Partially-Latent Class Models (pLCM) for Case-Control Studies of   Childhood Pneumonia Etiology
  In population studies on the etiology of disease, one goal is the estimation of the fraction of cases attributable to each of several causes. For example, pneumonia is a clinical diagnosis of lung infection that may be caused by viral, bacterial, fungal, or other pathogens. The study of pneumonia etiology is challenging because directly sampling from the lung to identify the etiologic pathogen is not standard clinical practice in most settings. Instead, measurements from multiple peripheral specimens are made. This paper introduces the statistical methodology designed for estimating the population etiology distribution and the individual etiology probabilities in the Pneumonia Etiology Research for Child Health (PERCH) study of 9; 500 children for 7 sites around the world. We formulate the scientific problem in statistical terms as estimating the mixing weights and latent class indicators under a partially-latent class model (pLCM) that combines heterogeneous measurements with different error rates obtained from a case-control study. We introduce the pLCM as an extension of the latent class model. We also introduce graphical displays of the population data and inferred latent-class frequencies. The methods are tested with simulated data, and then applied to PERCH data. The paper closes with a brief description of extensions of the pLCM to the regression setting and to the case where conditional independence among the measures is relaxed. 
Zhenke Wu, Maria Deloria-Knoll, Laura L. Hammitt, Scott L. Zeger
stat.AP