ESTABLISHING THE NADIR OF THE BODY-MASS INDEX MORTALITY RELATIONSHIP - A CASE-STUDY

Many studies have demonstrated a nonmonotonic relationship between mor tality and body mass index (BMI), with excess mortality occurring at b oth low and high levels. Although much discussion and many different a nalyses have appeared, to our knowledge no attempt has been made to qu antitatively establish the BMI at which minimum mortality (BMImin) occ urs or to establish confidence intervals for this BMI, accounting for the asymmetry of the relationship. We model the nonmonotonic relations hip between BMI and mortality in 13,242 black and white participants o f the NHANES-I Epidemiologic Follow-up Study to estimate the BMI at wh ich minimum mortality occurs. In our analyses we consider the joint re lationship of age, smoking status, and BMI to mortality. We present tw o methodologies for estimating BMImin: a logistic regression model wit h a transformation of BMI to accommodate asymmetry and a change point model as suggested by Goetghebeur and Pocock. We establish confidence intervals for BMImin using the delta method and bootstrap sampling for the logistic and the profile likelihood and bootstrap sampling for th e change point model. We also present formal tests for the heterogenei ty of BMImin by smoking status, sex, race, and age. Only the interacti on between race and BMI is significant; the BMImin is somewhat higher for blacks than whites. Finally, we discuss the problem of goodness-of -fit statistics when the relationship between the characteristic and t he outcome is nonmonotonic.