Using Routine Surveillance Data to Estimate the Epidemic Potential of Emerging Zoonoses: Application to the Emergence of US Swine Origin Influenza A H3N2v Virus

Cauchemez, Simon; Epperson, Scott; Biggerstaff, Matthew; Swerdlow, David; Finelli, Lyn; Ferguson, Neil M.

If the detection rate r is known, it is always possible to invert the relationship shown in Figure 2 to derive an unbiased estimator of R. However, assume that r is unknown and that we plan to use estimator 12F, which is unbiased so long as r is small. As the detection rate r increases, so does the bias of estimator 12F. However, for a fixed number of clusters occurring in the study population, larger detection rates increase precision through larger sample sizes. There is therefore a trade-off between the bias and precision of the estimator 12F. This is illustrated in Figure 4A , for a scenario with reproduction number R = 0.5, overdispersion parameter k = 0.5 and where a total of 10,000 clusters occur. In this scenario, the optimum (i.e., minimizing the root mean square error) trade-off in bias versus precision is obtained for a detection rate of r = 1.5%. We find that the optimum detection rate for estimator 12F is a decreasing function of the reproduction number R and the total number of clusters n, but an increasing function of overdispersion parameter k ( Figure 4B ). We also find that the absolute bias at the optimum detection rate remains relatively small (,0.06) ( Figure 4C ). In Figure S5 and Text S1, we show that thinning the data may eliminate the bias of the 12F estimator, though combining information from F and G (see below) is a simpler and more convenient approach to the same goal.