Estimation in meta-analyses of response ratios

Area of Science:

• Biostatistics
• Ecology
• Medical Research

Background:

• The ratio of means (RoM), or response ratio (RR), is commonly used in meta-analyses, especially in ecology.
• This effect measure is analyzed on a logarithmic scale as the log-response-ratio (LRR).

Purpose of the Study:

• To evaluate the performance of estimators for between-study variance (τ²) and overall effect (λ) in random-effects meta-analyses of LRR.
• To assess these estimators under normal and lognormal data distributions.

Main Methods:

• Conducted extensive simulations to assess bias and coverage of τ² estimators.
• Evaluated estimators of the overall effect (λ) in the log scale.
• Included empirical evidence from two case studies.

Main Results:

• Point estimators for τ² exhibited significant bias or unreliability.
• Interval estimators for τ² rarely achieved the desired 95% coverage with small to moderate sample sizes (n<40).
• Estimates of λ varied depending on whether data were normal or lognormal.

Conclusions:

• For lognormal data, the SSW estimator and its companion interval are recommended for sample sizes n≥40 and n≥10, respectively.
• Normal data presented greater challenges; SSW was nearly unbiased when means were sufficiently far from zero (e.g., >1 SD).