Meta-analysis is a process to estimate a summary statistic from all available studies. The statistic may be a difference in survival rate, hazard ratio, or others. To calculate a summary statistic, a method using variance by Taylor series, a Mantel-Haenszel method, Peto method, or DerSimonian-Laird method are used. Although they all give a close estimation; the DerSimonian- Laird method is most commonly applied. This method is based on a random effect model with the assumption that an estimate from each study distributes normally around a mean derived from whole studies.
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Hamajima, N., Matsuo, K., & Yuasa, H. (2000). Meta-analysis. Biotherapy, 14(2), 157–161. https://doi.org/10.53730/ijhs.v6ns3.9579