key: cord-0298111-3dt3now4
authors: Lyngse, F. P.; Molbak, K.; Denwood, M.; Christiansen, L. E.; Moller, C. H.; Rasmussen, M.; Cohen, A. S.; Stegger, M.; Fonager, J.; Sieber, R.; Ellegaard, K.; Nielsen, C.; Kirkeby, C. T.
title: Effect of Vaccination on Household Transmission of SARS-CoV-2 Delta VOC
date: 2022-01-06
journal: nan
DOI: 10.1101/2022.01.06.22268841
sha: d3c75601cac122b3d7e36e99590bfe83ad60e765
doc_id: 298111
cord_uid: 3dt3now4

The SARS-CoV-2 Delta variant of concern (VOC), which has shown increased transmission compared with previous variants, emerged rapidly globally during the first half of 2021, and became one of the most widespread SARS-CoV-2 variants worldwide. We utilized total population data from 24,693 Danish households with 53,584 potential secondary cases to estimate household transmission of the Delta VOC in relation to vaccination status. We found that the vaccine effectiveness against susceptibility (VES) was 61% (95%-CI: 59-63) and that the vaccine effectiveness against transmissibility (VET) was 42% (95%-CI: 39-45). We also found that unvaccinated individuals with an infection exhibited a higher viral load (one third of a standard deviation) compared to fully vaccinated individuals with a breakthrough infection. Our results imply that vaccinations reduce susceptibility as well as transmissibility. The results are important for policy makers to select strategies for reducing transmission of SARS-CoV-2.

We defined the overall household secondary attack rate (SAR) as the proportion of po-96 tential secondary cases that tested positive between 1-14 days following the identification 97 of the primary case within the same household. 98 We defined the combined vaccine effectiveness (VEC, the combined effect of vaccination 99 on both the infected primary case and the potential secondary case) as one minus the rel-100 ative risk (RR) of vaccinated individuals compared to unvaccinated individuals, following 101 Halloran et al. (2003) . 102 To estimate the vaccine effectiveness, we used a generalized linear model (GLM), with 103 Poisson distribution response and a log link function, comparing fully vaccinated individ-104 uals with unvaccinated individuals (see below). The modified GLM routine also included 105 standard errors clustered on the household level. The use of a Poisson distribution to 106 describe a binary response was to facilitate estimation of relative risks rather than odds 107 ratios. The regression model included fixed effects controls for age (categorical effects in 108 5-year age groups) and sex of both the primary and potential secondary cases, and fixed 109 effects for household size (categorical effects). We also included calendar week fixed ef-110 fects to control for temporal variation, e.g., behavior, changes in restrictions, vaccination 111 coverage and overall incidence. 112 To estimate the extent to which vaccination reduces susceptibility to infection (VES), we 113 estimated the relative risk (RR) of the SAR for potential secondary cases that were fully 114 vaccinated compared to the SAR for the potential secondary cases that were not vacci-115 nated. To separate the effect of vaccination affecting susceptibility (VES) from transmis-116 sibility (VET), we also stratified by vaccination status of the primary case. 117 To estimate the extent to which vaccination protects against transmissibility to other 118 household members, i.e., the VET, we estimated the RR of the SAR for primary cases that 119 were fully vaccinated compared to the SAR for primary cases that were not vaccinated. 120 To separate the effect of vaccination affecting transmissibility (VET) from susceptibility To estimate the combined effect of vaccine protection against susceptibility and transmissibility, we estimated the RR of the SAR for primary cases and potential secondary cases 124 that were fully vaccinated compared to primary cases and potential secondary cases that 125 were not vaccinated. 126 To explore the effect of vaccinations on infectiousness, we investigated the difference in 127 viral load (proxied by Ct values) for vaccinated and unvaccinated secondary cases testing 128 positive on the same day after exposure.

