Sensitivity analyses based on selection models

Copas developed a model in which the probability that a study is included in a meta-analysis depends on its standard error. Because it is not possible to estimate all model parameters precisely, he advocates sensitivity analyses in which the value of the estimated intervention effect is computed under a range of assumptions about the severity of the selection bias (Copas 1999). Rather than a single intervention effect estimated ‘corrected’ for publication bias, the reader can see how the estimated effect (and confidence interval) varies as the assumed amount of selection bias increases. Application of the method to epidemiological studies of environmental tobacco smoke and lung cancer suggests that publication bias may explain some of the association observed in meta-analyses of these studies (Copas 2000).