The Authors Respond.

To the Editor:

We thank Dr. Reyes Sanchez[1] for their thoughtful comments on our article.

We agree that causal inference assessment should not rely only on statistical methods but also on the evidence of biologic plausibility resulting from the conduct of experimental studies and on the strength of evidence supporting a particular scientific conclusion.[2] Assessing the extent to which an air pollution study provides evidence of a cause-and-effect relationship, in particular, requires the use of an appropriate study design,[2] and we cannot emphasize more that accurate assessments of assumptions, methods, and study designs should serve as the foundation for any causal findings. We thank the commenter for giving us the opportunity to re-emphasize this key message of our article.

We also thank the commenter for pointing out the prominent challenges associated with the selection of confounders in epidemiologic studies. We are aware of the limitations of data-driven methods, such as the change-in-estimate criterion, for selecting confounders,[3] and we agree that expert knowledge along with the use of causal graphs represent valid alternatives to choose confounders in multivariable models. In our study, we selected potential confounders of the associations between air pollution and overall mortality based on results from preliminary studies,[4-6] and we used the change-in-estimate criterion, which to date represents one of the most popular data-driven method for selecting confounders in epidemiologic studies,[7] to supplement such a priori knowledge and to help identify the final set of confounders to include in the analysis. With respect to this point, and to strengthen the validity of our results, we have added some additional analyses on our GitHub page (https://github.com/andreabellavia/causalpm), including the full set of possible relevant confounders in the multivariate generalized propensity score model. Results did not show any deviation from those presented in our article.

Finally, we appreciate discussing the specific issues related to the use of propensity score in this context in terms of confounding balance. We agree that assessing balance between exposure(s) and confounders is key when performing causal analysis using propensity scores.[8] This potential issue has also been addressed and the reader can find additional analyses on our GitHub page where we tested the balancing property of the weights using the set of balance diagnostics proposed by Williams and Crespi for inverse probability weighting (IPW), and available in the mvGPS package.[9]