Many continuous variables should be analyzed using the relative scale: a case study of β₂-agonists for preventing...

Area of Science:

• Pulmonary Medicine
• Biostatistics
• Pharmacology

Background:

• The relative scale adjusts for baseline variability, potentially allowing for more generalizable findings than the absolute scale.
• While common for binary outcomes, the relative scale is infrequently applied to continuous outcomes like forced expiratory volume in 1 second (FEV1).
• This study addresses the limited use of relative scale for continuous outcomes by comparing it with the absolute scale using existing data.

Purpose of the Study:

• To compare pooled outcomes on the relative versus absolute scale for inhaled beta-2 agonists.
• To analyze effects on exercise-induced decline in forced expiratory volume in 1 second (FEV1).
• To evaluate statistical model fit and heterogeneity between the two scales.

Main Methods:

• Utilized individual participant data (IPD) from placebo-controlled, cross-over studies identified in a Cochrane review.
• Modeled FEV1 decline reversal using linear mixed-effect models on absolute (percentage point change) and relative (percent change) scales.
• Performed random-effects, inverse-variance-weighting meta-analysis on study-level mean effects for relative estimates.

Main Results:

• Beta-2 agonists decreased FEV1 decline by 28 percentage points (absolute) and 90% (relative) on the IPD scale.
• The relative scale model demonstrated significantly better statistical fit and smaller median residuals compared to the absolute scale model.
• Meta-analysis of study-level data yielded similar relative effect reductions of 83% or 90%.

Conclusions:

• The relative scale more effectively captures variability in beta-2 agonist effects on exercise-induced FEV1 decline than the absolute scale.
• Previous analyses of FEV1 changes using the absolute scale may have resulted in suboptimal statistical outcomes.
• The choice of scale (absolute vs. relative) should be guided by biological rationale and empirical testing to minimize heterogeneity.