# Household transmission of the SARS-CoV-2 Omicron variant in Denmark

### Research design and participants

The Delta VOC has been the dominant variant in Denmark since July 2021. The first Danish case infected with the Omicron VOC was discovered on November 22, 202118and the community transfer was in place at the beginning of December 202119. On December 8, the Danish authorities stopped the intensive contact investigation of close contacts for cases specifically contaminated with the Omicron VOC. We therefore chose a study period starting on December 9, 2021, when cases of both variants were treated approximately equally, reducing the bias from the previously intensified contact tracing and active case finding of the Omicron VOC.20. The end of the admission period for primary cases was set for December 15, with household contacts being followed up to 7 days after the primary case, i.e. until December 22, 2021. We chose this as the end of our study period because the Christmas holidays start in Denmark often on December 23 and often include extended family visits, interrupting the typical transmission pattern within households. For additional information on the number of new cases, the proportion of Omicron and the number of tests taken in Denmark in December 2021, see Appendix Section 1.

For this study we used Danish registry data. All persons in Denmark have a unique identification number, which allows cross-linking between administrative registers. With this we obtained information at person level on all residential addresses from the central register of persons, complete data on all antigen and RT-PCR tests for SARS-CoV-2 from the Danish microbiological database (MiBa21), and all vaccination data from the Danish vaccination register22.

We identified households in Denmark using their unique residential address and assigned the same household identifier to all individuals registered at that address: this was used to determine household size. We only included households with 2-6 members to exclude healthcare facilities and other places where many individuals share the same address.

We defined a primary case as the first person in a household to test positive with an RT-PCR test within the study period. During the study period, we followed all the tests of other household members. A secondary case was defined by a positive RT-PCR test or a positive antigen test23. Nearly all samples that tested positive by RT-PCR were then tested by Variant PCR to determine the VOC. to decide24 (Appendix Table S1 and Fig. S1). Based on the result of the variant PCR test of the primary case, we classified households as associated with either the Omicron or the Delta VOC. The Delta VOC has been the dominant variant in Denmark since early July 2021, accounting for almost all positive RT-PCR samples August-November 202125. We excluded households with a positive RT-PCR test 60 days prior to the primary case and households where the primary case was equivocal because two individuals tested positive on the same day.

We classified individuals into three groups: (i) unvaccinated; (ii) fully vaccinated; or (iii) a booster vaccination. The definition of fully vaccinated included subjects infected more than 14 days previously, but was further defined as follows according to the vaccine used: 7 days after the second dose of Comirnaty (Pfizer/BioNTech); 15 days after the second dose of Vaxzevria (AstraZeneca); 14 days after the second dose of Spikevax (Moderna); 14 days after vaccination with Janssen (Johnson & Johnson); 14 days after the second cross-vaccination dose. Booster vaccination was defined as 7 days after the booster vaccination26, 27. On December 22, 2021, the distribution of vaccines in Denmark was: 85% Comirnaty, 14% Spikevax, 1% Janssen and about 0% AstraZeneca28. All other individuals, including 59 partially vaccinated individuals, were considered unvaccinated.

### static analysis

The causal effect of household exposure to the Omicron VOC rather than the Delta VOC on the SAR may be obscured. This is apparent from the difference in characteristics between households exposed to the Omicron and the Delta VOC, the latter of which was more widespread at the start of the study period (Table 1 and appendix figure S1b). We assume that these differences are caused by the time-space patterns of transmission of the Omicron VOC when it was first introduced. A causal interpretation of our findings depends on the assumption that all effects of the non-random assignment of variants to households are intercepted by the observed household characteristics. The causal assumptions are described in Appendix Section 2.

