The Pneumonia Etiology Research for Child Health (PERCH) study seeks to use
modern measurement technology to infer the causes of pneumonia for which
gold-standard evidence is unavailable. The paper describes a latent variable
model designed to infer from case-control data the etiology distribution for
the population of cases, and for an individual case given his or her
measurements. We assume each observation is drawn from a mixture model for
which each component represents one cause or disease class. The model addresses
a major limitation of the traditional latent class approach by taking account
of residual dependence among multivariate binary outcome given disease class,
hence reduces estimation bias, retains efficiency and offers more valid
inference. Such "local dependence" on a single subject is induced in the model
by nesting latent subclasses within each disease class. Measurement precision
and covariation can be estimated using the control sample for whom the class is
known. In a Bayesian framework, we use stick-breaking priors on the subclass
indicators for model-averaged inference across different numbers of subclasses.
Assessment of model fit and individual diagnosis are done using posterior
samples drawn by Gibbs sampling. We demonstrate the utility of the method on
simulated and on the motivating PERCH data.Comment: 30 pages with 5 figures and 1 table; 1 appendix with 4 figures and 1
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