Crossed random effect models for multiple outcomes in a study of teratogenesis

Human teratogens often manifest themselves through a broad spectrum of adverse effects. Although often not serious when considered individually, such outcomes taken together may represent a syndrome that can lead to serious developmental problems. Accordingly, studies that investigate the effect of human teratogens on fetal development typically record the presence or absence of a multitude of abnormalities, resulting in the data of multivariate binary form for each infant. Such studies typically have three objectives: (1) estimate an overall effect of exposure across outcomes, (2) identify subjects having the syndrome, and (3) identify those outcomes that constitute the syndrome so that doctors know what to look for when diagnosing the syndrome in other exposed newborns. This article proposes the use of a logistic regression model with crossed random effect structure to address all three questions simultaneously. We use the proposed models to analyze data from a study investigating the effects of in utero antiepileptic drug exposure on fetal development.