Background/Purpose: Previous studies assessing relationship between obesity and physical function used linear regression model that assumes effects of obesity on physical function were the same across the distribution of outcome variable. However, if this assumption is not true, linear regression model may fail to reveal important associations and fail to identify persons who might be best targeted for obesity modification. Quantile regression provides a more complete picture of the relationship between obesity and physical function when both lower and upper or all quantiles are of interest. We used quantile regression to examine the distribution-specific effect of obesity on physical function.  

Methods: The Osteoarthritis Initiative (OAI) Study is an observational study of people 45-79 years with or at high risk of knee osteoarthritis. Body Mass Index (BMI) was calculated from standardized assessments of height and weight and categorized into 3 groups: normal (< 25kg/m²), overweight (25 – <30 kg/m²), and obese (≥30 kg/m²). Physical function was measured with knee-specific WOMAC function (range: 0-68) at the 12-month visit. The knee with higher (worse) WOMAC function score was used to represent a person’s function level. We performed sex-specific quantile regression models to assess association between BMI categories and WOMAC function percentiles from 30^th to 90^th with increase by 10^th adjusting for age, race, and CES-D score. We also performed a traditional linear regression model.

Results: 4,243 subjects (mean age 62.3, 58% women, 81% Whites, mean CES-D score 62.3) were included in analysis. In men, WOMAC function score among obese subjects was > 6 units worse at the 70^th, 80^th, and 90^th percentile, but only 0.4 unit worse at the 30^th percentile compared with the score for those in a normal BMI category. Similarly, WOMAC function score among obese women was > 9 units worse at the 70^th, 80^th, and 90^th percentile, but only 2.2 units worse at the 30^th percentile of WOAMC physical function score than score for those in a normal BMI category. A similar pattern was observed for subjects who were overweight though with attenuated effects (see table).  Such findings were not revealed when using a linear regression approach. 

Conclusion: Using quantile regression model we demonstrated that the magnitude of association between obesity and physical function score was greater among subjects with worse physical function than those with better function. When research interest focuses on bounded outcomes, such as pain or function assessed with visual analogue scale, quantile regression models may provide more valuable insights into the relationships than methods that use single summary effect measure, such as difference in mean or median.  

Table. WOMAC function score and BMI categories (normal BMI as reference)