  In recent years, the development of technologies for causal inference with
privacy preservation of distributed data has gained considerable attention.
Many existing methods for distributed data focus on resolving the lack of
subjects (samples) and can only reduce random errors in estimating treatment
effects. In this study, we propose a data collaboration quasi-experiment
(DC-QE) that resolves the lack of both subjects and covariates, reducing random
errors and biases in the estimation. Our method involves constructing
dimensionality-reduced intermediate representations from private data from
local parties, sharing intermediate representations instead of private data for
privacy preservation, estimating propensity scores from the shared intermediate
representations, and finally, estimating the treatment effects from propensity
scores. Through numerical experiments on both artificial and real-world data,
we confirm that our method leads to better estimation results than individual
analyses. While dimensionality reduction loses some information in the private
data and causes performance degradation, we observe that sharing intermediate
representations with many parties to resolve the lack of subjects and
covariates sufficiently improves performance to overcome the degradation caused
by dimensionality reduction. Although external validity is not necessarily
guaranteed, our results suggest that DC-QE is a promising method. With the
widespread use of our method, intermediate representations can be published as
open data to help researchers find causalities and accumulate a knowledge base.
