  Missing data is a common problem in real-world settings and particularly
relevant in healthcare applications where researchers use Electronic Health
Records (EHR) and results of observational studies to apply analytics methods.
This issue becomes even more prominent for longitudinal data sets, where
multiple instances of the same individual correspond to different observations
in time. Standard imputation methods do not take into account patient specific
information incorporated in multivariate panel data. We introduce the novel
imputation algorithm MedImpute that addresses this problem, extending the
flexible framework of OptImpute suggested by Bertsimas et al. (2018). Our
algorithm provides imputations for data sets with missing continuous and
categorical features, and we present the formulation and implement scalable
first-order methods for a $K$-NN model. We test the performance of our
algorithm on longitudinal data from the Framingham Heart Study when data are
missing completely at random (MCAR). We demonstrate that MedImpute leads to
significant improvements in both imputation accuracy and downstream model AUC
compared to state-of-the-art methods.
