Sequential methods for random-effects meta-analysis

Although meta-analyses are typically viewed as retrospective activities, they are increasingly being applied prospectively to provide up-to-date evidence on specific research questions. When meta-analyses are updated account should be taken of the possibility of false-positive findings due to repeated significance tests. We discuss the use of sequential methods for meta-analyses that incorporate random effects to allow for heterogeneity across studies. We propose a method that uses an approximate semi-Bayes procedure to update evidence on the among-study variance, starting with an informative prior distribution that might be based on findings from previous meta-analyses. We compare our methods with other approaches, including the traditional method of cumulative meta-analysis, in a simulation study and observe that it has Type I and Type II error rates close to the nominal level. We illustrate the method using an example in the treatment of bleeding peptic ulcers.