title: On estimating the minima of BMI-mortality curves.
abstract: 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 (1984)8 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.
  
  
  METHODS
  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.
authors.affiliation: Obesity Research Center, St. Luke's/Roosevelt Hospital, Columbia University College of Physicians and Surgeons, New York, NY 10025, USA. DBA8@Columbia.Edu
authors.forename: D B
authors.initials: DB
authors.lastname: Allison
authors.forename: M S
authors.initials: MS
authors.lastname: Faith
mesh_terms: D015992:Body Mass Index; D006801:Humans; D008433:Mathematics; D009026:Mortality