Technical Comments

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

Abstract

Thakkar and McCarthy suggest that periodicity in measles incidence artifactually drives our estimates of a 2- to 3-year duration of measles “immune-amnesia.” We show that periodicity has a negligible effect relative to the immunological signal we detect, and demonstrate that immune-amnesia is largely undetectable in small populations with large fluctuations in mortality of the type they use for illustration.

Previously, we reported evidence for a 2- to 3-year period of “immune-amnesia” (IA) following measles infection (1), in line with experimental data (2, 3) and numerous subsequent human studies (47). This result emerged from the relationship between measles incidence and infectious disease mortality and was consistent across three countries, both pre- and post-vaccination. Thakkar and McCarthy question the IA model (8) on the basis of an epidemiological counterexample and a statistical argument. We show below that their critique is not supported by data.

They point out that if true, IA should manifest in other settings, and suggest Iceland as an appropriate country in which to look for long-term measles IA. However, there are a variety of reasons why IA would not be observable in many settings, including Iceland. As we described (1), effects should be especially evident in countries with relatively low mortality and sufficiently large population sizes to support endemic measles with large outbreaks. Our focus was the United States, the United Kingdom (UK), and Denmark (1).

Between 1900 and 1980, Iceland experienced erratic measles outbreaks, as the population (~200,000) was too small to sustain transmission without stochastic extinction (Fig. 1). During this period, all-cause childhood mortality was high, greater by a factor of 20 to 300 than the infectious disease mortality rates we evaluated previously (1). Note that the combination of high all-cause mortality and small numbers of measles cases (peaking at ~5000 reported childhood infections per outbreak, versus >3 million and >800,000 in the United States and UK, respectively) makes detection of acute measles or IA effects on mortality unlikely, particularly when the mortality evaluated is all-cause [as in (8)] and not infectious disease–specific.

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).

To demonstrate these ascertainment issues, we estimated the expected measles mortality over the time series, using reasonable estimates of the case fatality rates over the time series (i.e., from 1% to 0.5% for acute measles and from 0.5% to 0.25% for IA). The resulting mortality (Fig. 1A) is well within the scale of uncertainty and stochastic fluctuations in the all-cause mortality data. To detect an IA signal requires that variance in mortality rates reflects the underlying biological drivers of mortality (such as the landscape of infectious diseases), not stochastic events. Male-to-female mortality ratios are instrumental here; the ratios should be consistent over time. Large swings—seen in Iceland but not in the UK and United States (Fig. 1C)—suggest that stochastic effects are major drivers of mortality variance, precluding the detection of IA using mortality data.

Thakkar and McCarthy suggest that the relationships we describe might emerge spuriously. Indeed, integrating across past incidence of a regular periodic time course for a duration equal to the periodicity axiomatically smooths the cycles. This can lead to improved regression of cases against integrated incidence, especially in scenarios with a sharp change in incidence. Specifically, if measles dynamics were strictly biennial, summing over 2 years results in two smooth lines (Fig. 2A), one pre- and one post-vaccination, that crudely correlate with declining mortality. Although Thakkar and McCarthy correctly show that the statistical fit for regularly spaced simulated data thus improves with integration, we demonstrate that this consists essentially of joining their midpoints by drawing a line through two highly separated clouds of points (Fig. 2A).

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).

Furthermore, a crucial feature of the real epidemics is that periodicity is not constant, but varies among annual, biennial, and more irregular (vaccine era) epidemics (Fig. 2B). Our IA model with a constant amnesia kernel closely matches short- and long-term fluctuations in the non-measles infectious disease mortality time series in all these eras (Fig. 2B). We further tested whether the inferred IA effect is simply attributable to integrating over a duration equal to the period of the measles incidence curves (8) by randomizing the observed time series while retaining the biennial signal. To do so, we rearranged the incidence data across years in 2-year chunks and reestimated the fit for a range of durations (Fig. 2C). The results never approached the fraction of the variation explained by the observed time series even though the biennial periodicity was retained, making it extremely unlikely that our results emerge simply from smoothing effects (Fig. 2D). Furthermore, although R2 increases as the randomized measles incidence is integrated over durations from 1 to 40 months post-measles, the effect is minuscule [change in R2 = 0.03 (95% CI: 0.02 to 0.04)] compared to the very large effect seen only in the observed data (change in R2 = 0.51; Fig. 2E). Smoothing alone is thus likely to contribute only a small fraction to the improved R2.

Thakkar and McCarthy simulated a random walk around the UK mortality data, finding peak R2 values at IA durations between 18 and 34 months. That the range of durations encompasses the best fit from the observed data is, however, expected because their synthesized mortality essentially noisily recapitulates the observed data, retaining key secular trends in the mortality time series. The 95% CI for the peak R2 for their simulated mortality data (0.28 to 0.71) far exceeds the upper bound around our biennially randomized experiments (Fig. 2D). Crucially, we enforced a correlation of <0.4 with the true incidence, because comparisons with simulations close to the true incidence would provide little power to reject spurious associations. The 95% CI for their simulated data nonetheless remains well below the R2 obtained for the best fit to the true mortality data [R2 of 0.92 for a 27-month duration (1)]. Thus, only the true observed measles time series data best explain the infectious disease mortality.

To conclude, population signatures of prolonged measles IA (1, 3, 4, 7, 9) are most identifiable under low overall baseline mortality, large measles epidemic sizes, and population sizes sufficient to mitigate stochasticity. Consistent results across vaccine eras, and additional tests here, indicate that the estimated duration of a lag between measles incidence and mortality is not a result of smoothing of multiannual dynamics. Although the ultimate test of the IA hypothesis would be individual-scale evidence for reduced ability to detect diverse pathogens after a measles infection, to date no population-level analysis is inconsistent with this proposed effect. Finally, our findings here and in (1) further underscore the importance of measles vaccination as a means to avoid the well-recognized direct burden as well as the indirect IA burden of this infection.

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