Estimation of the Household Secondary Attack Rate: Binomial Considered Harmful

One of the primary goals of household studies of infectious disease transmission is to estimate the household secondary attack rate (SAR), the probability of direct transmission from an index case A to a susceptible household member B during A's infectious period. In a household with m susceptibles and a single index case, the number of secondary infections is often treated as a binomial(m, p) random variable where p is the SAR. This assumes that all subsequent infections in the household are transmitted directly from the index case. Because a given transmission chain of length k from A to B has probability p^k, it is thought that chains of length k > 1 can be ignored when p is small. However, the number of transmission chains of length k from A to B can be large, so the total risk of infection through any chain of length k can be much greater than p^k. In simulations, we show that estimation of the SAR using a binomial model is biased upward and produces confidence intervals with poor coverage probabilities. Accurate point and interval estimates of the SAR can be obtained using chain binomial models or pairwise survival analysis.