  Randomized controlled trials (RCTs) are the accepted standard for treatment
effect estimation but they can be infeasible due to ethical reasons and
prohibitive costs. Single-arm trials, where all patients belong to the
treatment group, can be a viable alternative but require access to an external
control group. We propose an identifiable deep latent-variable model for this
scenario that can also account for missing covariate observations by modeling
their structured missingness patterns. Our method uses amortized variational
inference to learn both group-specific and identifiable shared latent
representations, which can subsequently be used for {\em (i)} patient matching
if treatment outcomes are not available for the treatment group, or for {\em
(ii)} direct treatment effect estimation assuming outcomes are available for
both groups. We evaluate the model on a public benchmark as well as on a data
set consisting of a published RCT study and real-world electronic health
records. Compared to previous methods, our results show improved performance
both for direct treatment effect estimation as well as for effect estimation
via patient matching.
