Rules Into the Latent Overlapping Group Lasso for the Construction of Coherent Prediction Models

Prediction models are important in medical research, as such models enable health researchers to gain deeper insights into disease epidemiology and clinicians to identify patients at higher risk of adverse outcomes. One commonly employed approach to developing prediction models is variable selection through penalized regression. Integrating natural variable structures and predefined inclusion requirements into variable selection not only enhances model interpretability but can also potentially boost prediction accuracy. For example, the latent overlapping group Lasso can force the inclusion of the main terms in the resulting model if their interaction term is selected. However, when variable structures are complex, it is challenging to integrate such structures into the penalized regression. In this work, we first demonstrate how to convert variable structures and predefined variable inclusion requirements into "selection rules" (which represent rules for which or how variables can be included in the final prediction model) and present these rules mathematically. Then, we provide a structured approach for integrating complex rules into variable selection through the latent overlapping group Lasso so that the resulting prediction model follows the given selection rules. To illustrate our methodology, we applied these techniques to construct a coherent prediction model for major bleeding in hypertensive patients recently hospitalized for atrial fibrillation and subsequently prescribed oral anticoagulants. In this application, we account for a proxy of anticoagulant adherence and its interaction with dosage and the type of oral anticoagulants, in addition to drug-drug interactions.