A more detailed description of the statistical methods is provided in Appendix 8. Notes: The secondary attack rate (SAR) is expressed in percentages. Primary cases and potential secondary cases are here shown by groups of sex, age, household size and vaccination status, independent of each other. Appendix Table 3 provides summary statistics for potential and positive secondary cases are grouped based on the primary case characteristics. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; Notes: This table provides estimates of vaccine effectiveness (%) against susceptibility (VES) as a pooled estimate ("Pool") as well as stratified by whether the primary case was unvaccinated ("Not") or fully vaccinated ("Fully"). The estimates of vaccine effectiveness against transmissibility (VET) is given as a pooled estimate and stratified by the vaccination status of the potential secondary cases within the household. The combined vaccine effectiveness (VEC) is defined as both the primary and potential secondary case being vaccinated relative to them both being unvaccinated. Vaccine effectiveness is estimated as one minus the relative risk of vaccinated individuals relative to unvaccinated individuals. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model. VE estimates conditional on the potential secondary case being tested is presented in Appendix Table 7 . VE estimates controlling for Ct value of the primary case sample is presented in Appendix  Tables 8 and 9 . VE estimates of waning immunity is presented in Appendix Tables 10 and 11.

Further robustness of the VE estimates are presented in Appendix 7.6. Tables 10 and 11   179 show estimates of VE since time of vaccination, i.e., waning immunity. The VES and VET 180 decreased from 71% (95%-CI: 69-72) and 57% (95%-CI: 53-61), respectively, to 32% (95%-181 CI: 16-45) and 29% (95%-CI: 14-41), respectively, between time points corresponding to 182 0-1 months and 7-8 months after vaccination (Table 10) .

Vaccinated secondary cases have a significantly lower viral load (higher Ct value) com-184 pared to unvaccinated secondary cases, independent of the day of testing after identifi-185 cation of the primary case ( Figure 1 ). Vaccinated secondary cases have an increased Ct 186 value of 1.6, corresponding to a third of a standard deviation (Appendix Table 6 ). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; found a combined vaccine effectiveness (VEC) of 66% (95%-CI: 63-68), when both the 196 primary and potential secondary case were fully vaccinated.

Other studies used contact tracing data and found similar estimates. In the Netherlands, is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101/2022.01.06.22268841 doi: medRxiv preprint breakthrough infections with the Delta VOC resulted in lower viral loads in vaccinated 224 cases compared with unvaccinated cases. 225 Our study found that the pooled VES generally decreased from 71% (95%-CI: 69-72) at 0-1 226 months after vaccination, compared to 32% (95%-CI: 16-45) 7-8 months after vaccination 227 (Appendix Table 10 ). Similarly, the pooled VET generally decreased from 57% (95%-CI: at mass gatherings. This suggests that immunity passports can be an effective measure to 240 reduce transmission, as previously suggested (Brown et al., 2020) . Third, we showed that 241 vaccination also protects against transmissibility, conditional on having a breakthrough in-242 fection. This indicates that prioritizing the vaccination of groups that have many contacts 243 or work with vulnerable individuals-e.g., nursing home staff-is important for pandemic 244 control. Fourth, our estimates can be used to inform simulation models of the current 245 pandemic, which crucially rely on the parameters of susceptibility and transmissibility.

As vaccination affects both the susceptibility and transmissibility, accurate estimates of 247 these effects are critical to the models that are used to inform decision makers. 248 We here found a substantial degree of transmission to and from children. Unvaccinated 249 children aged 0-10 years were susceptible to the SARS-CoV-2 Delta VOC with a SAR of 250 27% (Table 1) . Furthermore, we found that unvaccinated children aged 0-20 years that 251 13 . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101/2022.01.06.22268841 doi: medRxiv preprint were primary cases were able to infect vaccinated household members aged 20-60 with a 252 SAR of 15% (Figure 7) .

This study has several strengths. First, we combined several national-level datasets in 254 order to control for individual specific factors relating to both the primary and potential 255 secondary case. This is unique because standard approaches to estimating VE usually 256 focus on VES or a combined measure. Second, throughout the study period, Denmark 257 had a large testing capacity: testing was free and widely used. Third, all positive cases ing that most secondary cases were infected with the same lineage as the primary case.

In the present study, the Delta VOC comprised more than 95% of all cases in society 268 ( Figure 3 ), making it impossible to investigate variation across different variants. How-269 ever, using the subtype lineages of the Delta VOC, we found no significant difference in 270 the intra-household correlation of lineages across vaccinated and unvaccinated individuals 271 (Appendix 7.2). The data were collected while the Danish vaccination program was rolled 272 out to all above 12 years of age. Therefore, unvaccinated individuals mainly represents 273 individuals who were not yet invited for vaccination. This is a major strength of our study 274 because a self-selected unvaccinated group might introduce a bias due to the fact that 275 reluctancy to receive immunizations may correlate with other types of behavior.

