Methods are introduced and illustrated for synthesizing evidence from case-control and cohort studies, and controlled trials, accounting for differences among the studies in their design, length of follow-up and quality. The methods, based on hierarchical but nonexchangeable Bayesian models, are illustrated in a synthesis of disparate information about the health effects of passive exposure to environmental tobacco smoke.
"Adjusted Likelihoods for Synthesizing Empirical Evidence from Studies that Differ in Quality and Design: Effects of Environmental Tobacco Smoke." Statist. Sci. 19 (3) 450 - 471, August 2004. https://doi.org/10.1214/088342304000000350