Inflated estimates of proportional recovery from stroke: the dangers of mathematical coupling and compression to ceiling

The proportional recovery rule states that most survivors recover a fixed proportion (≈70%) of lost function after stroke. A strong (negative) correlation between the initial score and subsequent change (outcome minus initial; ie, recovery) is interpreted as empirical support for the proportional recovery rule. However, this rule has recently been critiqued, with a central observation being that the correlation of initial scores with change over time is confounded in the situations in which it is typically assessed. This critique has prompted reassessments of patients’ behavioral trajectory following stroke in 2 prominent papers. The first of these, by van der Vliet et al presented an impressive modeling of upper limb deficits following stroke, which avoided the confounded correlation of initial scores with change. The second by Kundert et al reassessed the value of the proportional recovery rule, as classically formulated as the correlation between initial scores and change. They argued that while effective prediction of recovery trajectories of individual patients is not supported by the available evidence, group-level inferences about the existence of proportional recovery are reliable. In this article, we respond to the van der Vliet and Kundert papers by distilling the essence of the argument for why the classic assessment of proportional recovery is confounded. In this respect, we reemphasize the role of mathematical coupling and compression to ceiling in the confounded nature of the correlation of initial scores with change. We further argue that this confound will be present for both individual-level and group-level inference. We then focus on the difficulties that can arise from ceiling effects, even when initial scores are not being correlated with change/recovery. We conclude by emphasizing the need for new techniques to analyze recovery after stroke that are not confounded in the ways highlighted here.