Estimating Optimum Body Mass Index: A Simulation Study Comparing Fractional Polynomials and Generalized Additive Model

Introduction:

In recent years fractional polynomials (FP) as well as generalized additive models (GAM) have been increasingly used to estimate the optimum body mass index (BMI) in terms of lowest mortality. However, to date it has not been investigated which of these different models is most appropriate for estimating the optimum BMI.

Methods:

We assumed three different scenarios for the BMI mortality relation: symmetric u-shaped, non-symmetric u-shaped and symmetric v-shaped. We generated a hypothetical study sample of 5000 individuals for each scenario. FP and two types of GAM (thin plate splines and restricted cubic splines) were used to derive optima and corresponding confidence intervals (CIs) for each scenario. Bias of optima and coverage of CIs were evaluated after simulation of 10 000 replications.

Results:

Estimated BMI optima and size of CIs derived varied by type of model used. We found bias in optima to be smallest for symmetric u- or v-shaped relations when using thin plate splines (median:± 0.02 kg/m2). For the non-symmetric u-shaped relation, bias was smallest when using FP (median: +0.04 kg/m2). However, 95%-CIs were way too narrow for FP in any scenario (coverage of 59.7 to 85.3%). Thin plate splines were rather conservative and the only model type always maintaining the limit of 95% (coverage of 96.7 to 99.0%). The performance of restricted cubic splines varied by number of knots used.

Conclusions:

Based on the first results of this simulation study, thin plate splines might be most suited for the estimation of the optimum of the BMI mortality relation. However, the effect of parameters like sample size, number of events or the position of the opium relative to the mean needs further investigation.