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Response to Comment on “Long-term measles-induced immunomodulation increases overall childhood infectious disease mortality”

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Science  12 Jul 2019:
Vol. 365, Issue 6449, eaax6498
DOI: 10.1126/science.aax6498

Figures

  • Fig. 1 Measles and childhood mortality among children less than 10 years of age in Iceland, 1900–1975.

    (A) All-cause deaths (left) and death rates (right) among children under 10 years of age in Iceland (green shading), and expected acute measles-associated deaths (dark blue shading) and expected deaths associated with long-term measles-induced IA (light blue shading with black outline). Acute measles-associated deaths and deaths associated with IA were calculated from the measles incidence or prevalence of IA curves shown in (B). Mortality associated with acute measles infections (dark blue) was calculated assuming a reasonable measles case fatality rate that decreased linearly from 1% to 0.5% over the time series. Mortality-associated IA (light blue with black outline) was calculated assuming a (liberally high) mortality rate that decreases from 0.5% to 0.25% risk of mortality per person-year with IA. (B) Measles quarterly case counts (left) and quarterly incidence (right) are shown in dark blue shading; calculated numbers of children (left) or prevalence (right) of measles-induced IA are shown in light blue shading. IA curves were calculated assuming a 30-month duration of post-measles IA effects. Measles epidemic sizes were provided by Thakkar and McCarthy (8); childhood case counts were calculated after adjusting for expected spreading of total cases across age classes due to low seroprevalence even among older adults because measles was not endemic in Iceland (10). The proportion of total measles cases attributed to children under 15 years of age was 58% leading up to 1945 and 85% after 1945 (11); the increase after 1945 accounts for increased incidence in the post-1945 era, thereby concentrating cases among the young. Sensitivity analysis with as many as 100% of cases occurring exclusively in children over the time series showed no important differences. (C) Ratio of male to female mortality rates over time for children ages 1 to 4 (left) and 5 to 9 (right) in Iceland (all-cause mortality), England and Wales (infectious disease deaths only), and the United States (infectious disease deaths only).

  • Fig. 2 Relationship between measles and childhood mortality.

    (A to C) Data in (A) represent synthesized biennial measles epidemics including introduction of measles vaccination. Data were synthesized as in Thakkar and McCarthy (8), with measles outbreaks modeled as Gaussian distributions with 2-month standard deviations and synthesized to occur every 2 years, and mortality modeled assuming a linearly decreasing function with time over the duration of the time series. Data in (B) are derived from true reported measles and mortality time series (1) for England and Wales in children ages 1 to 9 years. Data in (C) derive from the same sources as in (B), except that the measles epidemic time course is randomized in biennial chunks (i.e., 2-year intervals are kept intact) to rearrange the order of measles outbreaks over the time series while preserving biennial dynamics; (C) is a single representative example from 200 distinct randomizations, summarized in (D) and (E). In (A) to (C), the upper two panels assume no long-term IA effects of measles; the lower two panels assume a duration of IA that persists for 24 months (A) or 27 months [(B) and (C)]. The left panels show measles incidence (solid gray lines), prevalence of measles IA (gray shaded region), mortality (dashed black line), and predicted mortality with 95% prediction interval (solid blue line and blue shaded region, respectively). Predictions shown in the left panels were based on the regressions [displayed in the right panels, as in (1)] of mortality versus measles incidence without long-term effects (upper panel) or versus calculated prevalence of IA (lower panel) for each dataset in (A) to (C). (D) Curves for the fit (R2) between childhood mortality and measles incidence derived from calculating the R2 at increasing durations of IA for the actual England and Wales mortality and measles data shown in (B) (blue curve) or from 200 “biennially constrained” randomizations of the actual measles incidence time series (gray lines with peak R2 per curve highlighted by a small dot). Annual (not biennially constrained) randomizations were reported in (1) with similar effect. The black curve represents the R2 curve for the particular randomization of the measles data shown in (C). The blue and black dots highlight the R2 corresponding to the regressions in (B) and (C), respectively. The 95% CI for the peak R2 across the randomized time series is 0.02 to 0.31. The R2 for the true time series is 0.91. (E) Mean change in R2 (and 95% CI) at each IA duration (relative to no IA) across the 200 randomized time series are shown by the gray bars [mean R2 = 0.03 (0.02 to 0.04) at 27-month IA]. The change in R2 for the true time series is in blue (peak change in R2 = 0.51).

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