Some limitations apply to this study. Firstly, we did not have access to clinical infor- is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; the biological aspect of susceptibility and transmissibility, as well as the behavioral aspects, and does not confer any information regarding severity of illness, which is expected 282 to be lower among vaccinated individuals.

There are several behavioral aspects relating to vaccination. Once a primary case is between fully vaccinated and unvaccinated potential secondary cases. We found that 298 vaccinated potential secondary cases were about 7 percentage points (10%) more likely 299 to be tested compared to unvaccinated individuals (Appendix 7.4). This suggests that 300 there are differences across the two groups that we cannot fully control for, e.g., general recommendations. This also implies that our VE estimates are a lower bound. When 304 we restrict our analyses to only include individuals with a test result, we obtain higher 305 VE estimates (Appendix Tables 7, 9, and 11). Moreover, there is likely a correlation of 306 vaccination status between household members. i) Individuals living together may be 307 more likely to share the same belief, for instance towards vaccination. ii) Individuals are 308 likely to have a partner around their own age. As vaccination roll-out is based on age, is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101/2022.01.06.22268841 doi: medRxiv preprint household members are likely to be eligible for vaccination around the same calendar time.

iii) There may be a fixed cost of being vaccinated, e.g., the travel from the home to the 311 vaccination location. Thus, a household might pool their day of vaccination together to 312 minimize travel costs. We found an intra-household correlation of vaccination status of 313 0.72 for individuals above age 12 years (Appendix 7.3).

Estimating VES and VET include several challenges. When few individuals are vacci-315 nated in a population, it is less complicated to estimate the approximate vaccine effec-316 tiveness against susceptibility (VES), because their exposure can be assumed to come 317 from unvaccinated cases. As vaccinations are rolled out in a country, the proportion of 318 the population that is vaccinated increases. As a consequence, the proportion of contacts 319 with vaccinated individuals also increases. Therefore, the real-life observed VES estimates 320 are a composition of exposure from and to both vaccinated and unvaccinated individuals.

If vaccination not only protects against infection, but also against transmission, the esti-322 mates are a combined effect of both VES and VET. The VET becomes increasingly more 323 important, as vaccination rates throughout society increase. Furthermore, it is necessary 324 to link primary cases to exposed contacts in order to estimate the VET.

Age is correlated with susceptibility and transmissibility as well as eligibility and roll-out 326 of vaccinations. This implies a natural imbalance in the number of primary and potential 327 secondary cases across age groups. To address this, we provide estimates of SAR and VE 328 in all combinations of age groups, stratified by vaccination status of both the primary and 329 potential secondary case (Appendix 7.1).

The estimates of VES are probably conservative compared with the general VES at the 331 overall population level. Transmission within household is associated with more intense 332 exposure than in the community in general, and since there is a relation between the is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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cine derived immunity, and may therefore be more likely to result in another breakthrough 338 infection.

In conclusion, we have demonstrated that vaccination was able to reduce the transmission 340 of the Delta VOC in Danish households over our study period. We estimated a vaccine is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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We thank Statens Serum Institut and The Danish Health Data Authority for data access. 440 We also thank the rest of the Expert Group for Mathematical Modelling of COVID-19 at is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10. 1101 /2022 In the study period, vaccinations were rolled out, going from below 40% fully vaccinated 465 to more than 75% fully vaccinated individuals (Figure 4 ). Denmark had a vaccination roll-out strategy with prioritization of vulnerable people.

Nursery home residents were prioritized (group 01), followed by citizens above age 65 468 who had the need of personal help and care (group 02), then elderly people above age 85 469 (group 03). The next three groups (04-06) contained employees in healthcare and social 470 work, high-risk patients, and relatives of high-risk patients. The remaining population 471 was subsequently prioritized based on birth year (groups 07-17). Naturally, this leads to 472 a correlation between calendar time and vaccination status conditional on age. Figure 5   473 shows the proportion of each group being fully vaccinated from January to November, 474 2021. We see that the compliance is generally high, and fast roll-out is seen in all groups.

