Abstract
BackgroundThe relative scale adjusts for baseline variability and therefore may lead to findings that can be generalized more widely. It is routinely used for the analysis of binary outcomes but only rarely for continuous outcomes. Our objective was to compare relative vs absolute scale pooled outcomes using data from a recently published Cochrane systematic review that reported only absolute effects of inhaled β2-agonists on exercise-induced decline in forced-expiratory volumes in 1 s (FEV1).MethodsFrom the Cochrane review, we selected placebo-controlled cross-over studies that reported individual participant data (IPD). Reversal in FEV1 decline after exercise was modeled as a mean uniform percentage point (pp) change (absolute effect) or average percent change (relative effect) using either intercept-only or slope-only, respectively, linear mixed-effect models. We also calculated the pooled relative effect estimates using standard random-effects, inverse-variance-weighting meta-analysis using study-level mean effects.ResultsFourteen studies with 187 participants were identified for the IPD analysis. On the absolute scale, β2-agonists decreased the exercise-induced FEV1 decline by 28 pp., and on the relative scale, they decreased the FEV1 decline by 90%. The fit of the statistical model was significantly better with the relative 90% estimate compared with the absolute 28 pp. estimate. Furthermore, the median residuals (5.8 vs. 10.8 pp) were substantially smaller in the relative effect model than in the absolute effect model. Using standard study-level meta-analysis of the same 14 studies, β2-agonists reduced exercise-induced FEV1 decline on the relative scale by a similar amount: 83% or 90%, depending on the method of calculating the relative effect.ConclusionsCompared with the absolute scale, the relative scale captures more effectively the variation in the effects of β2-agonists on exercise-induced FEV1-declines. The absolute scale has been used in the analysis of FEV1 changes and may have led to sub-optimal statistical analysis in some cases. The choice between the absolute and relative scale should be determined based on biological reasoning and empirical testing to identify the scale that leads to lower heterogeneity.
Highlights
The relative scale adjusts for baseline variability and may lead to findings that can be generalized more widely
Meta-analyses have shown that the relative scale leads to less heterogeneity in the analysis of binary outcomes compared with the absolute scale, which indicates that the relative scale better captures the biological effects [2]
The absolute scale has been widely used in the analysis of forced-expiratory volumes in 1 s (FEV1) changes and it may have led to sub-optimal statistical analysis in some cases
Summary
The relative scale adjusts for baseline variability and may lead to findings that can be generalized more widely. The relative scale has been used for decades for estimating the effects on binary outcomes, such as calculating that heavy alcohol consumption increases the occurrence of liver cirrhosis by the rate ratio (RR) of over 10 [1]. Meta-analyses of continuous outcomes typically use the absolute scale, i.e., the original measurement units (mean difference, MD), or the standardized mean difference (SMD) scale in which the mean difference is expressed in the pooled standard deviation units. Both of these approaches (MD and SMD) are available as options in popular meta-analysis software [3]
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