Estimation in meta-analyses of response ratios

Abstract

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