  Understanding how and why certain communities bear a disproportionate burden
of disease is challenging due to the scarcity of data on these communities.
Surveys provide a useful avenue for accessing hard-to-reach populations, as
many surveys specifically oversample understudied and vulnerable populations.
When survey data is used for analysis, it is important to account for the
complex survey design that gave rise to the data, in order to avoid biased
conclusions. The field of Bayesian survey statistics aims to account for such
survey design while leveraging the advantages of Bayesian models, which can
flexibly handle sparsity through borrowing of information and provide a
coherent inferential framework to easily obtain variances for complex models
and data types. For these reasons, Bayesian survey methods seem uniquely
well-poised for health disparities research, where heterogeneity and sparsity
are frequent considerations. This review discusses three main approaches found
in the Bayesian survey methodology literature: 1) multilevel regression and
post-stratification, 2) weighted pseudolikelihood-based methods, and 3)
synthetic population generation. We discuss advantages and disadvantages of
each approach, examine recent applications and extensions, and consider how
these approaches may be leveraged to improve research in population health
equity.