We defined the secondary attack rate (SAR) as the proportion within the household of contacts with households defined as secondary cases16. Adjusted odds ratios (OR) of infection were estimated using multivariate logistic regression models with the binary outcome of the test result of each household contact as the response variable and the household variant (Omicron vs Delta VOC) as the main explanatory variable of interest. Variables representing age and gender of the primary case, age and gender of household contact, and household size (2-6 persons) were included as additional explanatory variables to account for confounding factors . To test whether the vaccine status provided differential protection against the Omicron and Delta VOC, we included an interaction term between the vaccination status of primary cases and contacts and the variant. We found no evidence of an interaction between vaccination status of primary cases and the variant (P = 0.14). In particular, we estimate the following equation:

$${{\log }}\left(\frac{{{\Pr }}({y}_{c,p}=1)}{1-{{\Pr }}({y}_{c ,p}=1)}\right)= {{{{{\rm{Constant}}}}}}}+{{{{{{\rm{Variant}}}}}}}}}_{ p}+{{{{{\rm{VaccinStatu}}}}}}}{{{{{\rm{s}}}}}}}_{c} \\ +{{{{{{ { {\rm{Variant}}}}}}}}_{p}\times {{{{{{\rm{VaccineStatu}}}}}}}}{{{{{\rm{s}}} } }}}_{c}+{{{{{{\rm{VaccineStatu}}}}}}}{{{{{\rm{s}}}}}}}}_{p} \\ +{ {{{{\rm{Ag}}}}}}}{{{{{\rm{e}}}}}}}_{p}+{{{{{{{\rm{ Sex} }}}}}}}_{p}+{{{{{\rm{HouseholdSiz}}}}}}}{{{{{\rm{e}}}}}}}}_{ p} +{{{{{\rm{Ag}}}}}}}{{{{{\rm{e}}}}}}}_{c}+{{{{{{{{ \rm{ Gender}}}}}}}}_{c},$$

(1)

Where Yesc,p equals one if the contact c tested positive 1-7 days after primary case exposure p, otherwise zero. Variantp determines whether the primary case p was infected with Omicron or Delta. Vaccine status represents the fixed effects of vaccination status (categorical variable) for the primary case p and the contact person c. Age represents fixed effects of age in 10-year intervals (categorical variable), Gender represents fixed effects of gender and HouseholdSize represents fixed effects of household size (categorical variable). Cluster robust standard errors were used in household level clustering by using Taylor series linearization to estimate the covariance matrix of the regression coefficients29.

To support the main analysis, we also performed a number of additional analyses. To test the robustness of the findings, we compared different specifications of the main logistic regression model (Appendix Section 4.4). To investigate the possible mediating role of viral load of primary cases infected with the Omicron VOC relative to the Delta VOC, we plotted the distributions of cycle thresholds (Ct) for each variant (Appendix Fig. S3). We also investigated to what extent the Ct value of the primary case could explain the difference in transmission between the variants (appendix table S21). Our research is based on the assumption that we correctly distinguish primary cases from secondary cases, and that secondary cases of households are infected by the primary case and not by the outside community. To assess this potential misclassification of cases, we performed a series of robustness checks (Appendix Section 4.2). First, to investigate the possible role of differential occurrence of tertiary cases in different variants, we compared the relative SAR between two-person and multi-person households, as tertiary cases are not possible in two-person households. Second, to investigate the possible role of primary case misclassification, we took advantage of the fact that a large proportion of the contacts in our sample were tested multiple times. Because contacts without a test or secondary cases that tested positive on the first test could potentially be the true primary case, we limited our sample to only households where all contacts tested negative after the point where the primary case tested positive. Third, to investigate the possible misclassification of secondary cases infected by the outdoor community and not by the household, we estimated the probability that secondary cases were infected with the same variant as the primary case. In addition, to maximize the likelihood of identifying misclassification, we focused on households infected with a variant that was different from the variant most prevalent in their corresponding location.

Our study also relies on variant PCR testing to determine whether each primary case was infected with the Omicron or Delta VOC. To investigate whether there was bias in the selection of samples for variant PCR testing, we examined the probability of sampling for variant PCR based on the Ct value and age of the sample (Appendix Fig. S1). Furthermore, we validated the variant PCR using whole genome sequencing data (Appendix Table S5). Finally, we tested the robustness of household contacts that tested and tested positive by using only RT-PCR tests, which have higher sensitivity and specificity than antigen tests (Appendix Fig. S7).

### Ethical Statement

In this study only data from the national registers was used. Under Danish law, this type of research does not require ethical approval. All data management and analysis was performed on the limited research servers of the Danish Health Data Authority with project number FSEID-00004942. The survey contains only aggregated results and no personal data.