Proportional Recovery After Stroke: Addressing Concerns Regarding Mathematical Coupling and Ceiling Effects

Baseline scores after stroke have long been known as a good predictor of post-stroke outcomes. Similarly, the extent of baseline impairment has been shown to strongly correlate with spontaneous recovery in the first 3 to 6 months after stroke, a principle known as proportional recovery. However, recent critiques have proposed that proportional recovery is confounded, most notably by mathematical coupling and ceiling effects, and that it may not be a valid model for post-stroke recovery. This article reviews the current understanding of proportional recovery after stroke, discusses its supposed confounds of mathematical coupling and ceiling effects, and comments on the validity and usefulness of proportional recovery as a model for post-stroke recovery. We demonstrate that mathematical coupling of the true measurement value is not a real statistical confound, but rather a notational construct that has no effect on the correlation itself. On the other hand, mathematical coupling does apply to the measurement error and can spuriously amplify correlation effect sizes, but should be negligible in most cases. We also explain that compression toward ceiling and the corresponding proportional recovery relationship are consistent with our understanding of post-stroke recovery dynamics, rather than being unwanted confounds. However, while proportional recovery is valid, it is not particularly groundbreaking or meaningful as previously thought, just like how correlations between baseline scores and outcomes are relatively common in stroke research. Whether through proportional recovery or baseline-outcome regression, baseline scores are a starting point for investigating factors that determine recovery and outcomes after stroke.