Estimating the effect size of surgery to improve walking in children with cerebral palsy from retrospective observational clinical data

Single-event multilevel surgery (SEMLS) is a standard treatment approach aimed at improving gait for patients with cerebral palsy, but the effect of this approach compared to natural progression without surgical intervention is unclear. In this study, we used retrospective patient history, physical exam, and three-dimensional gait analysis data from 2,333 limbs to build regression models estimating the effect of SEMLS on gait, while controlling for expected natural progression. Post-hoc classifications using the regression model results identified which limbs would exhibit gait within two standard deviations of typical gait at the follow-up visit with or without a SEMLS with 73% and 77% accuracy, respectively. Using these models, we found that, while surgery was expected to have a positive effect on 93% of limbs compared to natural progression, in only 37% of limbs was this expected effect a clinically meaningful improvement. We identified 26% of the non-surgically treated limbs that may have shown a clinically meaningful improvement in gait had they received surgery. Our models suggest that pre-operative physical therapy focused on improving biomechanical characteristics, such as walking speed and strength, may improve likelihood of positive surgical outcomes. These models are shared with the community to use as an evaluation tool when considering whether or not a patient should undergo a SEMLS.

The propensity score ( ) for a limb is the probability of that limb undergoing a specified treatment ( ) conditioned on pre-treatment variables ( ). For the surgery model, the specified treatment assignment was a SEMLS ( = 1), and for the control model, the treatment assignment was only conservative treatment ( = 0): = ( = | ). (A1)

Feature selection
The / -regularized model error was defined as: 3 = GDI at follow-up visit for limb < 3 = vector of 0-mean, 1-variance standardized features variables for limb , 7 = unknown feature coefficients and constant term, and = regularization weight To select features for the regression models, we chose the largest such that the mean 10-fold cross validation error, , was within 1 standard deviation of the minimum mean cross-validation error. The selected features were those corresponding to the resulting non-zero coefficients, .

Regression model
The regression coefficients for the chosen features, * , were computed as , 7 = argmin 1 3 ( 3 − ( 7 + : Covariance of the coefficients were computed as e,e f = = h * : * j k/ , (A4) where * is the matrix containing the n selected features for all observations, is a diagonal matrix of observation weights, and = = / ∑p F kq r k/ ∑ 3 ( 3 − ( 7 + :

New predictions
For a new observation with features, , we estimate outcome, , as ~h 7 + : , : e,e f j.
SUPPLEMENTARY TABLE S1 Candidate feature variables.