International Journal of Obesity | 2021
The protective effect of obesity on mortality among those with (or without) CVD cannot be fully explained by collider-stratification bias
Abstract
We thank Stovitz et al. for their interest in our paper [1] and to bring up an important issue. Collider bias may play a role in obesity paradox, but the protective effect of obesity on mortality cannot be completely justified by collider-stratification bias [2]. An unmeasured confounder (such as a gene) for the effects of CVD on death can cause selection bias for the effects of obesity on death among those with (or without) CVD, but the bias should be huge to be able to change the direction of the effects of interest, which is unlikely in our study for the following reasons: (1) The path of selection bias (BMI→ CVD← U→ death) in the causal diagram [3] (Fig. 1) requires strong associations transmitted via all three arrows to reverse the direction of the effect of BMI on mortality upon conditioning on CVD [4, 5]. According to our results (Table 2), the effect of BMI to CVD (BMI→ CVD) is not strong (hazard ratio= 1.64) [1]; thus a very strong confounder U with huge effects on both CVD and death is needed. In fact, the E value for the effect of obesity (obese vs. normal weight) on death among those without CVD is 5.2 indicating U should have unrealistically strong relationships with both BMI (through conditioning on CVD) and death to fully explain the protective HR estimate of 0.35, let alone it could reverse the direction of the effect [6, 7]. (2) We adjusted for family history of premature CVD, as a surrogate of genes affecting CVD in the analysis. This confounder was associated with 58 and 33% increase in hazard for incident CVD and all-cause mortality after adjustment for confounders among Iranian population [8]. So any concern about the likely effect of unmeasured genetic confounder was dispelled by including family history in the model. The numerical example (incorrectly called simulation in the last paragraph) in the letter looks too simplified to indicate that there is a selection bias, which reverses the direction of the effect estimate of interest. A probabilistic bias analysis is needed, which should be based on realistic assumptions taking into account the features of our study including multistate analysis, time-varying setting [9], and adjustment for the family history of CVD. As mentioned in our paper, there is also an alternative explanation to support our findings: compared to normal group, obese and overweight individuals experience nonfatal CVD at an earlier age, so they start secondary preventive therapies, including healthy diet, exercise and treatments for hyperlipidemia, hypertension, and other obesity-related comorbidities earlier [1, 10].