Inverse propensity score weighting (IPSW)

In addition to PSM, we considered a secondary sensitivity analysis for high-risk patients (diabetes, hypertension, or renal disease). We limited the analysis to the severity outcome to avoid a multiplicity problem. In this technique, we used “Weightit” and “ipw” packages in R to calculate inverse propensity weights [^32,33]. The following covariates were considered in the IPSW analysis: age, gender, diabetes, hypertension, renal disease, cardiovascular disease, body mass index, and asthma, and several comorbidities. For specifics, see Fig. S3 on covariates selected and balance distribution. Again, various models were fitted and toughly tested before selecting the best model for each data subsets. Following the recommendation from Desai et al. [³⁴], the estimand was the average treatment effect. Stabilized weights were utilized in our analysis and then we examined weights with plots and summary statistics to prevent variance inflation from extreme weights. Love plots for SMD distribution presented in supplementary. Lastly, we fitted a structural causal model using “Survey” package to obtain robust variance estimation (sandwich type).