  Determining causes of deaths (COD) occurred outside of civil registration and
vital statistics systems is challenging. A technique called verbal autopsy (VA)
is widely adopted to gather information on deaths in practice. A VA consists of
interviewing relatives of a deceased person about symptoms of the deceased in
the period leading to the death, often resulting in multivariate binary
responses. While statistical methods have been devised for estimating the
cause-specific mortality fractions (CSMFs) for a study population, continued
expansion of VA to new populations (or "domains") necessitates approaches that
recognize between-domain differences while capitalizing on potential
similarities. In this paper, we propose such a domain-adaptive method that
integrates external between-domain similarity information encoded by a
pre-specified rooted weighted tree. Given a cause, we use latent class models
to characterize the conditional distributions of the responses that may vary by
domain. We specify a logistic stick-breaking Gaussian diffusion process prior
along the tree for class mixing weights with node-specific spike-and-slab
priors to pool information between the domains in a data-driven way. Posterior
inference is conducted via a scalable variational Bayes algorithm. Simulation
studies show that the domain adaptation enabled by the proposed method improves
CSMF estimation and individual COD assignment. We also illustrate and evaluate
the method using a validation data set. The paper concludes with a discussion
on limitations and future directions.
