We used data from a study that determined the antibody responses to a number of vaccine and viral antigens in a group of 45 individuals over a period of between 5 and 26 years, with a mean range of about 15.2 years (see [12 (link)] for details). These samples were taken as part of a center-wide, comprehensive program to permit serologic testing of people working in close proximity to nonhuman primates. We focused on the antibody responses to measles, rubella, vaccinia, mumps, and VZV antigens that were elicited either by a live-attenuated vaccine or natural infection, as well as antibodies to tetanus and diphtheria antigens that were elicited by immunization with inactivated protein toxin (i.e., toxoid) vaccines.
Because we wanted to consider the decay of antibody in the absence of boosting, the antibody data were curated to remove spikes due to revaccination or infection as described in more detail previously [12 (link)]. This involved censoring to exclude the following: timepoints for 3 years after immunization, when there was a rapid change in antibody levels [12 (link),16 (link)], seronegative or unvaccinated individuals, and individuals with fewer than 4 contiguous data points. We then kept the time series with the largest number of contiguous data points for the response of each individual to each vaccine or virus antigen.
As previously described, antibody titers were measured using ELISA and calibrated when possible in terms of international units (IUs). This allowed us to rescale the antibody concentration by dividing it by the level at which protection is lost [8 (link),17 (link)–21 (link)]. In our plots and analysis, the magnitude of responses is shown as the log of the scaled titer. We did not have a level at which protection is lost for mumps and VZV, and for these, we scaled against the threshold of detection for the ELISA assay for that antigen. The level of antibody required for protection for different infections was taken from the literature and was assumed to be the same for all individuals—we did not consider variation in the protective threshold between different individuals due to lack of relevant data (seeDiscussion ). Note that we did not consider the absolute magnitude of the antibody response (e.g., moles/L or mg/mL) because the ELISA assays used do not measure this quantity.
Estimating the variability in the magnitude of the responses of different individuals to a given vaccine required taking into account uncertainty in the time of vaccination or infection and the different ages covered by the time series for different individuals. Because we do not find a significant correlation of antibody titer with age (and gender), but do find a strong correlation with time (see analysis in [12 (link)]), we used time rather than age as the main factor governing antibody titer. Because we did not know the time of vaccination, we shifted the time axis so that time equal to 0 corresponded to the mean age of the time series for each individual, and we used the intercept as a summary measure of the average magnitude of the response of the individual. We emphasize that the magnitude is not the peak magnitude just after vaccination or infection but rather the magnitude at the mean timepoint for that time series, which is expected to be many years or decades after vaccination or infection.
Because we wanted to consider the decay of antibody in the absence of boosting, the antibody data were curated to remove spikes due to revaccination or infection as described in more detail previously [12 (link)]. This involved censoring to exclude the following: timepoints for 3 years after immunization, when there was a rapid change in antibody levels [12 (link),16 (link)], seronegative or unvaccinated individuals, and individuals with fewer than 4 contiguous data points. We then kept the time series with the largest number of contiguous data points for the response of each individual to each vaccine or virus antigen.
As previously described, antibody titers were measured using ELISA and calibrated when possible in terms of international units (IUs). This allowed us to rescale the antibody concentration by dividing it by the level at which protection is lost [8 (link),17 (link)–21 (link)]. In our plots and analysis, the magnitude of responses is shown as the log of the scaled titer. We did not have a level at which protection is lost for mumps and VZV, and for these, we scaled against the threshold of detection for the ELISA assay for that antigen. The level of antibody required for protection for different infections was taken from the literature and was assumed to be the same for all individuals—we did not consider variation in the protective threshold between different individuals due to lack of relevant data (see
Estimating the variability in the magnitude of the responses of different individuals to a given vaccine required taking into account uncertainty in the time of vaccination or infection and the different ages covered by the time series for different individuals. Because we do not find a significant correlation of antibody titer with age (and gender), but do find a strong correlation with time (see analysis in [12 (link)]), we used time rather than age as the main factor governing antibody titer. Because we did not know the time of vaccination, we shifted the time axis so that time equal to 0 corresponded to the mean age of the time series for each individual, and we used the intercept as a summary measure of the average magnitude of the response of the individual. We emphasize that the magnitude is not the peak magnitude just after vaccination or infection but rather the magnitude at the mean timepoint for that time series, which is expected to be many years or decades after vaccination or infection.
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