Estimating and interpreting secondary attack risk: Binomial considered biased

Abstract

The household secondary attack risk (SAR), often called the secondary attack rate or secondary infection risk, is the probability of infectious contact from an infectious household member A to a given household member B, where we define infectious contact to be a contact sufficient to infect B if he or she is susceptible. Estimation of the SAR is an important part of understanding and controlling the transmission of infectious diseases. In practice, it is most often estimated using binomial models such as logistic regression, which implicitly attribute all secondary infections in a household to the primary case. In the simplest case, the number of secondary infections in a household with m susceptibles and a single primary case is modeled as a binomial(m, p) random variable where p is the SAR. Although it has long been understood that transmission within households is not binomial, it is thought that multiple generations of transmission can be neglected safely when p is small. We use probability generating functions and simulations to show that this is a mistake. The proportion of susceptible household members infected can be substantially larger than the SAR even when p is small. As a result, binomial estimates of the SAR are biased upward and their confidence intervals have poor coverage probabilities even if adjusted for clustering. Accurate point and interval estimates of the SAR can be obtained using longitudinal chain binomial models or pairwise survival analysis, which account for multiple generations of transmission within households, the ongoing risk of infection from outside the household, and incomplete follow-up. We illustrate the practical implications of these results in an analysis of household surveillance data collected by the Los Angeles County Department of Public Health during the 2009 influenza A (H1N1) pandemic.

Increased household transmission and immune escape of the SARS-CoV-2 Omicron variant compared to the Delta variant: evidence from Norwegian contact tracing and vaccination data

“…We used binomial regression with a log link to estimate the secondary attack rate (SAR) within households, comparing Delta with Omicron, assuming test activity and case nding did not vary by variant [13]. The binomial regression model was strati ed for different covariates, including vaccination status, age group, and gender, of the contacts and primary cases to nd the relative risk (RR) between them.…”

Increased household transmission and immune escape of the SARS-CoV-2 Omicron compared to Delta variants

“…We used binomial regression with a log link to estimate the SAR within the household, comparing Delta with Omicron, assuming test activity and case finding did not vary by variant 18 as …”

Increased household transmission and immune escape of the SARS-CoV-2 Omicron variant compared to the Delta variant: evidence from Norwegian contact tracing and vaccination data

“…We used binomial regression with a log link to estimate the secondary attack rate (SAR) within households, comparing Delta with Omicron, assuming test activity and case finding did not vary by variant [13]. The binomial regression model was stratified for different covariates, including vaccination status, age group, and gender, of the contacts and primary cases to find the relative risk (RR) between them.…”