Examining the BMI-mortality relationship using fractional polynomials.

Background: Many previous studies estimating the relationship between body mass index (BMI) and mortality impose assumptions regarding the functional form for BMI and result in conflicting findings. This study investigated a flexible data driven modelling approach to determine the nonlinear and asymmetric functional form for BMI used to examine the relationship between mortality and obesity. This approach was then compared against other commonly used regression models.

Methods: This study used data from the National Health Interview Survey, between 1997 and 2000. Respondents were linked to the National Death Index with mortality follow-up through 2005. We estimated 5-year all-cause mortality for adults over age 18 using the logistic regression model adjusting for BMI, age and smoking status. All analyses were stratified by sex. The multivariable fractional polynomials (MFP) procedure was employed to determine the best fitting functional form for BMI and evaluated against the model that includes linear and quadratic terms for BMI and the model that groups BMI into standard weight status categories using a deviance difference test. Estimated BMI-mortality curves across models were then compared graphically.

Results: The best fitting adjustment model contained the powers -1 and -2 for BMI. The relationship between 5-year mortality and BMI when estimated using the MFP approach exhibited a J-shaped pattern for women and a U-shaped pattern for men. A deviance difference test showed a statistically significant improvement in model fit compared to other BMI functions. We found important differences between the MFP model and other commonly used models with regard to the shape and nadir of the BMI-mortality curve and mortality estimates.

Conclusions: The MFP approach provides a robust alternative to categorization or conventional linear-quadratic models for BMI, which limit the number of curve shapes. The approach is potentially useful in estimating the relationship between the full spectrum of BMI values and other health outcomes, or costs.