Estimation in meta-analyses of response ratios
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(2020) 20:263
RESEARCH ARTICLE
Open Access
Estimation in meta-analyses of response ratios Ilyas Bakbergenuly1† , David C. Hoaglin2† and Elena Kulinskaya1*†
Abstract Background: For outcomes that studies report as the means in the treatment and control groups, some medical applications and nearly half of meta-analyses in ecology express the effect as the ratio of means (RoM), also called the response ratio (RR), analyzed in the logarithmic scale as the log-response-ratio, LRR. Methods: In random-effects meta-analysis of LRR, with normal and lognormal data, we studied the performance of estimators of the between-study variance, τ 2 , (measured by bias and coverage) in assessing heterogeneity of study-level effects, and also the performance of related estimators of the overall effect in the log scale, λ. We obtained additional empirical evidence from two examples. Results: The results of our extensive simulations showed several challenges in using LRR as an effect measure. Point estimators of τ 2 had considerable bias or were unreliable, and interval estimators of τ 2 seldom had the intended 95% coverage for small to moderate-sized samples (n < 40). Results for estimating λ differed between lognormal and normal data. Conclusions: For lognormal data, we can recommend only SSW, a weighted average in which a study’s weight is proportional to its effective sample size, (when n ≥ 40) and its companion interval (when n ≥ 10). Normal data posed greater challenges. When the means were far enough from 0 (more than one standard deviation, 4 in our simulations), SSW was practically unbiased, and its companion interval was the only option. Keywords: Between-study variance, Heterogeneity, Random-effects model, Meta-analysis, Log-response-ratio, Ratio of means
Background Users of meta-analysis assemble estimated effects from several studies in order to assess their heterogeneity and obtain an overall estimate. Here we focus on the measure of effect known as the response ratio (RR, also known in medical applications as the ratio of means, RoM), analyzed in the logarithmic scale as the log-response-ratio, LRR. In ecology almost half of all meta-analyses use this outcome measure [1, 2]. When some studies report means *Correspondence: [email protected] † Ilyas Bakbergenuly, David C. Hoaglin and Elena Kulinskaya contributed equally to this work. 1 School of Computing Sciences, University of East Anglia, Norwich Research Park, NR4 7TJ Norwich, UK Full list of author information is available at the end of the article
but include no information on the corresponding variances, the alternative of analyzing the standardized mean difference is not available. The RR was introduced by Hedges et al. [3] and rediscovered as RoM by Friedrich et al. [4]; they assumed normality of the underlying data. To avoid confusing RR with relative risk, we use RoM on the original scale and LRR on the log-scale. Because the LRR is not defined for negative values of the study means, Lajeunesse [5] modeled the data by lognormal distributions. We explore
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