Bringing proportional recovery into proportion: Bayesian modelling of post-stroke motor impairment

Anna K. Bonkhoff, Thomas Hope, Danilo Bzdok, Adrian G. Guggisberg, Rachel L. Hawe, Sean P. Dukelow, Anne K. Rehme, Gereon R. Fink, Christian Grefkes, Howard Bowman

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Accurate predictions of motor impairment after stroke are of cardinal importance for the patient, clinician, and healthcare system. More than 10 years ago, the proportional recovery rule was introduced by promising that high-fidelity predictions of recovery following stroke were based only on the initially lost motor function, at least for a specific fraction of patients. However, emerging evidence suggests that this recovery rule is subject to various confounds and may apply less universally than previously assumed. Here, we systematically revisited stroke outcome predictions by applying strategies to avoid confounds and fitting hierarchical Bayesian models. We jointly analysed 385 post-stroke trajectories from six separate studies-one of the largest overall datasets of upper limb motor recovery. We addressed confounding ceiling effects by introducing a subset approach and ensured correct model estimation through synthetic data simulations. Subsequently, we used model comparisons to assess the underlying nature of recovery within our empirical recovery data. The first model comparison, relying on the conventional fraction of patients called 'fitters', pointed to a combination of proportional to lost function and constant recovery. 'Proportional to lost' here describes the original notion of proportionality, indicating greater recovery in case of a more severe initial impairment. This combination explained only 32% of the variance in recovery, which is in stark contrast to previous reports of >80%. When instead analysing the complete spectrum of subjects, 'fitters' and 'non-fitters', a combination of proportional to spared function and constant recovery was favoured, implying a more significant improvement in case of more preserved function. Explained variance was at 53%. Therefore, our quantitative findings suggest that motor recovery post-stroke may exhibit some characteristics of proportionality. However, the variance explained was substantially reduced compared to what has previously been reported. This finding motivates future research moving beyond solely behaviour scores to explain stroke recovery and establish robust and discriminating single-subject predictions.

Original languageEnglish (US)
Pages (from-to)2189-2206
Number of pages18
Issue number7
StatePublished - Jul 1 2020

Bibliographical note

Funding Information:
We thank Michael Moutoussis for valuable observations and discussions. A.K.B.'s clinician scientist position is supported by the dean's office, Faculty of Medicine, University of Cologne. G.R.F. gratefully acknowledges support by the Marga and Walter Boll foundation.

Publisher Copyright:
© The Author(s) (2020). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved. For permissions, please email:


  • Bayesian hierarchical models
  • Learning from data
  • Model comparison
  • Motor outcome post-stroke
  • Proportional recovery
  • Stroke/complications
  • Humans
  • Bayes Theorem
  • Recovery of Function/physiology
  • Motor Disorders/etiology

PubMed: MeSH publication types

  • Research Support, Non-U.S. Gov't
  • Journal Article


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