Table 2.

The coverage probabilities for our 95% confidence intervals for VE. We let the true VE be either 0.99, 0.95, 0.90, 0.80, 0.60, or 0.50 and we let either the baseline infection rate (cluster = “Baseline”), the relative risk (cluster = “Relative Risk”), neither (cluster = “None”), or both (cluster = “Both”) vary across cluster. For each scenario, we simulated 20,000 studies in which the trial arm and survey cohort each contain 5000 individuals from 100 clusters. We report the mean $\text{VE}\left(V{\widehat{E}}^{*}\right)$ and the proportions, P(VE > UB) and P(VE < LB), of simulations where VE was outside the the upper and lower bounds of the 95% confidence interval. Bootstrapped confidence intervals were based on either the bias-corrected and accelerated (BC_a) procedure with resampled individuals, bootstrap distribution quantiles (BC-Q) with resampled individuals, or the BC_a procedure with resampled DU’s. For our simulations, we assumed that without vaccination, the expected rate of incident infections that would be detectable in the last two visits is 0.0407, the rate of baseline infections is 0.013, the proportion of baseline infections that persist throughout the trial is 0.039, and 10% of trial participants miss each of the last two visits. The VE is estimated based on the methods described in Section 2.8, with the vaccinated arm sampling fraction (propensity) assumed to be known as 0.5.

Cluster	VE	$V\widehat{E}$	BCa confidence intervals (resampled individuals)		BC-Q confidence intervals (resampled individuals		BCa confidence intervals (resampled DU’s)
			P(VE < LB)	P(VE > UB)	P(VE < LB)	P(VE > UB)	P(VE < LB)	P(VE > UB)
None	0.99	0.99	0	0.018	0	0.008	0	0.019
None	0.95	0.95	0.022	0.021	0.048	0.014	0.023	0.023
None	0.90	0.899	0.026	0.024	0.039	0.019	0.027	0.025
None	0.80	0.799	0.026	0.024	0.034	0.021	0.028	0.026
None	0.60	0.598	0.026	0.024	0.03	0.023	0.029	0.026
None	0.50	0.497	0.027	0.025	0.03	0.023	0.029	0.027
Baseline	0.99	0.99	0	0.019	0	0.008	0	0.02
Baseline	0.95	0.95	0.023	0.022	0.046	0.014	0.026	0.023
Baseline	0.90	0.899	0.026	0.024	0.04	0.018	0.029	0.025
Baseline	0.80	0.799	0.025	0.024	0.031	0.021	0.028	0.027
Baseline	0.60	0.598	0.025	0.023	0.028	0.021	0.028	0.026
Baseline	0.50	0.498	0.026	0.024	0.028	0.023	0.029	0.026
RR	0.99	0.99	0	0.019	0	0.008	0	0.02
RR	0.95	0.95	0.024	0.022	0.046	0.015	0.025	0.021
RR	0.90	0.899	0.028	0.027	0.04	0.021	0.028	0.024
RR	0.80	0.799	0.032	0.03	0.04	0.025	0.03	0.025
RR	0.60	0.597	0.036	0.036	0.041	0.033	0.03	0.025
RR	0.50	0.497	0.036	0.036	0.038	0.035	0.027	0.025
Both	0.99	0.99	0	0.018	0	0.008	0	0.018
Both	0.95	0.95	0.025	0.024	0.05	0.015	0.028	0.022
Both	0.90	0.899	0.028	0.028	0.043	0.022	0.031	0.026
Both	0.80	0.799	0.036	0.031	0.045	0.026	0.033	0.023
Both	0.60	0.598	0.038	0.036	0.043	0.034	0.029	0.025
Both	0.50	0.497	0.039	0.042	0.043	0.04	0.029	0.027