  The analysis of large scale medical claims data has the potential to improve
quality of care by generating insights which can be used to create tailored
medical programs. In particular, the multivariate probit model can be used to
investigate the correlation between multiple binary responses of interest in
such data, e.g. the presence of multiple chronic conditions. Bayesian modeling
is well suited to such analyses because of the automatic uncertainty
quantification provided by the posterior distribution. A complicating factor is
that large medical claims datasets often do not fit in memory, which renders
the estimation of the posterior using traditional Markov Chain Monte Carlo
(MCMC) methods computationally infeasible. To address this challenge, we extend
existing divide-and-conquer MCMC algorithms to the multivariate probit model,
demonstrating, via simulation, that they should be preferred over mean-field
variational inference when the estimation of the latent correlation structure
between binary responses is of primary interest. We apply this algorithm to a
large database of de-identified Medicare Advantage claims from a single large
US health insurance provider, where we find medically meaningful groupings of
common chronic conditions and asses the impact of the urban-rural health gap by
identifying underutilized provider specialties in rural areas.
