Reply

We thank Drs Tanaka and Vander Weg for their interest in our research exploring COVID-19 vaccination in liver transplant recipients.¹ They discuss several excellent points and clarifications on the methodology, and we appreciate the opportunity to respond.

We chose not to adjust for the etiology of the liver disease that led to transplantation. The most common indication for liver transplantation in the VA during the study period were alcohol and chronic hepatitis C–related cirrhosis, both of which are uncommon causes of significant liver disease after transplantation.^{2 , 3} Therefore, we thought that unlike studies of participants with cirrhosis, the condition that led to cirrhosis was not a potential confounder in a study of transplant recipients.⁴ The variables we chose to adjust for in our multivariable analysis included those that were used in early studies published on the topic.^{5 , 6} However, we agree that diabetes mellitus, race/ethnicity, and geographic location within the US are important risk factors for COVID-19.⁷ We therefore repeated our analysis by controlling for the suggested variables, including location within the US (northeast, southeast, midwest, south, northwest, and southwest), race/ethnicity, and diabetes mellitus, in estimating the propensity scores. We also controlled for diabetes mellitus and race in the Cox hazard model. Our revised analysis shows that the observed associations are similar to those from the original analysis, with full COVID-19 vaccination being associated with a significant reduction in COVID-19 (adjusted hazard ratio [aHR] 0.33, 95% confidence interval [CI] 0.23–0.49; P < 0.0001), symptomatic COVID-19 (aHR 0.32, 95% CI 0.19°0.55; P < 0.0001), and COVID-19 related death (aHR 0.11, 95% CI 0.03–0.37; P = 0.0001).

Regarding outcomes, we reported the time to a positive PCR test, time to symptomatic COVID-19, and the time to COVID-19–related death. By definition, participants with a positive SARS-CoV-2 PCR test (defined as COVID-19) are either symptomatic or asymptomatic, and COVID-19–related death occurs only after being infected with COVID-19. Therefore, we do not consider these as competing events.

We did set different “time zeros” for the fully vaccinated and control subjects to match for the time of exposure to COVID-19. We agree that an alternative would be to designate time zero as when vaccines first become available for both groups and treat vaccination status as a time-dependent covariate. However, the number of partially vaccinated participants in our study sample was low, and evaluating the effect of partial vaccination was outside the aims of the study.

We confirm that we applied Cox proportional hazard regression to the pseudo-population generated through IPTW, as adjusted for variables that were thought to be associated with outcomes. As Tanaka and Vander Weg pointed out, we did not attempt a doubly robust procedure owing to the possibility of significant unobserved confounding.

We agree on the importance of addressing confounding and selection bias in observational studies. Propensity score weighting and matching are widely accepted to account for observed characteristics in observational studies.^{8 , 9} In our study, we tried to control for observed covariates that might confound the relation between COVID-19 vaccination and outcomes. Sensitivity analysis is a great tool to evaluate the size of confounding and bias of some potential confounders that were not observed, and we performed an analysis to estimate the E-value as suggested.

Our results estimated the aHR of COVID-19 infection at 0.36 (95% CI 0.26–0.51). The E-value for this was 5.0, with the upper confidence limit of 3.33, meaning that residual confounding could explain the observed association if there exists an unmeasured covariate having a relative risk association at least as large as 5.0 with both COVID-19 infection and vaccination. Similarly, the E-values and the upper confidence limits were large: respectively, 4.19 and 2.45 for symptomatic COVID-19 and 14.87 and 4.85 for COVID-19–related death. Compared with the observed risk factors (ranges from 0.93 to 1.29), the unmeasured confounding would need to have a much stronger effect to explain away the reported vaccination association.

We think that the observed variables we used cover most potential confounders. Although, factors such as psychosocial factors, political beliefs, and vaccine hesitancy related to these beliefs may represent unmeasured confounding, it is unlikely that these confounders would significantly change the associations observed, based on the calculated E-values.

All of the above analyses revealed consistent associations as described in our original estimates, indicating that our analyses are consistent and the findings robust.