Estimation of the incubation period of influenza A (H1N1-2009) among imported cases: addressing censoring using outbreak data at the origin of importation

Empirical estimates of the incubation period of influenza A (H1N1-2009) have been limited. We estimated the incubation period among confirmed imported cases who traveled to Japan from Hawaii during the early phase of the 2009 pandemic (n=72). We addressed censoring and employed an infection-age structured argument to explicitly model the daily frequency of illness onset after departure. We assumed uniform and exponential distributions for the frequency of exposure in Hawaii, and the hazard rate of infection for the latter assumption was retrieved, in Hawaii, from local outbreak data. The maximum likelihood estimates of the median incubation period range from 1.43 to 1.64 days according to different modeling assumptions, consistent with a published estimate based on a New York school outbreak. The likelihood values of the different modeling assumptions do not differ greatly from each other, although models with the exponential assumption yield slightly shorter incubation periods than those with the uniform exposure assumption. Differences between our proposed approach and a published method for doubly interval-censored analysis highlight the importance of accounting for the dependence of the frequency of exposure on the survival function of incubating individuals among imported cases. A truncation of the density function of the incubation period due to an absence of illness onset during the exposure period also needs to be considered. When the data generating process is similar to that among imported cases, and when the incubation period is close to or shorter than the length of exposure, accounting for these aspects is critical for long exposure times.