On the meta-analysis of treatment differences in heteroscedastic samples

In many meta-analysis cases the estimator of the overall effect in independent trials or experiments leads to unjustified significant results. This paper considers trials with two arms where the summary statistic of interest is either the mean difference or the risk difference. By using convexity principles of the relevant composed functions and the moments of the chi-square distribution, corrections are made on the estimated standard deviation of the estimator of the overall treatment difference. It is shown, analytically and by simulations, that by making such corrections on the estimated standard deviation, significance levels are attained which are relatively closer to the nominal level.