# Application of functional regression in biomechanical assessment of neck disability: Selection of clinically relevant variables

## TL;DR

This study uses functional regression to better predict neck disability scores by analyzing motion patterns, finding that acceleration and deceleration phases are most informative.

## Contribution

The novel use of functional regression on cervical angular velocity curves to predict NDI scores in nonspecific neck pain patients.

## Key findings

- Bivariate flexion–extension plus lateral flexion model outperformed non-functional models in predicting NDI scores.
- Acceleration and deceleration phases of motion were most informative for predicting disability scores.
- Adding anthropometric variables did not improve model performance.

## Abstract

Background: The Neck Disability Index (NDI) is widely used to assess neck pain-related disability. It is commonly combined with objective measures, particularly range of motion and peak velocity, but these variables usually show weak correlations with patient-reported outcomes. Functional data analysis (FDA) makes it possible to analyze complete kinematic waveforms and provides tools to identify relevant motion features most related to disability.

Objective: This study aimed to examine whether scalar-on-function regression of cervical angular velocity curves can predict NDI scores in patients with nonspecific neck pain and which motion variables and sub-phases contribute most to the prediction.

Methods: We analyzed 56 recordings from 28 patients, each paired with an NDI questionnaire, which were collected over two sessions. Cervical flexion–extension, lateral flexion, and axial rotation velocities were processed using functional principal component analysis to reduce dimensionality while retaining the main modes of variation.

Univariate and bivariate scalar-on-function regression models were estimated. Model selection was based on a procedure that combined the Akaike Information Criterion, Bayesian Information Criterion, and measures of goodness-of-fit, ensuring a balance between model simplicity and predictive accuracy. Comparisons were made using non-functional regressions, including demographic and anthropometric variables.

Results: The bivariate flexion–extension plus lateral flexion model showed the best performance (r = 0.677), which was clearly higher than that of the non-functional regressions (r ≤ 0.391). The coefficient functions indicated that the acceleration and deceleration phases were the most informative in explaining variability in NDI scores. The inclusion of anthropometric variables did not improve model performance.

Conclusions: Functional regression of velocity curves improves the prediction of NDI scores and highlights specific phases of movement that are clinically relevant. Larger studies are required to confirm these findings and assess their clinical applicability.