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# Quantifying Common Support between Multiple Treatment Groups Using a Contrastive-VAE

*Proceedings of the Machine Learning for Health NeurIPS Workshop*, PMLR 136:41-52, 2020.

#### Abstract

Estimating the effect of a given medical treatment on individual patients involves evaluating how clinical outcomes are affected by the treatment in question. Robust estimates of the treatment effect for a given patient with a prespecified set of clinical characteristics, are possible to obtain when there is sufficient common support for these features. Essentially, features having the greatest common support correspond to regions of significant overlap between the distributions of the different treatment groups. In observational datasets, however, all possible treatment options may not be uniformly represented, and therefore robust estimation of their effect may only be possible for the patients in the overlapping region. In this work, we propose a Contrastive Variational Autoencoder (ContrastiveVAE) to estimate where there is significant overlap between patient distributions corresponding to different treatment options. A Contrastive-VAE exploits shared information between different groups by modeling the shared information as arising from a shared set of latent variables to approximate distributions for treatment options that are not well represented in observational datasets. The result is an improved estimation of the distribution of the groups with a small number of data points. By estimating the likelihood for each group with annealed importance sampling, we are able to quantitatively identify the area of overlap between multiple treatment groups and obtain an effective confidence interval for the estimated individual treatment effect.