Statistical limitations on drawing inferences about proportional recovery
AbstractBackgroundNumerous studies have found large statistical relationships between the amount of recovery and initial impairments in people with stroke. When change scores are regressed onto initial impairments, the resulting slope is approximately ≈0.7for a variety of outcomes. These findings have led to the 70% “proportional recovery rule” and the argument that proportional recovery represents a biological phenomenon. Previous studies of proportional recovery are confounded by statistical limitations that come from regressing change scores onto initial impairments in bounded scales.ObjectiveOur goal is to show that data claimed as evidence for proportional recovery are generally consistent with random patterns of recovery, once statistical limitations are taken into account.MethodsUsing a pooled dataset of N = 373 Fugl-Meyer Assessment (FMA) upper extremity scores extracted from published literature, we ran simulations to illustrate three main arguments: (1) Mathematical coupling renders the traditional null-hypothesis significance test irrelevant in proportional recovery studies; (2) Proportional recovery is one of many alternative hypotheses; (3) Current evidence claimed in favor of proportional recovery is consistent with uniform random recovery.ResultsOur simulations show that if all data were included (no exclusion of “non-fitters”) regressing change scores onto initial impairments in a bounded scale would lead to a slope of ≈ 0.5. Similarly, cluster analysis will spuriously identify groups of fitters and non-fitters, leading to a slope for the fitters of ≈ 0.7, when the underlying recovery is random.ConclusionsThese results cast doubt on the validity of “proportional recovery” as a population level-statistic and a biological phenomenon.