The inclusion of partially reported studies in a Bayesian meta-analysis

Suppose we wish to carry out a meta-analysis of a collection of case-control studies each of which investigates the association between a given potential risk factor and the development of a particular disease. We describe a Bayesian formulation of the meta-analysis problem for which standard random effects meta-analysis provides an approximate solution. One of the problems with standard methods of meta-analysis is that they require detailed results of analysis for each individual study which is to be included. This requirement leads to the exclusion from the meta-analysis of some studies (particularly negative studies). It will be shown how studies, whose results are only partially reported, may be accommodated in the Bayesian framework. As an example, we consider a collection of case-control studies pertaining to the association between parental smoking and middle-ear disease in children. The results of a Bayesian meta-analysis of all available studies are compared with those of a similar analysis based only on fully reported studies. The effect of including the partially reported studies is to lower the estimate of the pooled log odds ratio and to reduce the length of the corresponding 95% high probability interval. The first effect occurs because most of the partially reported studies report no association between parental smoking and middle-ear disease and the second due to the increase in information achieved by the inclusion of a larger number of studies. (C) 2002 Elsevier Science B.V. All rights reserved.