A logician's approach to meta-analysis with unexplained heterogeneity

Meta-analysis is a powerful tool for combining related studies but such an aggregation would be flawed if studies investigated different populations or applied different methods in this investigation. While studies with differences that are statistically detected but not explained can be analysed by techniques of random-effects meta-analysis, it is difficult to analyse a study if it provides us with complex knowledge. This paper introduces a new method for meta-analysis that deals with both complex knowledge and unexplained heterogeneity, and which shares some properties with Bayesian methods. The newly developed method is applicable in a wide range of medical and also non-medical problems. A demonstration will be provided on a real medical example concerning the one-year incidence of diagnosis of cancer in patients with unprovoked venous thromboembolism. Our main findings based on several recent statistically heterogeneous studies indicate significant improvement in the cancer detection rate if routine evaluation for those patients is performed jointly with extensive screening techniques.