In this paper, we have revisited the traditional interpretation of paired serological measurements of influenza antibody titers. Until now, data on 2-fold rises have been largely ignored because of the belief that measurement errors made them unreliable. Although this may be a valid concern if the aim is to get a specific diagnosis for individual cases, we argue that this is less so when the objective is to interpret antibody titer variations at the population level. We have shown that it is possible to quantify measurement errors, and to reconstruct the distribution of paired serology corrected for measurement errors. Our method gave unbiased estimates in a simulation study.
After correction for measurement errors for the Vietnamese data examined here, we found that for some seasons and subtypes the proportions of individuals with 2-fold rises in antibody titers was too large to be explained by measurement errors alone. Estimates of infection attack rates varied greatly depending on whether or not 2-fold rises were included. It is therefore important to determine the biological phenomenon that could cause such increases, in particular whether they are caused by exposure to influenza viruses.
A first hypothesis is that 2-fold titer increases are caused by infection by an influenza virus. In support of this hypothesis, it is clear that a proportion of virologically- or RT-PCR- confirmed influenza cases do not achieve a 4-fold rise in HI titer. This proportion was 27% in our dataset, similar to a large cohort of confirmed pandemic cases in the US 
. However, past work has shown this proportion to be as high as 77% in people who have high pre-existing antibody titers 
, or as low as 10% in patients seeking medical care for pandemic H1N1 infection in 2009 
. It is clear that antibody titer changes following infection vary between individuals and are affected by factors including pre-existing titer and timing of serum collection. In particular, since there is an upper limit to antibody concentrations, individuals with high pre-existing titers are limited in their ability to generate 4-fold rises and may produce only a 2-fold titer increase in response to infection 
. However, the analysis performed here shows that 2 fold titer changes are common even among individuals with low pre-existing titers. Antibody concentrations reach a peak 4–7 weeks after infection and then decay over a period of around six months to a plateau that is maintained for several years 
. Although the profile of HA antibody decay is not well characterised, the probability of detecting 2- or 4- fold rises will vary with the interval following infection. However, in our data the longest interval between the peak transmission period and blood sampling was in season 3, when the proportion of 2-fold titer rises was lowest.
A second hypothesis is that 2-fold rises correspond to infection which is attenuated by mucosal or serological antibodies to homologous or heterologous strains, or by innate or cell mediated immunity. Antibody responses to inactivated influenza vaccines clearly demonstrate the potential for antigenic stimulation without active infection and the phenomenon of boosting of immunity in exposed yet uninfected individuals is well documented for other viruses (e.g.
varicella zoster 
A third hypothesis is that 2-fold rises are an artefact unrelated to influenza infection or exposure. Seasonal variation in titres independent of infection might result from the presence of non-specific inhibitors of agglutinination. For example, this could happen if the circulation of other viruses boosted the immune system, leading to small increases in all antibody titers. In such a scenario, one might expect the effect to be similar on the different subtypes. However, in 2007, a large proportion of individuals exhibited 2-fold increases for H1N1 but not for H3N2 or B, suggesting that this hypothesis is not strongly supported by the data.
It is also important to understand why 2-fold titers changes were prominent during some seasonal influenza epidemics but not during the pandemic. One possibility may be that there was greater antigenic mismatch for some seasonal strains because of unrecognised co-circulation of different influenza strains from those used as antigens in the HI assay. In this situation, anti-HA antibodies generated by infection have lower avidity for the HA of the assay virus. Conversely, original antigenic sin, where an infection results in an anamnestic response and the generation of antibodies directed towards an earlier infecting strain, might also explain 2-fold titer rises in response to infection 
. In all these scenarios however, 2-fold increases would still represent infection by an influenza virus.
It is unlikely that 2-fold increases represent cross-reactivity of HI antibodies to strains of one subtype with strains of other subtypes. This is confirmed by our analysis that did not reject the hypothesis of an absence of cross-reactivity between subtypes.
It is therefore important for future work to determine if 2-fold titer increases represent infection, antigenic stimulation (attenuated infection), or artefact. If influenza infection rates are higher than currently recognised this might change our understanding of influenza transmission and of intra-host and inter-host immune mediated evolutionary pressures, and may have implications for the feasibility of control measures.