This roll-out strategy also meant that most of the vulnerable population was fully vacci- is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101/2022.01.06.22268841 doi: medRxiv preprint nated, when the Delta VOC was first detected in Denmark. For example, more than 90% 477 of individuals above age 65 (group 09) were fully vaccinated. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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The copyright holder for this this version posted January 6, 2022. ; care track and the community track are based on RT-PCR detection of SARS-CoV-2 in 7 Additional Analyses 514 Notes: The secondary attack rate (SAR) is expressed in percentages. Potential and positive secondary cases are grouped based on the primary case characteristics. See table 1 for potential and positive secondary cases grouped by their own characteristics.

To investigate the age-related transmission patterns, we split the data into 20-year age 516 groups of both the primary cases and potential secondary cases and estimated the sec-517 ondary attack rate between all combinations of age groups, stratified by vaccination status 518 of both the primary and potential secondary case (Figure 7) . Generally, the SAR was is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. Notes: This figure presents attack rates stratified by the age of the primary and potential secondary case, stratified by the vaccination status of the primary and potential secondary case. Numbers show the estimated secondary attack rates with 95% confidence intervals clustered on the household level in parentheses. Table 4 provides number of observations used to estimate the SAR for each combination.

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The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101/2022.01.06.22268841 doi: medRxiv preprint Next, we estimated the pooled VES, pooled VET, and VEC for each combination of age 525 group ( Figure 8) . Generally, there was a positive VE across all age group combinations, 526 implying that the SAR is reduced by vaccination of both the susceptible and infectious 527 individual. Also, there was generally a decreasing VE with age of both the primary and 528 potential secondary case, which could be related to waning immunity. 529 Figure 8 : Crude VE estimates, stratified by age of the primary case and potential secondary case. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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We find an overall intra-household correlation of SARS-CoV-2 lineages of 88% (95%-CI: 531 87-89) (Table 5) However, it could also be due to uncertainty in the classification of subtype lineages of the 537 Delta VOC, which is changing over time. In the present study, we used PANGO Lineage 538 classifications from 2021-11-10. 539 In the present study, there is potential bias in the intra-household correlation of lineages 540 across vaccinated and unvaccinated individuals, which could invalidate our comparisons 541 of the relative risks. Table 5 presents the intra-household correlation of lineages across all 542 combinations of vaccinated and unvaccinated primary and secondary cases. We found no 543 statistically significant difference across any of the combinations, so there is no evidence 544 for differential bias across our groups of comparison. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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Vaccination status among household members are likely correlated due to several reasons. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101/2022.01.06.22268841 doi: medRxiv preprint When estimating the probability that an individual tests positive, it is conditional on the 564 individual actually being tested. Selection bias is a potential concern, if the vaccination 565 status of a potential secondary case within the household is correlated with the probability 566 of being tested after the identification of the primary case. Overall, we find that potential 567 secondary cases that are fully vaccinated are 7 percentage points (on a basis of 75%) more 568 likely to be tested 1-14 days after exposure, compared to unvaccinated individuals (Table   569 10). Furthermore, potential secondary cases being exposed to primary cases that are fully 570 vaccinated are also more likely to be tested. This suggests that there is a correlation 571 35 . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted January 6, 2022. ; https://doi. org/10.1101 org/10. /2022 between the household vaccination status and the compliance with being tested after 572 exposure to a close contact. Notes: This figure provides estimates of the difference in the probability that a fully vaccinated potential secondary cases have been tested after identification of a primary case compared with an unvaccinated potential secondary case. It shows that the potential secondary cases are exhibiting the same trend in testing since vaccination, unconditional of the vaccination status. Vaccinated potential secondary cases have a significantly higher rate of being tested after diagnosis of a primary case in the same household. Shaded areas are 95%-confidence intervals clustered on the household level.

One concern in investigating the transmissibility among vaccinated and unvaccinated cases 575 is that the viral load may differ across the two groups. Indeed the literature has shown is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101/2022.01.06.22268841 doi: medRxiv preprint samples from vaccinated primary cases had a lower viral load distribution (higher Ct values) compared to samples from unvaccinated primary cases (Figure 11 ). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101/2022.01.06.22268841 doi: medRxiv preprint cases had a lower viral load-a 1.6 point higher Ct value, translating into a third of a 589 standard deviation. This section addresses the robustness of the VE estimates presented in Table 2 . Table 7 592 provides VE estimates, conditional on the potential secondary case having a test result.

