Predicting Upper Limb Motor Impairment Recovery after Stroke: A Mixture Model

Abstract

Objective: Spontaneous recovery is an important determinant of upper extremity recovery after stroke and has been described by the 70% proportional recovery rule for the Fugl-Meyer motor upper extremity (FM-UE) scale. However, this rule is criticized for overestimating the predictability of FM-UE recovery. Our objectives were to develop a longitudinal mixture model of FM-UE recovery, identify FM-UE recovery subgroups, and internally validate the model predictions.

Methods: We developed an exponential recovery function with the following parameters: subgroup assignment probability, proportional recovery coefficient r _k , time constant in weeks τ _k , and distribution of the initial FM-UE scores. We fitted the model to FM-UE measurements of 412 first-ever ischemic stroke patients and cross-validated endpoint predictions and FM-UE recovery cluster assignment.

Results: The model distinguished 5 subgroups with different recovery parameters ( r₁ = 0.09, τ₁ = 5.3, r₂ = 0.46, τ₂ = 10.1, r₃ = 0.86, τ₃ = 9.8, r₄ = 0.89, τ₄ = 2.7, r₅ = 0.93, τ₅ = 1.2). Endpoint FM-UE was predicted with a median absolute error of 4.8 (interquartile range [IQR] = 1.3-12.8) at 1 week poststroke and 4.2 (IQR = 1.3-9.8) at 2 weeks. Overall accuracy of assignment to the poor (subgroup 1), moderate (subgroups 2 and 3), and good (subgroups 4 and 5) FM-UE recovery clusters was 0.79 (95% equal-tailed interval [ETI] = 0.78-0.80) at 1 week poststroke and 0.81 (95% ETI = 0.80-0.82) at 2 weeks.

Interpretation: FM-UE recovery reflects different subgroups, each with its own recovery profile. Cross-validation indicates that FM-UE endpoints and FM-UE recovery clusters can be well predicted. Results will contribute to the understanding of upper limb recovery patterns in the first 6 months after stroke. ANN NEUROL 2020;87:383-393 Ann Neurol 2020;87:383-393.

Figure 1

Longitudinal mixture model of Fugl–Meyer motor upper extremity (FM‐UE) recovery. (A) FM‐UE recovery data of the 412 ischemic stroke patients in our data set. Individual patients are color‐coded according to the subgroup they were assigned to most by the longitudinal mixture model of FM‐UE recovery. The average subgroup recovery patterns are shown in bold. Estimated model parameters for the 5 different subgroups: subgroup assignment probability (B), recovery coefficient (C), time constant (D), and initial distribution of the FM‐UE (E). Whiskers indicate 95% equal‐tailed intervals.

Figure 2

Cross‐validation of model predictions. (A) Number of patients who had at least 1 measurement at a specific time poststroke and were therefore included in the cross‐validation. (B) Median number of measurements per patient available for cross‐validation at a specific time poststroke. Error bars indicate 95% equal‐tailed intervals [ETIs] across patients with at least 1 measurement. Whiskers represent 1.5 times the interquartile range; outliers not shown. (C) Future recovery, defined as endpoint Fugl–Meyer motor upper extremity (FM‐UE) minus last available FM‐UE for each patient at a specific time poststroke. (D, E) Boxplot of the absolute error across all 412 patients times 100 samplings of the endpoint FM‐UE (A) and the ΔFM‐UE (B). Whiskers represent 1.5 times the interquartile range; outliers not shown. (F) Correlation between predicted and observed FM‐UE (blue circles) and ΔFM‐UE (red triangles) with error bars indicating the 95% ETIs over the 100 samplings. FM‐UE recovery cluster assignment accuracy (G), positive predictive value (H), and miss rate (I) with error bars indicating the 95% ETIs across the 100 samplings.

Figure 3

Model Fugl–Meyer motor upper extremity (FM‐UE) predictions for 3 typical patients. Model FM‐UE predictions for example patients from the optimal (given all FM‐UE data) poor (A–C), moderate (D–F), or good (G–I) FM‐UE recovery cluster. The left column illustrates predictions made using data available at 2 weeks poststroke, the second column at 4 weeks poststroke, and the final column at 3 months poststroke. Open circles represent data used for prediction modeling. Filled markers indicate the actual endpoint FM‐UE. The prediction is shown as the mean profile (dark line) with 68% equal‐tailed intervals (dark shaded area) and 95% equal‐tailed intervals (light shaded area). The figure titles and the colors of the credible intervals (poor [purple], moderate [orange], or good [green]) indicate the predicted FM‐UE clusters as well as the probability of cluster assignment.