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.
