Research ArticleEpidemiology

The impact of past vaccination coverage and immunity on pertussis resurgence

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Science Translational Medicine  28 Mar 2018:
Vol. 10, Issue 434, eaaj1748
DOI: 10.1126/scitranslmed.aaj1748
  • Fig. 1 Pertussis incidence data in Massachusetts, United States, 1990–2005.

    The figure displays temporal trends of age-specific pertussis incidence data. (A) Monthly case reports by age group. (B) Annual case reports (per 100,000) by age group. The black line represents the overall incidence. (C) Case fraction among age groups. (D) Cumulative case fraction among age groups. For each age group on the x axis, the corresponding value on the y axis represents the fraction of cases of lower or equal age. Each line represents a distinct calendar year.

  • Fig. 2 Testing of transmission model.

    The figure shows several analyses of the model fit to the observed incidence data. (A) Annual case reports (thick lines), five stochastic realizations (thin lines), and prediction range (gray area) from 1000 stochastic realizations of the model. These are not one-step-ahead predictions; simulations were started in 1990, with initial conditions fixed by conditioning on the first data point (see Model assessment in Supplementary Materials and Methods). The y axis differs between panels for visual clarity. (B) Quantitative comparison of the agreement between model and data based on 1-month-ahead predictions. Each point is colored according to the age group. The observed monthly cases (x axis) and the simulated monthly cases (y axis) were calculated by averaging across 5000 stochastic realizations. The dashed gray line has slope 1 and intercept 0, corresponding to a perfect fit. The overestimation at low case numbers is due to the fact that predictions are not single realizations but expectations of non-negative random variables and, as such, are bounded away from 0 (see fig. S11 for the comparable figure on simulated data). The corresponding generalized R2—measuring the proportion of variance explained by the model to that not explained by age alone—is 0.35. (C) Predictability as a function of the generation time. For each generation time, the figure shows the distribution of R2 for 100 synthetic data sets, generated assuming the true model is known (see fig. S10). The dashed gray line indicates the R2 obtained by comparison with the real data. (D) Quantitative comparison of the agreement between model and data based on 6-month-ahead predictions started annually in August (R2 = 0.40; see figs. S12 and S13 for values of R2 calculated at other forecast horizons and other base months). For visual clarity, the y axis does not start at 0 in (A) and (C).

  • Fig. 3 Dissecting pertussis epidemiology in Massachusetts.

    (A to D) Model hindcasts during 1990–2005. The panels represent the filtering means (that is, the average predicted values at each time conditioned on all the data up to that time) for several state variables: naïve infections (A), post-vaccine infections (B), fraction susceptible to a post-vaccine infection (C), and fraction recovered (D). (A and B) Total predicted infections, before applying the reporting model. (E) Model hindcasts before 1990. Five stochastic realizations of the total incidence (naïve plus post-vaccine infections) are presented. The dotted line at year 1940 indicates the start date of mass vaccination assumed in the model. In the absence of immunization data before 1970, we assume that the vaccine coverage had ramped up between 1940 and 1955 (see Model formulation in Materials and Methods). For visual clarity, the y axis does not start at 0. (F) Comparison of model predictions with empirical studies that quantified DTaP vaccine failure by estimating relative changes (over age) in the odds of acquiring pertussis. We simulated the waning model (with identical wP- and DTaP-derived immunity) during 2006–2015 and used log-linear regression to calculate the yearly relative change (over age) in the odds of acquiring pertussis in children aged 5 to 10 years, that is, 0 to 5 years after receipt of the fifth vaccine dose (see model predictions in the DTaP era in Materials and Methods). The distribution is based on 104 simulations, accounting for parametric uncertainty by sampling from the bootstrap distribution. Also presented are estimates from three empirical studies in the United States [Klein et al. (46), Misegades et al. (48), and Tartof et al. (49)] and from a meta-analysis [McGirr and Fisman (47)].

  • Fig. 4 Predicted impact of single-booster vaccination.

    Simulations of the waning model were run until the end of 2005, at which point a 25% fraction of susceptible individuals in a target age group (5 to 10, 10 to 20, 20 to 40, or ≥40 years old) was moved to the vaccinated class. The model was run for the subsequent 10 years (2006–2015), and the age-specific total annual infections (that is, naïve and post-vaccine infections, calculated before applying the observation model) were compared to a control scenario without booster vaccination. Each boxplot is based on 104 stochastic simulations, accounting for parametric uncertainty of the waning model by sampling parameters from the bootstrap distribution. For each intervention, the number indicates the relative difference between the median simulated incidence and that of the control scenario. The figure shows the predicted impact in unvaccinated infants aged 0 to 4 months, the age group most at risk of severe disease (see fig. S14 for the corresponding figure in every age group). For visual clarity, the y axis does not start at 0.

  • Table 1 Model comparison.

    The maximum likelihood estimates (95% CI) are presented for the stochastic variant of the models, estimated using the MIF algorithm. The best AIC value is indicated in boldface. SE, standard error.

