On estimating the minima of BMI-mortality curves

OBJECTIVE: To identify the 'optimal' BMI, that is, the BMI associated with minimal mortality, researchers frequently fit a quadratic function to data and identify the nadir of the BMI-mortality curve. However, Waaler has argued that this approach 'systematically overestimates the optimal BMI because the true curve might not be quadratic. The purpose of this study was to test this proposition. DESIGN: We simulated 25 decidedly nonquadratic curves in which the true minimum corresponded to a BMI of 24. RESULTS : When fitting a quadratic model to this data and solving for the nadir of the curve, the estimated optimal BMI was 21.14 (SD = 0.586). CONCLUSIONS: It is concluded that there is no way of knowing a priori whether the BMI associated with minimum mortality will systematically overestimate, underestimate, or estimate in an unbiased manner the true optimal BMI when the true model underlying the data is not known.