Logistic Regression with Missing Covariates -- Parameter Estimation, Model Selection and Prediction within a Joint-Modeling Framework

TL;DR

This paper introduces a comprehensive method for logistic regression with missing covariates using a stochastic EM algorithm, improving parameter estimation, model selection, and prediction accuracy over existing approaches.

Contribution

It develops a complete, efficient framework for logistic regression with missing data, including variance estimation, confidence intervals, and a novel prediction method, implemented in R.

Findings

The proposed method outperforms multiple imputation in bias reduction.

Simulation studies demonstrate good coverage and variable selection properties.

Application to trauma data effectively predicts hemorrhagic shock risk.

Abstract

Logistic regression is a common classification method in supervised learning. Surprisingly, there are very few solutions for performing logistic regression with missing values in the covariates. We suggest a complete approach based on a stochastic approximation version of the EM algorithm to do statistical inference with missing values including the estimation of the parameters and their variance, derivation of confidence intervals and a model selection procedure. We also tackle the problem of prediction for new observations (on a test set) with missing covariate data. The methodology is computationally efficient, and its good coverage and variable selection properties are demonstrated in a simulation study where we contrast its performances to other methods. For instance, the popular approach of multiple imputation by chained equations can lead to estimates that exhibit meaningfully greater biases than the proposed approach. We then illustrate the method on a dataset of severely traumatized patients from Paris hospitals to predict the occurrence of hemorrhagic shock, a leading cause of early preventable death in severe trauma cases. The aim is to consolidate the current red flag procedure, a binary alert identifying patients with a high risk of severe hemorrhage. The methodology is implemented in the R package misaem.