Thus, we do not assume that all untested contacts are negative. Table 8 provides VE 594 estimates, including Ct values of the primary case as a proxy for viral load. Table 9 595 provides VE estimates, including Ct values of the primary case as a proxy for viral load, 596 conditional on the potential secondary case having a test result. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101/2022.01.06.22268841 doi: medRxiv preprint Notes: This table provides VE estimates from the same model as Table 2 , conditional on the potential secondary case having a test result. The estimates of vaccine effectiveness against transmissibility (VET) is given as a pooled estimate and stratified by the vaccination status of the potential secondary cases within the household. The combined vaccine effectiveness (VEC) is defined as both the primary and potential secondary case being vaccinated relative to them both being unvaccinated. Vaccine effectiveness is estimated as one minus the relative risk of vaccinated individuals relative to unvaccinated individuals. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model. Notes: This table provides VE estimates from the same model as Table 2 , controlling for the sample Ct value of the primary case. The estimates of vaccine effectiveness against transmissibility (VET) is given as a pooled estimate and stratified by the vaccination status of the potential secondary cases within the household. The combined vaccine effectiveness (VEC) is defined as both the primary and potential secondary case being vaccinated relative to them both being unvaccinated. Vaccine effectiveness is estimated as one minus the relative risk of vaccinated individuals relative to unvaccinated individuals. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model. VES for primary cases fully vaccinated only includes primary cases with a sample Ct value >20.

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The copyright holder for this this version posted January 6, 2022. ; Notes: This table provides VE estimates from the same model as Table 2 , controlling for the sample Ct value of the primary case, conditional on the potential secondary case having a test result. The estimates of vaccine effectiveness against transmissibility (VET) is given as a pooled estimate and stratified by the vaccination status of the potential secondary cases within the household. The combined vaccine effectiveness (VEC) is defined as both the primary and potential secondary case being vaccinated relative to them both being unvaccinated. Vaccine effectiveness is estimated as one minus the relative risk of vaccinated individuals relative to unvaccinated individuals. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model. VES for primary cases fully vaccinated only includes primary cases with a sample Ct value >20.

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The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10.1101 https://doi.org/10. /2022 Notes: This table provides VE estimates from the same model as Table 2 by time since vaccination (bi-monthly). The estimates of vaccine effectiveness against transmissibility (VET) is given as a pooled estimate and stratified by the vaccination status of the potential secondary cases within the household. The combined vaccine effectiveness (VEC) is defined as both the primary and potential secondary case being vaccinated relative to them both being unvaccinated. Vaccine effectiveness is estimated as one minus the relative risk of vaccinated individuals relative to unvaccinated individuals. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model. For VES, the waning immunity is estimated for the potential secondary case. For VET, the waning immunity is estimated for the primary case. Note, the negative VET estimates, when the potential secondary case was fully vaccinated, suggest that there is bias in the comparison of the vaccinated and unvaccinated population that we do not fully control for. We did not find negative VET estimates, when we conditioned on the potential secondary case having a test test result (Appendix Table 11 ), indicating that differences in the probability of being tested across unvaccinated and fully vaccinated potential secondary cases is a bias in our model (Appendix 7.4). Other behavioral biases across unvaccinated and fully vaccinated are also likely. Thus it is most likely that there is a waning effect of vaccination, but it is very unlikely that the effect is negative.

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The copyright holder for this this version posted January 6, 2022. ; Notes: This table provides VE estimates from the same model as Table 2 by time since vaccination (bi-monthly), conditional on the potential secondary case having a test result. The estimates of vaccine effectiveness against transmissibility (VET) is given as a pooled estimate and stratified by the vaccination status of the potential secondary cases within the household. The combined vaccine effectiveness (VEC) is defined as both the primary and potential secondary case being vaccinated relative to them both being unvaccinated. Vaccine effectiveness is estimated as one minus the relative risk of vaccinated individuals relative to unvaccinated individuals. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parentheses. FE = included as fixed effects in the model. For VES, the waning immunity is estimated for the potential secondary case. For VET, the waning immunity is estimated for the primary case. Note that the VE estimates across columns are not directly comparable as they are estimated on stratified samples. 95% confidence intervals clustered on the household level in parenthesis.

