What the Proportional Recovery Rule Is (and Is Not): Methodological and Statistical Considerations

Abstract

In 2008, it was proposed that the magnitude of recovery from nonsevere upper limb motor impairment over the first 3 to 6 months after stroke, measured with the Fugl-Meyer Assessment (FMA), is approximately 0.7 times the initial impairment ("proportional recovery"). In contrast to patients with nonsevere hemiparesis, about 30% of patients with an initial severe paresis do not show such recovery ("nonrecoverers"). Hence it was suggested that the proportional recovery rule (PRR) was a manifestation of a spontaneous mechanism that is present in all patients with mild-to-moderate paresis but only in some with severe paresis. Since the introduction of the PRR, it has subsequently been applied to other motor and nonmotor impairments. This more general investigation of the PRR has led to inconsistencies in its formulation and application, making it difficult to draw conclusions across studies and precipitating some cogent criticism. Here, we conduct a detailed comparison of the different studies reporting proportional recovery and, where appropriate, critique statistical methodology. On balance, we conclude that existing data in aggregate are largely consistent with the PRR as a population-level model for upper limb motor recovery; recent reports of its demise are exaggerated, as these excessively focus on the less conclusive issue of individual subject-level predictions. Moving forward, we suggest that methodological caution and new analytical approaches will be needed to confirm (or refute) a systematic character to spontaneous recovery from motor and other poststroke impairments, which can be captured by a mathematical rule either at the population or at the subject level.

Keywords: methods; proportional recovery; recovery; rehabilitation; statistics; stroke.

Figure 1.

Three simulated datasets illustrating appropriate and nonappropriate application of the proportional recovery rule (PRR). Red line: Ceiling line, data points cannot lie above the ceiling line. Blue dots: Simulated datapoints. Blue line: Linear regression line of the simulated datapoints. (1a): Simulated canonical PRR. (1b): Randomly distributed data drawn from a uniform distribution. (1c): Simulated data of close to full recovery; UE, upper extremity subscale.

Figure 2.

The relation between predicted FMA-UE (upper extremity subscale of the Fugl-Meyer Assessment) recovery and observed recovery shown in Prabhakaran et al. The data shown represents the results of the multivariate linear regression and not the results of the univariate equation ΔFMA-UE = 0.7 * FMA-UE_ii + 0.4 leading to the formulation of the proportional recovery rule (PRR). Adapted from Prabhakaran et al copyright © 2008 by The American Society of Neurorehabilitation. Reprinted by permission of SAGE Publications, Inc.

Figure 3.

Overview of publications replicating and extending the results of the proportional recovery rule (PRR) proposed by Prabhakaran et al. Red line: Ceiling line. Blue dots: Recoverers. Red dots: Nonrecoverers. Blue line: Linear regression line as computed from the measured datapoints. The data points were measured from the following table and figures in the respective articles: Zarahn et al (Table 1), Winters et al (Figure 2), Byblow et al (A and B) (Figure 1e, Figure 3a), Feng et al (Figure 5), Stinear et al (Figure A); UE, upper extremity subscale.

Figure 4.

Proportional recovery rule (PRR) applied to lower extremity motor function, visuospatial neglect, aphasia and resting motor threshold. Red line: Ceiling line. Blue dots: Recoverers. Red dots: Nonrecoverers. Blue line: Linear regression line as computed from the measured datapoints. The data datapoints were measured from the following figures in the respective articles: Smith et al (Figure B), Veerbeek et al (Figure 2), Winters et al (Figure 2), Lazar et al (Figure), Byblow et al (figure 2d).