Establishing the Nadir of the Body Mass Index-Mortality Relationship: A Case Study

Abstract

Many studies have demonstrated a nonmonotonic relationship between mortality and body mass index (BMI), with excess mortality occurring at both low and high levels. Although much discussion and many different analyses have appeared, to our knowledge no attempt has been made to quantitatively establish the BMI at which minimum mortality (BMI_min) occurs or to establish confidence intervals for this BMI, accounting for the asymmetry of the relationship. We model the nonmonotonic relationship between BMI and mortality in 13,242 black and white participants of the NHANES-I Epidemiologic Follow-up Study to estimate the BMI at which minimum mortality occurs. In our analyses we consider the joint relationship of age, smoking status, and BMI to mortality. We present two methodologies for estimating BMI_min: a logistic regression model with a transformation of BMI to accommodate asymmetry and a changepoint model as suggested by Goetghebeur and Pocock. We establish confidence intervals for BMI_min using the delta method and bootstrap sampling for the logistic and the profile likelihood and bootstrap sampling for the changepoint model. We also present formal tests for the heterogeneity of BMI_min by smoking status, sex, race, and age. Only the interaction between race and BMI is significant; the BMI_min is somewhat higher for blacks than whites. Finally, we discuss the problem of goodness-of-fit statistics when the relationship between the characteristic and the outcome is nonmonotonic.

Key Words:

• Changepoint
• Logistic regression
• Mortality
• Obesity
• Quetelet index.