We thank Dr. André Cerejeira for his interest in our study [1, 2]. His main concern is about propensity-score matching (PSM), which was used in our study. His comments are based on a political scientist’s criticism of PSM in a previous report [3]. We acknowledge that there are arguments by statisticians both for and against PSM. We are not in a position to make any comments on a statistician’s criticism of a particular statistical method; however, there is general agreement that PSM is the most popular method for causal analysis in observational studies, which is why we used it in our study.

We also conducted inverse probability of treatment weighting (IPTW), which is a propensity score analytical method. The previous criticism of PSM does not apply to other propensity score analytical methods (including IPTW, regression adjustment, and stratification) [2]. Our analysis confirmed that the PSM and IPTW results were consistent.