The obesity paradox rests on a comparison between the populations with and without certain types of a serious injury or illness. Hence we suggest a model that is often referred to as the cause-specific survival model. Specifically, we attempt to make a distinction of the type of mortality between individuals according to the ‘cause of death’. To do so, we will consider the mortality of the following sub-populations separately.
- C = 0: Those without any affliction of type A at the time of death
- C = 1: Those with an affliction of type A at the time of death
Recall that an affliction of type A
is any serious injury or illness for which the MR of the infected individuals decreases monotonically as BMI increases. For example, evidence for such a relationship has been found among individuals with kidney failure (15
), heart failure (12
), and others (19
Using a Gompertz model for the cause-specific hazard functions, we specify parameter values of the model to produce a mathematical example that demonstrates that the obesity paradox could conceivably explain the data observed in the literature. Using the model we create herein, we obtain a U-shaped relation between MR and BMI very close to that which has been observed in data in the literature and an increasing optimal BMI (the value of BMI corresponding to the lowest MR) with aging (). The result observed herein suggests that the obesity paradox may indeed explain data that has previously been observed in literature (). Thus we have shown that the obesity paradox, if true, can be represented as a mathematical model that effectively recapitulates associations that are observed in literature among MRs, age, and BMI. Moreover, this recapitulation can be accomplished with remarkable facsimile. See our Methods section for the explicit details of the model and choice of parameters.
In our analyses, we took no position as to the veracity of the premises of the obesity paradox. Moreover, our result clearly does not capture all variation; instead we merely claim to have demonstrated that the obesity paradox may
partly explain observations in the literature. Certainly, we agree with others that some of the observed association between obesity and reduced MR among persons with major illnesses or injuries that has been observed in the literature may be due to confounding (25
). Yet, there are also reasons to speculate that increased fat reserves might offer some benefit in times of illness or injury (26
) and omental fat, which is increased among obese persons (27
), is also believed to have some beneficial immune-modulating effects in times of biological stress or trauma (28
). In addition, our demonstration indicates that these reasons are mathematically feasible. Hence, we should not prematurely exclude the possibility of causation.
The implication of this demonstration is that the obesity paradox could parsimoniously explain at least two phenomena that have puzzled obesity researchers, namely the U-shaped curve and the increasing nadir of the BMI MR association with age. In turn, from an evolutionary point of view, to the extent that extended survival into late adulthood enhances genetic fitness (29
), this could in turn partially explain the increase in body weight that tends to occur with aging (30
). Moreover such an explanation, if veridical, could reconcile divergent points of view in the obesity field. People who maintain that, at least until true ‘underweight’ levels are achieved, thinner is better would be correct for people who are neither diseased nor seriously injured. Of course, since we all have some probability of becoming diseased or injured, had we the ability to control our weights, we might wish to hedge our bets and gradually increase our weight with age to match the nadir of the BMI MR curves. However, these should not be taken as recommendations at this time, but only as speculation. Clearly our model, like virtually all models, is an oversimplification. We have not built in factors such as the differences in body composition that occur with age, the fact that illness often leads to weight loss, and the fact that height typically decreases in late adulthood. Nevertheless, our model is a plausible starting point and future research may incorporate these additional factors. These conceptions may also have implications for the conduct of BMI mortality analyses in terms of the treatment of BMI as a time-varying covariate and the use of multi-state survival models and this deserves further consideration.
Future research should endeavor to test the hypotheses embedded herein. This will be challenging because people cannot be randomly assigned to body weights nor to becoming diseased or injured. Nevertheless, animal models may be used in which, to some extent, one may be able to randomly assign to body composition status (31
) and also to injury or illness status.