Recovery after stroke: not so proportional after all?

The proportional recovery rule asserts that most stroke survivors recover a fixed proportion of lost function. Reports that the rule accurately predicts empirical recovery are rapidly accumulating. However, Hope et al. show that there is a fallacy at the heart of the rule that confounds many of these results.The proportional recovery rule asserts that most stroke survivors recover a fixed proportion of lost function. To the extent that this is true, recovery from stroke can be predicted accurately from baseline measures of acute post-stroke impairment alone. Reports that baseline scores explain more than 80%, and sometimes more than 90%, of the variance in the patients recoveries, are rapidly accumulating. Here, we show that these headline effect sizes are likely inflated. The key effects in this literature are typically expressed as, or reducible to, correlation coefficients between baseline scores and recovery (outcome scores minus baseline scores). Using formal analyses and simulations, we show that these correlations will be extreme when outcomes are significantly less variable than baselines, which they often will be in practice regardless of the real relationship between outcomes and baselines. We show that these effect sizes are likely to be over-optimistic in every empirical study that we found that reported enough information for us to make the judgement, and argue that the same is likely to be true in other studies as well. The implication is that recovery after stroke may not be as proportional as recent studies suggest.