In studies where gold-standard data are infeasible to obtain, scientists need to integrate multiple data of distinct quality to draw inference about the population. For example, direct sampling of the infected lungs among pneumonia children may have serious clinical complications. Epidemiologists test for the presence or absence of >30 pathogens in multiple peripheral body fluids to estimate the population fractions of pneumonia-causing pathogens, or "etiologic fractions". The talk will introduce a novel family of Bayesian latent class models to analyze such case-control data for estimating etiologic fractions. Each class represents a cause of unobserved lung infection and a subset of subjects have observed classes (“controls”). The method infers the population fraction of pneumonia cases caused by pathogen(s) (alone or in combination) while accounting for complex measurement dependence, covariates and missingness patterns. The talk will also demonstrate the models and software (https://github.com/zhenkewu/baker) through an analysis of ~5K cases and ~5K controls with the population health goal of estimating the etiologic fractions of childhood pneumonia in 7 developing countries.