Modeling the effects of body mass index and waist-to-hip ratio on mortality

Abstract

Lindqvist et al. [1] investigated the effect of body mass index (BMI) and waist-to-hip ratio (WHR) on mortality in a cohort of women with 24 years of follow-up. The authors conclude that BMI and WHR have a U-shaped and linear effect, respectively, on the log-hazard for mortality in younger women while BMI and WHR are reported to both have a linear effect on the log-hazard for older women. The analysis of these data presents some methodological concerns. First, the women were originally sampled stratified by age (38, 46, 50, 54, or 60 years old), but the authors collapse the age groups into two categories (‘‘younger women’’ = 38 and 46 years old, and ‘‘older women’’ = 50, 54, and 60 years old). The authors claim that this stratification roughly categorizes the cohort into preand peri/postmenopausal women. However, using these collapsed groups assumes that, after adjusting for selected covariates, the hazard rate for mortality is the same for the 50, 54, and 60 year-old women. Similarly, the adjusted hazard for the 38 and 46 year-olds must also be the same. Furthermore, creating separate models for the ‘‘younger’’ and ‘‘older’’ women makes any direct statistical comparison between these groups impossible. If the decision to develop two separate models was based on a suspected departure from the assumption of proportional hazards, then solutions exist [2, 3] that would have allowed the data to be analyzed in a single model, thus permitting the direct assessment of differences in survival between the age groups and a better summary of the data. Secondly, while BMI is modeled with a quadratic term for younger women, other factors (e.g., triglyceride concentration) are assumed without justification to have linear effects on the log-hazard. In particular, the authors provide no reason why WHR should have a linear effect. The choice of a linear effect for BMI for older women is based on an insignificant test for the quadratic term. It is well known, however, that model choices based on prior tests of the data result in biased estimation and testing in the final model [4]. Indeed the reported p-value for the linear effect of BMI in older women (P = 0.026) is incorrect as this test is performed conditional on a non-significant test and subsequent removal of the quadratic term. Moreover, the reported U-shaped effect for BMI in younger women is a self-fulfilling inference as no other shape is possible under a quadratic fit. It should also be noted that a significant quadratic term does not necessarily imply a quadratic shape in the relationship between BMI and the log-hazard, as higher order terms may be necessary. Smooth estimates of the effects of BMI and WHR (e.g., using cubic splines) are necessary to gain an unrestricted estimate of the relationship between these two potential risk factors and mortality [4]. If the degrees of freedom are insufficient to consider other nonlinear effects in the model(s), then analysis of these data should be undertaken with extreme caution.