A total of 3,160 individuals participated in the studies in 2008/09 or 2009/10 including 301 who participated in both studies [16, 17]. Participants were then followed up for three additional years with an average annual drop-out rate of 15% [18]. Based on the surveillance data, there were three epidemics of influenza A(H1N1)pdm09 and three seasonal influenza A(H3N2) epidemics (hereafter abbreviated as H1N1 and H3N2 respectively) in the study period (Figure 1A). Among each of the the 6 epidemics, there are between 1321 and 1851 individuals with at least one mid-/post-epidemic HAI titers among individuals and included in the analysis (Figure S1, Table S1). Figure 1B illustrates titer trajectories for three individuals that are considered uninfected based on the traditional 4-fold rise approach.
HAI titer dynamics
We estimate that, after infection, geometric mean HAI titers are boosted 3.98 (95% CrI: 3.89, 4.07) log2 titers on average, with standard deviation 1.82 (95% CrI: 1.77, 1.88), and 14% (95% CrI: 12%, 16%) of infections are associated with less than 4-fold rises (Figure 1C). For H1N1, a strain change is associated with a mean boost in adults that was 1.26 log2 titers (95% CrI: 0.78, 1.73) higher in epidemic 1 (with strain change; Table S3) than in epidemics 3 and 5 (without strain change; Table S3). The effect was similar in children (1.58 log2 titers; 95% CrI: 1.10, 2.07). For H3N2, the mean boost in epidemic 4 (with strain change; Table S3) was also higher than in epidemics 2/6 (without strain change; Table Sxx): 1.54 log2 titers (95% CrI: 0.73, 2.39) higher for children and 1.45 log2 titers (95% CrI: 0.94, 1.96) higher for adults. For H1N1, the mean boosting in children was 0.64 log2 titers (95% CrI: 0.21, 1.04) and 0.95 log2 titers (95% CrI: 0.41, 1.50) higher than in adults, in epidemic 1 and epidemic 3/5, respectively. There was no difference in boosting in children and adults for H3N2.
After the boost following infection, the HAI titer starts to wane, with a mean waning rate of 14% (95% CrI: 12%, 15%) a year after infection, and a standard deviation of 22% (95% CrI: 21%, 23%). We also observe substantial differences in the waning rate depending on the epidemic (Figure 1D). For H1N1, we estimate that the waning in epidemic 1 (with strain change) is 27% (95% CrI: 11%, 40%) and 53% (95% CrI: 27%, 84%) more than in epidemic 3/5 (without strain change) for children and adults respectively. For H3N2, we estimate that the waning in epidemic 4 (with strain change) is 21% (95% CrI: 8%, 40%) larger than in epidemic 2/4 (without strain change) for children, but no difference for adults. Overall, we find that when the circulating strain is substantially different than the previous ones, HAI titers exhibit larger boost and waning than those seen in other years.
We estimate that the 1-sided probability of a 2-fold error is 2.8% (95% CrI: 2.3%, 3.6%) and 5.5% (95% CrI: 4.9%, 6.1%) for H1N1 and H3N2, respectively. The probability that the measurement is erroneous and that observed HAI titer level is a random value from <10 to 5120 is 3.3% (95% CrI: 2.9%, 3.7%).
Our framework allows us to reconstruct the antibody titer dynamics to identify infections probabilistically, integrating information on observed titers, the boosting and waning distribution, measurement error, and influenza activity. For example, our model suggests that the Child 1 in Figure 1B that has a 2-fold rise in epidemic 1 was likely infected with probability 0.81. Due to irregular seasonality in Hong Kong and unpredictable timing of influenza circulation [12, 19–21], the pre-epidemic titer may be missing and infection may have occurred before the collection of the first sample (Figure S1). For example, Adult 1 in Figure 1B has HAI titer equal to 3 in log2 scale in the first and second sample but we infer that this individual has an 80% chance to have been infected. This is because almost all individuals have an HAI titer <10 before the pandemic while there was also high prevalence of infection in the community during the pandemic (estimates shown in the next section). In contrast, Adult 2 in Figure 1B has the same observed titer pattern in a seasonal epidemic but since the probability of infection in the community is low during this epidemic, it is unlikely this individual was infected (probability of 0.08). These simple examples illustrate the additional insight one can gain from an analysis that goes beyond the 4-fold rise case definition and can integrate additional contextual information.
Using the same technique for each individual, among 9463 person-epidemic investigated over six epidemics, we probabilistically identify 1731 infections (95% credible interval (CrI): 1657, 1791). Among these, 45% of those infections (779; 95% CrI: 736, 807) have no pre-epidemic titers and could therefore not be identified by the traditional 4-fold cutoff point. Among 662 individuals with 2-fold rise in paired sera, we estimate that 24% of those (160; 95% CrI: 139, 192) were infected.