  Deep Learning (DL) methods have dramatically increased in popularity in
recent years, with significant growth in their application to supervised
learning problems in the biomedical sciences. However, the greater prevalence
and complexity of missing data in modern biomedical datasets present
significant challenges for DL methods. Here, we provide a formal treatment of
missing data in the context of deeply learned generalized linear models, a
supervised DL architecture for regression and classification problems. We
propose a new architecture, \textit{dlglm}, that is one of the first to be able
to flexibly account for both ignorable and non-ignorable patterns of
missingness in input features and response at training time. We demonstrate
through statistical simulation that our method outperforms existing approaches
for supervised learning tasks in the presence of missing not at random (MNAR)
missingness. We conclude with a case study of a Bank Marketing dataset from the
UCI Machine Learning Repository, in which we predict whether clients subscribed
to a product based on phone survey data. Supplementary materials for this
article are available online.
