# Non-specific neck pain evaluation using functional linear models with the limma correction

## TL;DR

This study evaluates how neck movement patterns relate to disability in non-specific neck pain using statistical models that adjust for false discoveries.

## Contribution

The novelty lies in applying the limma correction to functional linear models for kinematic analysis in neck pain research.

## Key findings

- Raw and adjusted p-values show significant differences, revealing spurious effects like neck length on velocity and acceleration curves.
- NDI and age significantly affect velocity and acceleration curves after adjusting for false discovery rates.
- Velocity and acceleration curves provide complementary information and should be analyzed together in kinematic studies.

## Abstract

We have analyzed the relationship between disability and neck flexion-extension kinematics in non-specific neck pain subjects. A functional approach is used considering the angle, velocity, and acceleration curves. Different regression models have been fitted for each time in order to obtain these curves using scalar predictors such as the Neck Disability Index (NDI), age, sex, and neck length. In addition to classical regression, a limma (Linear Models for Microarray Data) model has been used, which improves the fit by modifying the estimation of the variances of the different fits using an empirical Bayes approach. As point-by-point adjustments are performed, this introduces a multiple comparison problem, and the corresponding p-values have to be adjusted in order to control the false discovery rate (FDR). In particular, a Benjamini-Hochberg method was used. The results show significant differences between raw and adjusted p-values for all variables, so spurious results were detected, e.g., the effect of neck length on velocity and acceleration curves. Differences between usual multiple linear regressions and the modified fits using the limma method (limma models) are minor, with a slight decrement of p-values in limma models. Once the p-values are adjusted, none of the variables analyzed significantly affects the angular curves. In contrast, NDI and age affect velocity and acceleration curves. Furthermore, the study of p-values throughout the movement shows that velocity and acceleration curves provide complementary information, so they should be used together in neck kinematics studies.

The online version contains supplementary material available at 10.1007/s11517-025-03400-3.