A linear regression model for quantile function data applied to paired pulmonary 3d CT scans

TL;DR

This paper develops a parametric linear regression model for quantile function data derived from pulmonary CT scans to objectively assess treatment response in asthmatic patients, enabling statistical inference and reproducibility.

Contribution

It introduces a novel parametric linear regression model for quantile functions with distributional error assumptions, allowing for statistical inference in medical imaging analysis.

Findings

Model provides explicit regression coefficient estimators.

Enables calculation of confidence intervals for treatment response.

Applicable to paired CT scan data for asthma treatment assessment.

Abstract

This paper introduces a new objective measure for assessing treatment response in asthmatic patients using computed tomography (CT) imaging data. For each patient, CT scans were obtained before and after one year of monoclonal antibody treatment. Following image segmentation, the Hounsfield unit (HU) values of the voxels were encoded through quantile functions. It is hypothesized that patients with improved conditions after treatment will exhibit better expiration, reflected in higher HU values and an upward shift in the quantile curve. To objectively measure treatment response, a novel linear regression model on quantile functions is developed, drawing inspiration from Verde and Irpino (2010). Unlike their framework, the proposed model is parametric and incorporates distributional assumptions on the errors, enabling statistical inference. The model allows for the explicit calculation of regression coefficient estimators and confidence intervals, similar to conventional linear regression. The corresponding data and R code are available on GitHub to facilitate the reproducibility of the analyses presented.