Response to concerns about the interpretation of subgroup analysis.

Dear Editor,We appreciate Albuquerque, et al.'s interest in our paper [1,2], who raised the concern that we did not accurately interpret the interaction test, noting that "one should directly compare the estimates (interaction test)" and "the authors concluded that the association was only present in the AA population, which is not compatible with their analysis."We would like to clarify that our primary clinical question is whether ACE-I/ARB use is associated with the COVID-19 outcomes in each sub-group. We used stratified analysis to answer the question because when race/ethnicity serves as a non-specific proxy for numerous (confounding) factors, these can be (partially) controlled for through stratification [3]. Joint modeling of multiple groups is often used to gain power, but one needs to assume certain coherent distributions across different groups, which is not always true. Additionally, testing the interaction term is to assess association heterogeneity between groups, but it does not directly address whether the treatment is effective in each group.Specifically, we would like to elaborate on the following:1) Our conclusion: "the use of ARB was associated with a significant reduction in in-hospital mortality among African American (AA) patients but not non-AA patients" was based on results from the stratified analysis. We reported that ARB in-hospital use was associated with reduced mortality in the AA stratum (OR=0.196; 95%CI:0.074-0.516; P=0.001) with statistical significance. On the other hand, the association in the non-AA stratum is not statistically significant (OR=0.687; 95%CI:0.427-1.106; P=0.122). As stated previously, our primary objective is to assess whether ACE-I/ARB use among AA patients is associated with COVID-19 mortality, rather than the difference between AA and non-AA patients. We were also aware that the estimated ORs across different stratum were not comparable as noted in [4-6].2) We performed the joint modeling of AA and non-AA patients as suggested by [6]. Here, ARB in-hospital use was associated with reduced mortality in entire study population (OR=0.560; 95%CI:0.371-0.846; P=0.006). The interaction term added to the model was not significant (95%CI:0.185-1.292; P=0.149). Interpreting interaction terms in logistic regression is complex and a significant interaction term in log-odds may not be significant in difference-in-differences for probability[7]. Furthermore, the assumption of the additive effects and imbalanced sample sizes could impact the inference.We believe these results and the interpretation are appropriate. We acknowledge that there are cases where comparing the interaction term in greater detail would be an important next step for understanding the association between COVID-19 mortality and race/ethnicity.