ObjectiveStudy how to quantify the bias of each study and how to estimate them. MethodIn the random-effect model, it is commonly assumed that the effect size of each study in meta-analysis follows a skew normal distribution which has different shape parameter. Through introducing a shape parameter to quantify the bias and making use of Markov estimation as well as maximum likelihood estimation to estimate the overall effect size, bias of each study, heterogeneity variance. ResultIn simulation study, the result was closer to the real value when the effect size followed a skew normal distribution with different shape parameter and the impact of heterogeneity of random effects meta-analysis model based on the skew normal distribution with different shape parameter was smaller than it in a random effects metaanalysis model. Moreover, in this specific example, the length of the 95%CI of the overall effect size was shorter compared with the model based on the normal distribution. ConclusionIncorporate the bias of each study into the random effects meta-analysis model and by quantifying the bias of each study we can eliminate the influence of heterogeneity caused by bias on the pooled estimate, which further make the pooled estimate closer to its true value.
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.