In Reply Dr Fraser and colleagues and Dr Kiran and colleagues underscore important methodologic issues surrounding J-shaped curves—particularly reverse causality and the need for rigorous research on the precise trajectories of exposure-outcome associations.
We agree with Fraser and colleagues that improvements in causal inference methods are crucial to understanding the public health implications of interventions. However, we caution that instrumental variables may have some limitations in cases in which nonlinear exposure-outcome relationships actually exist. At issue is the assumption that the instrument itself has a linear effect on the exposure variable at all levels of the distribution. Therefore, investigators must ensure that instruments behave similarly at the extremes of the exposure distribution for these tools to be helpful in the setting of J-shaped curves.
Chokshi DA, El-Sayed AM, Stine NW. Nonlinear Exposure-Outcome Associations and Public Health Policy—Reply. JAMA. 2016;315(12):1288. doi:10.1001/jama.2015.18035