Meta analysis is the use of statistical techniques to synthesize and describe the results from a (possibly large) number of similar studies attempting to measure the same thing. The most useful approach is to perform a quantitative analysis that can incorporate the results from all the studies, and demonstrate their consistency (or otherwise) with a meta-analytic model of the studies. The simplest such model is that the studies agree about their individual measurements of the same quantity (i.e., they are homogeneous), allowing a better estimate for that quantity by combining the results. More complex models build on this (although usually with less justification the more complex the meta-analytic model). Simple forms of inhomogeneity (e.g. consistency except for unexplained random variation with a pre-specified distributional form) can be readily incorporated; and indeed are needed for testing the simplest model. Our work often involves construction of meta-analytic models of some form or another, particularly since we must often evaluate substantial literature. We have performed and published formal meta-analyses (e.g. on asbestos, on the dose-response for diarrhea caused by Clostridium perfringens), and multiple analyses that are meta-analytic in nature although not formally so labeled (e.g. dose-response assessment for sulfur dioxide, combining results from multiple experiments).
Cancer potency of asbestos
A manufacturing company sponsored our research on the potency of asbestos as a cause of lung cancer. Existing estimates of this parameter had not been updated to account for results from about a decade of epidemiologic research; and prior attempts to combine epidemiologic studies were only semi-quantitative. We assimilated dose-response data from 15 groups of asbestos-exposed workers detailed in 22 publications, using maximum likelihood techniques to obtain measures of the relationship between cumulative exposure to asbestos and relative risk of lung cancer. Our meta-analysis (Lash, Crouch, and Green, Occup. Environ. Med. 54:254-263, 1997) explored sources of heterogeneity in the dose-response coefficient, generating a potency estimate under a fixed-effect model and another under a random effects model. These estimates were 24-fold smaller and fourfold smaller, respectively, than the OSHA (1986) estimate relied upon for rule-making.
Dose response assessment for sulfur dioxide
An industry group requested an evaluation of the EPA's analysis of the potential effects of implementing a new National Ambient Air Quality Standard (NAAQS) for sulfur dioxide. EPA needed to estimate the population dose-response for the effect of sulfur dioxide on exercising asthmatics by combining the observations reported in multiple studies. However, EPA's contractor performed the requested meta-analysis by combining group-level statistics from those studies without examination of the data on individuals. We realized that the method proposed by EPA's contractor failed to account for individuals common to the different dose groups, the variation of individuals' responses from measurement occasion to measurement occasion, and the uncertainties in measurement of the responses involved. We obtained the individual data and performed a meta-analysis that took account of these variabilities and uncertainties on an individual basis. The resultant population dose-response curve was considerably steeper that estimated by EPA's contractor, so that estimates of population effects were substantially smaller at the concentrations of sulfur dioxide expected in ambient air. Full details can be found in the sulfur dioxide docket at http://www.regulations.gov in Attachment 1 to EPA-HQ-OAR-2007-0352-0031.1 and EPA-HQ-OAR-2007-0352-1061.1.