In the dataset examined here, 2-fold increases exceeded 4-fold increases for H1N1 in 2008 and H1N1, H3N2 and B in Spring 2009. There was no clear pattern with respect to subtype or strain. The seasonal H1N1 strain circulating in 2008 (A/Brisbane/59/2007) was antigenically distinct from those circulating previously (A/Solomon Islands/03/2006 and A/New Caledonia/20/1999-like), but this strain continued to circulate in Spring 2009. The seasonal H3N2 strain circulating in Spring 2009 (A/Perth/16/2009) was antigenically distinct from the 2007/8 strain (A/Brisbane/10/2007). H3N2 A/Perth/16/2009-like viruses have been difficult to propagate and we had difficulty propagating sufficient virus for the HI assays using A/Perth/16/2009-like viruses isolated from the cohort during the Spring 2009 season. We therefore used a virus isolated from a patient in Hanoi by the National Influenza Center, and propagated in eggs followed by MDCK cells (TX265M2E1) for undertaking HI testing of sera collected in Spring 2009. It is possible that the propagation in eggs this virus underwent might have resulted in some antigenic change, resulting in lower titers in the HI assay. National influenza surveillance data indicates that both influenza B lineages - Yamagata and Victoria- co-circulated during the study period, with the Yamagata lineage dominating in 2007 and 2008 and the Victoria lineage in 2009. For all HI assays, we used the same influenza B virus, which was isolated in 2008 and was characterized antigenically as Yamagata lineage-like, as with all influenza B viruses isolated from the cohort in 2008. While Yamagata viruses dominated the influenza B samples we collected in 2007 and 2008, the Victoria lineage was predominant in 2009. This may be a factor explaining the lower influenza B titer increases seen in that year. If heterogeneities in the proportion of 2-fold titer rises are largely attributable to a poor match between assay antigen and infecting virus, future seroprevalence and seroincidence surveys will need to use a greater diversity of antigens than typically used currently.
There are often strong age-related patterns in influenza serology. Ideally, we would therefore like to fit our statistical model independently for each age group. However, simulation studies indicate that the relatively small number of observations per age group would lead to relatively inaccurate estimates. We have therefore opted for an intermediate estimation strategy. Our statistical model fits a single distribution of true paired serology to all subjects; but since we infer true paired serology for each individual, we can reconstruct a posteriori the distribution of true paired serology for the different age groups. Even with such a conservative approach (i.e. it favours scenarios where the different age groups exhibit similar distributions), we were able to detect clear age-related patterns. In particular, it indicated that age may be another factor that influences the occurrence of a 2-fold rise. Larger sample sizes will be needed to investigate this possibility further.
The presence of relatively large proportions of individuals experiencing a 2-fold increase in antibody titers is not a peculiarity of the Vietnamese data examined here. Similar shifts were observed on data gathered by Cowling et al, with micro-neutralization assays for 2009 H1N1pdm09 influenza and on HI assays for seasonal influenza 
It is well known that there may be substantial within- and between- laboratory variability in HI assays as well as in other serological assays such as virus neutralisation (VN) 
. The level of intra-laboratory variations may depend on both the laboratory and the type of assay used 
. Here, we have introduced an approach that allows controlling for within-laboratory variations. The only additional data needed compared with standard serological surveys is that replicate measurements are performed for a subset of subjects. These replicate measurements allow within-laboratory quantification of variation in assay performance. With this information, it is then possible to reconstruct the distribution of paired serology that is corrected for the estimated level of within-laboratory variations. Although our approach gives a better control on within-laboratory variation, it does not address the problem of between-laboratory variation. The use of standards in bioassays is critical for minimising the impact of the latter problem 
To conclude, while a 4-fold titer increase may be a highly specific diagnostic of infection by an influenza virus for individual cases, this criterion is less justifiable when the objective is to estimate community ARs. Our work shows that requiring a 4-fold titer increase may lead to ARs being substantially underestimated. More research is needed to determine what proportion of 2-fold rises are causally linked to exposure to influenza, and what proportion may be caused by other mechanisms. It will be important to determine whether the high proportion of 2-fold titer increases seen in the settings of Vietnam and Hong Kong 
are also observed in other (e.g. temperate climate) settings.