  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.
