Developing an Innovative Jackknife Estimator for Quantifying Between-Study Variance in Meta-Analysis of Proportions

The DerSimonian and Laird (DL) method, commonly used in meta-analysis, often underestimates the between-study variance. The underestimation causes the confidence intervals to have less than the expected 95% coverage, resulting in inconclusive research findings. The present study introduces the use of the jackknife technique to improve the DL between-study variance estimator for meta-analyses of proportions from single-arm studies, as well as suggests certain transformations in combination with the jackknife technique. The proposed methodology is intended for settings in which the parameter of interest is an event probability or proportion, particularly for small numbers of studies with large variation. Simulation studies for binomial observations are conducted to compare the relative biases and coverage probabilities of the mean ( $\mu$ ) obtained by the DL, Paule and Mandel (PM), Restricted Maximum Likelihood (REML), and Hartung-Knapp-Sidik-Jonkman (HKSJ) methods with our proposed DerSimonian and Laird jackknife (DLJ) and transformed DerSimonian and Laird jackknife (TDLJs) methods. The simulation results show that our proposed DLJ and TDLJ estimators better quantify the between-study variance in meta-analysis of binary events, especially for small numbers of studies with larger variation and high probability of $\mu$ respectively. Three real life examples are presented to determine the performance of our new proposed between-study variance estimators.