Given limited number of useful methods to analyze household transmission data of influenza, House and colleagues went one important step forward. Specifically, they provided a framework that connects the final state of a stochastic epidemic model with a statistical estimation approach so that one can infer the risk of transmission within households using the data stratified by household size, while accounting for differential levels of case ascertainment. Case ascertainment is particularly important when not all suspected cases are laboratory tested for influenza or other respiratory viruses. In the House et al. study , the risk of household transmission, denoted by T, is theoretically regarded as a less biased measure of household transmissibility than the observed 'crude' secondary attack risk (that is, the proportion of household secondary cases among the total of susceptible household members). This is because the final size model using T addresses multiple chains of transmission in households and the dependence of the risk of infection between households . Using the parameter T, one may be able to assess the transmissibility in households without serious bias, such as, for example, those arising from household structure (for example, size and membership), community risk, and tertiary transmission or additional chains of transmission in households. To illustrate their estimation framework, House et al.  used an epidemiological dataset comprising 424 index cases from 424 separate households and their 1612 household contacts in Birmingham, one of the first cities in the UK to be affected by the 2009 pandemic. An overall secondary attack risk of infection was calculated at 39.7% (95% CI 34.9 to 44.0). They also showed that transmission risk at the household level based on laboratory confirmed A/H1N1 cases would be underestimated. A negative correlation between the transmission probability and household size was also identified. The authors also conducted a review of household transmission studies of 2009 A/H1N1 influenza, identifying large variation in estimates of T and secondary attack risks, which could be attributed to differences in household size distribution, underlying demographic characteristics (such as age structure), case ascertainment, and the effects of changes in population behaviors and specific public health interventions .
To the best of our knowledge, the study by House et al.  is the first to use statistical methods to integrate the final size equation, derived by Ball , with empirical household transmission data stratified by household size. Compared to classical models such as those based on chain binomial model or those separating household transmission risk from community risk of infection , the series of studies by Ball and his colleagues clearly addressed the dependence of the risk of infection between households, showing that the so-called community risk of infection is explained by the household size distribution in a community and distribution of infected individuals in those households. In their statistical estimation approach, House and colleagues jointly estimated the transmission probability and the diagnostic performance parameters of differential case definitions to better integrate all the epidemiological data available. Achieving such joint estimation will eventually permit us to precisely estimate the efficacy of antiviral treatments and vaccination without suffering from ascertainment bias.