A robust and readily implementable method for the meta‐analysis of response ratios with and without missing standard deviations. (26th December 2022) - Nakagawa, Shinichi; Noble, Daniel W. A.; Lagisz, Malgorzata; Spake, Rebecca; Viechtbauer, Wolfgang; Senior, Alistair M.
Abstract: The log response ratio, lnRR, is the most frequently used effect size statistic for meta‐analysis in ecology. However, often missing standard deviations (SDs) prevent estimation of the sampling variance of lnRR. We propose new methods to deal with missing SDs via a weighted average coefficient of variation (CV) estimated from studies in the dataset that do report SDs. Across a suite of simulated conditions, we find that using the average CV to estimate sampling variances for all observations, regardless of missingness, performs with minimal bias. Surprisingly, even with missing SDs, this simple method outperforms the conventional approach (basing each effect size on its individual study‐specific CV) with complete data. This is because the conventional method ultimately yields less precise estimates of the sampling variances than using the pooled CV from multiple studies. Our approach is broadly applicable and can be implemented in all meta‐analyses of lnRR, regardless of 'missingness'. Abstract : We propose four new methods to deal with missing standard deviations (SDs) in meta‐analyses of log response ratio (lnRR). Our simulation shows that all the methods perform well and, rather surprisingly, two of our methods with missing data perform better than traditional methods without missing data. All future meta‐analyses of lnRR can take advantage of our methods.