Coefficients for imprinting variables and model comparisons for GAMs fit to participants’ H3N2 HI titers.

(A) The coefficients for the imprinting variables, relative to the reference H3N2 cohort. Each panel in (A) represents different adjustments for age, with “Both” indicating models incorporating both age at sampling and at isolation. Within each panel, the red points and lines depict the coefficients and uncertainty intervals for the non-probabilistic imprinting variable. Red stars highlight coefficients consistent with the imprinting hypothesis (i.e., coefficients for the H1N1 and H2N2 cohorts that are significantly lower than the H3N2 reference cohort). The violin plots show the distributions of 1000 coefficients for the probabilistic imprinting variable, with numbers below indicating the proportion of the 1000 coefficients that are both statistically significant and consistent with the imprinting hypothesis. The orange points and lines show the coefficients for the best model by BIC. See Table S3 in SI for the coefficients for the three best models by BIC. (B) BIC values relative to the model with the lowest BIC, across all models, both without and with (non-probabilistic and probabilistic) imprinting variables. (C) The differences in BICs between models with and without the imprinting variable; negative values suggest better performance of the model with the imprinting variable. The numbers below the violin plots in (C) show the proportions of the comparisons for which the difference in BIC is three or more in favour of the model with the imprinting variable. See Fig S11 in SI for analogous results using deviance explained and root mean square error (RMSE) rather than BIC.

Coefficients for imprinting variables, and model performance comparisons for GAMs fit to simulation output.

The coefficients for the GAMs are for fits to both the null model (without an imprinting mechanism) and the positive control model (including imprinting via increased boosting; Methods and Materials). (A) The coefficients for the imprinting variables, relative to the reference H3N2 cohort. Each panel in (A) represents different adjustments for age, with “Both” indicating models incorporating both age at sampling and at isolation. Within each panel, the red violin plots show the distributions of the coefficients for the non-probabilistic imprinting variable (one for each of the 100 stochastic realisations of the model). The green violin plots show the distributions of 1000 coefficients for the probabilistic imprinting variable. The numbers below the violin plots indicate the proportions of the coefficients that are both statistically significant and consistent with the imprinting hypothesis (i.e., coefficients for the H1N1 and H2N2 cohorts that are significantly lower than those for the reference H3N2 cohort). Orange points and lines indicate the coefficients and 95% confidence intervals for the best models by BIC. (B) BIC values are relative to the model with the lowest BIC, across all models, both without and with (non-probabilistic and probabilistic) imprinting variables. (C) The differences in BICs between models with and without the imprinting variable; negative values suggest better performance of the model with the imprinting variable. The numbers below the violin plots in (C) show the proportions of the comparisons for which the difference in BIC is three or more in favour of the model with the imprinting variable.

Overview of the Fluscape dataset, with emphasis on the patterns of HI titers with age.

The middle panel displays the HI titers predicted for each H3N2 strain as a function of age at isolation, for visit 4 (2014–2015) and lab round 3. The predictions were generated using GAMs fitted independently to each strain, including household ID as a random effect (these differ from the GAM models used in the main analysis, in which all strains were included in the models). Red and grey points indicate the locations of peaks and nadirs in the predicted HI titers for each strain. The diagonal contour lines follow birth cohorts, with thicker lines representing birth cohorts of specific influenza relevance: 1918, 1957, 1968, 1977. For explanation, we select two strains (1972 on the bottom panel and 2002 on the top panel), both highlighted in the heatmap with red dotted lines, and overlay the predicted titers from the GAM on the data used for the fits. The colour of the points in the top and bottom panels indicates the total number of overlaid points. Note the systematically higher titers in individuals who were young when each strain was circulating (as previously observed by Lessler et al. (2012) using a subset of the same data), and how individuals born shortly after the introduction of H2N2 in 1957 appear to have systematically low titers. In an analogous heatmap expressed as a function of age at sampling, the left and right edges of each row would vertically line up.

Proportions of each birth cohort with an initial exposure to each subtype.

These proportions correspond to 2014 in China, as obtained from Gostic et al. (2016). The top panel assumes that participants get infected in their first year of life, while the bottom panel relaxes this assumption, leading to non-zero probabilities of being infected and imprinted to more than one subtype in the years prior to the introduction of a new subtype (Gostic et al., 2016).