# Quantile Regression in Epidemiology: Capturing Heterogeneity Beyond the Mean

## TL;DR

This paper shows how quantile regression can better capture variability in BMI associations compared to traditional methods in epidemiology.

## Contribution

The study demonstrates the advantages of quantile regression in revealing heterogeneity in BMI determinants across different distribution points.

## Key findings

- Quantile regression showed varying associations between BMI and factors like physical activity and gender across different BMI quantiles.
- The relationship between physical activity and BMI became stronger at higher BMI levels.
- Gender effects on BMI reversed at the upper tail of the distribution, not captured by mean-based models.

## Abstract

Ordinary linear regression is the most common approach for modeling relationships between continuous outcomes and explanatory variables in epidemiological research. However, this method relies on restrictive assumptions—normality, homoscedasticity, and linearity—that are often violated in real-world biomedical data. When these assumptions fail, mean-based estimates may obscure important heterogeneity across the outcome distribution. This study aims to illustrate the methodological and interpretive advantages of quantile regression over ordinary regression in the analysis of epidemiological data. Secondary data were derived from a cross-sectional study of 1415 healthy Greek adults aged 25–82 years. Body mass index (BMI) served as the outcome variable, while sex, age, physical activity, dieting status, and daily energy intake were considered predictors. Both ordinary and quantile regression models were applied to estimate associations between BMI and its determinants across the 25th, 50th, 75th, and 90th quantiles. Ordinary regression identified positive associations of BMI with age and energy intake and a negative association with physical activity. Quantile regression revealed that these relationships were not constant across the BMI distribution. The inverse association with physical activity intensified at higher quantiles, and the gender effect reversed direction at the upper tail, suggesting heterogeneity was not captured by mean-based models. Quantile regression provides a distribution-sensitive alternative to ordinary regression, offering insight into covariate effects across different points of the outcome distribution and serving as both a robust analytical tool and an educational framework for applied epidemiological research.