Kathryn S. Hayward,
In this entry, I discuss a recent publication by Rachel Hawe and colleagues (1) regarding the potential biases of the mathematical properties of the proportional recovery rule and how this may impact application in the field of stroke recovery. Proportional recovery is the idea that most individuals post-stroke (“fitters” to the rule) will recover 70% of their potential on a given outcome (see paper for rule equation). The authors cite multiple studies that have demonstrated proportional recovery for upper limb motor impairment using a single outcome (Fugl Meyer Upper Limb assessment, out of 66 points), and recent work extending this rule to lower limb, aphasia and hemispatial neglect recovery outcomes.
The principal mathematical concept discussed as a limitation of the proportional recovery rule is mathematical coupling. This concept refers to when one variable directly or indirectly contains all or a part of another. For example, in the case of proportional recovery of the upper limb post-stroke, the initial score on Fugl Meyer Upper Limb assessment is part of both the independent and dependent variables of the proportional recovery rule.
To demonstrate the impact of mathematical coupling in the context of the proportional recovery rule, the authors present two datasets. First, using simulations of random recovery data (n=200), Hawe et al demonstrate that over 80% of simulations approximate prior proportional recovery findings in terms of slope and R2 values. Second, using data compiled from six published upper limb proportional recovery papers (n = 373 subjects), the authors demonstrate high variability in upper limb recovery (SD=33.4%) despite an R2 of 0.86. Further, the number of subjects displaying ~70% recovery was near chance levels. They subsequently go on to examine the impact of mathematical coupling using other measures (Purdue Pegboard and Functional Independence Measure), highlighting similar issues.
Predicting recovery after stroke remains a major challenge for the field. Proportional recovery has been suggested to be a benchmark for testing the effect of future interventions. However, such a proposal requires careful consideration of the mathematical limitations raised in the current paper. A very large dataset with common data elements may advance our understanding of prediction in stroke recovery. But, impacting this goal is the limitation of ceiling and floor effects demonstrated in the current paper, emphasizing the need for greater sensitivity in indexing recovery to inform meaningful predictions at the level of the individual stroke survivor.
This paper is not the first to challenge the proportional recovery rule from a mathematical perspective. A recent paper by Tom Hope and colleagues (2) also discussed the methodological limitations of the proportional recovery rule. Linked to this paper is a letter to the editor from one of the groups that has investigated the proportional recovery rule (3), with a reply from Hawe and colleagues (4) available.
1. Hawe RL, Scott SH, Dukelow S. Taking proportional out of stroke recovery. Stroke. 2019;50:204-11.
2. Hope TMH, K. F, Price CJ, Leff AP, Rotshtein P, Bowman H. Recovery after stroke: not so proportional after all? Brain. 2019;142:15-22.
3. Byblow W, Stinear C. Letter by Byblow and Stinear Regarding Article “Taking Proportional Out of Stroke Recovery”. Stroke. 2019;50:e125.
4. Hawe RL, Scott SH, Dukelow SP. Response by Hawe et al to Letter Regarding Article, “Taking Proportional Out of Stroke Recovery”. Stroke. 2019;50:e126.