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The copyright holder for this this version posted January 6, 2022. This section provides more details of the statistical methods used to generate the results 603 presented in the main manuscript. 604 We defined the secondary attack rate (SAR) as the proportion of potential secondary cases 605 that were infected within each household 1-14 days after exposure to a primary case. We 606 only included individuals that were either fully vaccinated (V) or not vaccinated (N), thus 607 excluding individuals that were partially vaccinated.

To compare attack rates across different vaccination status of primary cases and potential 609 secondary cases, we estimated the relative risk (RR). The vaccine effectiveness (VE) is 610 given by one minus the relative risk (1-RR) of the SAR of vaccinated individuals compared 611 to the SAR of the unvaccinated individuals. We stratified our analyses in order to separate 612 the effect of susceptibility (VES), the effect of transmissibility (VET), and the combined 613 effect (VEC). In particular, we use the following 7 equations, with underlying estimates 614 for SAR produced using generalized linear models that control for age, sex, household 615 size, and calendar week, with standard errors clustered on the household level.

Let SAR θp,θ i denote the SAR, where θ is the vaccination status θ ∈ {V, N } (Fully Vacci-617 nated or Not vaccinated ) of primary cases (p) and potential secondary cases (i). Let "." 618 denote the pooled sample of both vaccination statuses. Thus, the pooled SAR is denoted 619 as SAR .,.

Vaccine effectiveness of susceptibility (V ES) 621 First, we compared the SAR across potential secondary cases that were fully vaccinated 622 and potential secondary cases that were not vaccinated, unconditional of the vaccination 623 status of the primary case.

The pooled vaccine effectiveness against susceptibility (V ES) is given by: 

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The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10. 1101 /2022 i.e., the SAR of vaccinated potential secondary cases relative to the SAR of unvaccinated 626 potential secondary cases. 627 Next, we hold the vaccination status of the primary case fixed, and compare the SAR 628 across potential secondary cases that are fully vaccinated and not vaccinated.

Vaccine effectiveness of susceptibility among unvaccinated primary cases is given by:

Vaccine effectiveness of susceptibility among fully vaccinated primary cases is given by:

Vaccine effectiveness of transmissibility (V ET )

First, we compared the SAR across primary cases that were fully vaccinated and not 633 vaccinated, unconditional of the vaccination status of the potential secondary cases.

The pooled vaccine effectiveness of transmissibility (V ET ) is given by: 

Next, we hold the vaccination status of the potential secondary cases fixed, and compare 636 the SAR across primary cases that are fully vaccinated and not vaccinated.

Vaccine effectiveness of transmissibility among unvaccinated potential secondary cases is 638 given by:

Vaccine effectiveness of transmissibility among fully vaccinated potential secondary cases 640 is given by:

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The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10. 1101 /2022 Combined effectiveness (V EC) 642 Finally, we compared the SAR, where both the primary and potential secondary cases 643 were fully vaccinated, with the SAR, where both the primary and potential secondary 644 cases were unvaccinated.

The combined vaccine effectiveness is given by:

Estimation 647

We estimated the relative risks for VES, VET and VEC using the following generalized log(λ i,p ) = V acc + Age i + Age p + Sex i + Sex p + HouseholdSize p + W eek t ,

where V acc is a binary fixed effect representing one of the following explanatory variables 650 for each model:

-For VES, V acc refers to vaccination status of the potential secondary case i.

-For VET, V acc refers to vaccination status of the primary case p.

-For VEC, V acc refers to vaccination status of both the primary and potential secondary 654 case p, i.

Age denotes categorical fixed effects of age group in 10 year intervals, Sex is a binary is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 6, 2022. ; https://doi.org/10. 1101 /2022 Note that the Poisson distribution is used with binary outcome in order to facilitate the 661 calculation of relative risks. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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Primary case: Not vaccinated \Contact: Not Vaccinated Age of contact (years) 704/1,373

Primary case: Fully vaccinated \Contact: Not Vaccinated Age of contact (years)

Primary case: Not vaccinated \Contact: Fully Vaccinated Age of contact (years)

Primary case: Fully vaccinated \Contact: Fully Vaccinated Age of contact (years) primary case (years) Notes: This table provides number of observations used for estimating the SAR stratified by age and vaccination status in Figure 7