To put forward a simple algorithm for the pooled effect size of cumulative meta-analysis based on the random effects model. Firstly, the heterogeneity variance based on the previous k studies and the combined effect size of the previous k studies are both calculated. When adding the effective size of k+1 study, we use recursive method to calculate heterogeneity variance and the corresponding pooled size of the previous k+1 studies. Whenever we add one new study to the previous studies, we carry out one recursive operation to rapidly calculate the heterogeneity variance and the corresponding overall effect size by using recursive formulas. This method is easy and effective, with no need to write programs to obtain these results.
