Abstract
BackgroundFor 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.MethodsIn random-effects meta-analysis of LRR, with normal and lognormal data, we studied the performance of estimators of the between-study variance, τ2, (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.ResultsThe results of our extensive simulations showed several challenges in using LRR as an effect measure. Point estimators of τ2 had considerable bias or were unreliable, and interval estimators of τ2 seldom had the intended 95% coverage for small to moderate-sized samples (n<40). Results for estimating λ differed between lognormal and normal data.ConclusionsFor 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.
Highlights
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), called the response ratio (RR), analyzed in the logarithmic scale as the log-response-ratio, LRR
We focus on the measure of effect known as the response ratio (RR, known in medical applications as the ratio of means, RoM), analyzed in the logarithmic scale as the log-response-ratio, LRR
In studying estimation for meta-analysis of LRR, we focus first on τ 2 and proceed to the overall effect, which we denote by λ
Summary
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), called the response ratio (RR), analyzed in the logarithmic scale as the log-response-ratio, LRR. We focus on the measure of effect known as the response ratio (RR, known in medical applications as the ratio of means, RoM), analyzed in the logarithmic scale as the log-response-ratio, LRR. Because the LRR is not defined for negative values of the study means, Lajeunesse [5] modeled the data by lognormal distributions. We explore meta-analysis of LRR under both normal and lognormal distributions, combined with the fixed-effect model and the random-effects model
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