Many continuous variables should be analyzed using the relative scale: a case study of β2-agonists for preventing exercise-induced bronchoconstriction
Bibliographic record
Abstract
Abstract Background The 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 β 2 -agonists on exercise-induced decline in forced-expiratory volumes in 1 s (FEV 1 ). Methods From the Cochrane review, we selected placebo-controlled cross-over studies that reported individual participant data (IPD). Reversal in FEV 1 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. Results Fourteen studies with 187 participants were identified for the IPD analysis. On the absolute scale, β 2 -agonists decreased the exercise-induced FEV 1 decline by 28 pp., and on the relative scale, they decreased the FEV 1 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, β 2 -agonists reduced exercise-induced FEV 1 decline on the relative scale by a similar amount: 83% or 90%, depending on the method of calculating the relative effect. Conclusions Compared with the absolute scale, the relative scale captures more effectively the variation in the effects of β 2 -agonists on exercise-induced FEV 1 -declines. The absolute scale has been used in the analysis of FEV 1 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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.010 | 0.002 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".