    QuantityNo-loss modelLeaky modelWaning modelWaning+Leaky model
    log L−3726.9 (SE: 0.4)−3664.9 (SE: 0.9)−3594.5 (SE: 0.6)−3598.5* (SE: 1.8)
    AIC7474735672157217*
    ΔAIC25914102
    Rp2.4 (1.8, 2.7)1.6 (1.3, 2.2)1.8 (1.5, 2.0)1.8 (1.6, 2.0)
    R013.6 (7.5, 23.0)12.6 (9.0, 19.4)10.1 (6.5, 17.2)9.1 (5.3, 16.2)
    Vaccine impact0.85 (0.70, 0.95)0.90 (0.81, 0.95)0.85 (0.75, 0.93)0.83 (0.70, 0.92)

    *Because the two models are nested, the likelihood of the full model should be higher or equal to that of the waning model. The small difference indicates that the MLE of the leakiness for the full model is 0. Consequently, the AIC was calculated with the likelihood of the waning model.

    Supplementary Materials

    • www.sciencetranslationalmedicine.org/cgi/content/full/10/434/eaaj1748/DC1

      Materials and Methods

      Fig. S1. Pertussis transmission model schematic.

      Fig. S2. Pertussis vaccine coverage in Massachusetts.

      Fig. S3. Demographic data in Massachusetts.

      Fig. S4. Age-specific contact matrix.

      Fig. S5. Monthly reported cases by age group.

      Fig. S6. Age-specific seasonality in reported cases.

      Fig. S7. Cross-correlations between age groups, with age group 0 to 1 year old taken as the reference age group.

      Fig. S8. Estimated seasonal forcing in children aged 5 to 10 and adolescents aged 10 to 20.

      Fig. S9. Contact matrix in Massachusetts.

      Fig. S10. One hundred data sets of monthly reports generated for the simulation study.

      Fig. S11. Quantitative comparison of model-data agreement for different generation times.

      Fig. S12. Model predictive ability at different forecast horizons and base months, with R2 calculated on log-transformed data and model predictions.

      Fig. S13. Model predictive ability at different forecast horizons and base months, with R2 calculated on raw data and model predictions.

      Fig. S14. Impact of single-booster vaccination in different age groups.

      Table S1. Timeline of pertussis surveillance effort and of pertussis vaccination in Massachusetts.

      Table S2. Estimates of age-specific reporting probabilities.

      Table S3. Age-specific trends (SEs) estimated by Poisson regression.

      Table S4. Fixed model parameters.

      Table S5. Parameter ranges used to generate starting parameter sets for trajectory matching.

      Table S6. Parameter estimates of the deterministic variant of the base model (similar DTaP- and wP-derived immunity, perfect infection-derived immunity).

      Table S7. Parameter estimates of the stochastic variant of the base model (similar DTaP- and wP-derived immunity, perfect infection-derived immunity).

      Table S8. Parameter estimates with a contact matrix in Massachusetts.

      Table S9. Parameter estimates of models with identical infection- and wP-derived immunity but separate DTaP-derived immunity.

      Table S10. Parameter estimates of an extension of the base model, with separate primary vaccine failure for wP and DTaP.

      References (6471)

    • Supplementary Material for:

      The impact of past vaccination coverage and immunity on pertussis resurgence

      Matthieu Domenech de Cellès,* Felicia M. G. Magpantay, Aaron A. King, Pejman Rohani

      *Corresponding author. Email: matthieu.domenech-de-celles{at}pasteur.fr

      Published 28 March 2018, Sci. Transl. Med. 10, eaaj1748 (2018)
      DOI: 10.1126/scitranslmed.aaj1748

      This PDF file includes:

      • Materials and Methods
      • Fig. S1. Pertussis transmission model schematic.
      • Fig. S2. Pertussis vaccine coverage in Massachusetts.
      • Fig. S3. Demographic data in Massachusetts.
      • Fig. S4. Age-specific contact matrix.
      • Fig. S5. Monthly reported cases by age group.
      • Fig. S6. Age-specific seasonality in reported cases.
      • Fig. S7. Cross-correlations between age groups, with age group 0 to 1 year old taken as the reference age group.
      • Fig. S8. Estimated seasonal forcing in children aged 5 to 10 and adolescents aged 10 to 20.
      • Fig. S9. Contact matrix in Massachusetts.
      • Fig. S10. One hundred data sets of monthly reports generated for the simulation study.
      • Fig. S11. Quantitative comparison of model-data agreement for different generation times.
      • Fig. S12. Model predictive ability at different forecast horizons and base months, with R2 calculated on log-transformed data and model predictions.
      • Fig. S13. Model predictive ability at different forecast horizons and base months, with R2 calculated on raw data and model predictions.
      • Fig. S14. Impact of single-booster vaccination in different age groups.
      • Table S1. Timeline of pertussis surveillance effort and of pertussis vaccination in Massachusetts.
      • Table S2. Estimates of age-specific reporting probabilities.
      • Table S3. Age-specific trends (SEs) estimated by Poisson regression.
      • Table S4. Fixed model parameters.
      • Table S5. Parameter ranges used to generate starting parameter sets for trajectory matching.
      • Table S6. Parameter estimates of the deterministic variant of the base model (similar DTaP- and wP-derived immunity, perfect infection-derived immunity).
      • Table S7. Parameter estimates of the stochastic variant of the base model (similar DTaP- and wP-derived immunity, perfect infection-derived immunity).
      • Table S8. Parameter estimates with a contact matrix in Massachusetts.
      • Table S9. Parameter estimates of models with identical infection- and wP-derived immunity but separate DTaP-derived immunity.
      • Table S10. Parameter estimates of an extension of the base model, with separate primary vaccine failure for wP and DTaP.
      • References (6471)

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