Adaptive predictor-set linear model: an imputation-free method for linear regression prediction on datasets with missing values

Abstract

Linear regression (LR) is vastly used in data analysis for continuous outcomes in biomedicine and epidemiology. Despite its popularity, LR is incompatible with missing data, which frequently occur in health sciences. For parameter estimation, this short-coming is usually resolved by complete-case analysis or imputation. Both workarounds, however, are inadequate for prediction, since they either fail to predict on incomplete records or ignore missingness-induced reduction in prediction accuracy and rely on (unrealistic) assumptions about the missing mechanism. Here, we derive adaptive predictor-set linear model (aps-lm), capable of making predictions for incomplete data without the need for imputation. It is derived by using a predictor-selection operation, the Moore-Penrose pseudoinverse and the reduced QR-decomposition. aps-lm is an LR generalization that inherently handles missing values. It is applied on a reference dataset, where complete predictors and outcome are available, and yields a set of privacy-preserving parameters. In a second stage, these are shared for making predictions of the outcome on external datasets with missing entries for predictors without imputation. Moreover, aps-lm computes prediction errors that account for the pattern of missing values even under extreme missingness. We benchmark aps-lm in a simulation study. aps-lm showed greater prediction accuracy and reduced bias compared to popular imputation strategies under a wide range of scenarios including variation of sample size, goodness-of-fit, missing value type and covariance structure. Finally, as a proof-of-principle, we apply aps-lm in the context of epigenetic aging clocks, linear models that predict a persons biological age from epigenetic data with promising clinical applications.