060 - The Corrected Average Attack Rate from Measles Among City Children

Today’s post is not directly related to vaccines, but indirectly: it’s about measles epidemiology, or the observation of patterns of measles in populations over time; how many cases, in which ages, when it’s fatal, etc.¹

Specifically, A.W. Hedrich suspected that reports of measles cases in cities didn't always indicate the true level of measles that existed; the reports were incomplete. So he calculated a correction factor that should help health workers determine if their reports were complete, or estimate what the true rate might be.

The rate of measles varies seasonally, attacking more in winter than in summer (like the flu I guess), but it also cycles up and down in what’s called “epidemic swing,” as you can see in Figure 1 from the paper. Sometimes there could be 13 times more cases in one year than in the next.

Figure 1: Reported measles case rates. Baltimore, MD. 1897-1927. Hedrich 1930.

This is because in a high year, many people are infected and become immune naturally, so there aren’t as many susceptible people to be infected the next year. Levels of immunity might even be high enough to produce some herd immunity effect, where the virus can’t transmit from infected people to susceptible people, because the only contact between those groups is via immune people (who block the transmission). So that’s a low year. But as more people are born, the proportion of susceptible people rises until there’s another epidemic. That’s the natural cycle of measles, in cities at least.

This cycle made it difficult to compare between cities though, because obviously comparing a low year in one city to a high year in another would be inaccurate. So it’d be better to compare averages, say over ten years, to even out the variation.

Measles is pretty much a disease of childhood, or at least it was in pre-vaccine days in cities, because hardly anyone avoided it for that long, and generally one time is enough to be immune for life. (Not to say it can’t infect adults if they’re susceptible; see Panum's report on measles in the Faroes to see what the disease could do to a completely susceptible population.²) But in these days, almost everyone in cities had been exposed by age 15, so Hedrich decided that comparing case rates in people under 15 would be the best strategy. This was especially true because including those over 15 could introduce bias in cities that had a lot of immigrants from the countryside, who were often over 15 but still susceptible (since measles didn't spread as well in rural settings due to low population density), so that could inflate the case rate.

Hedrich compared some surveys of different cities, figuring out what proportion of the population had ever been exposed to measles by their 15^th birthday. It was pretty consistent between cities, countries, and over time that this proportion was about 95%.

Figure 2: Measles history rates by age. Hedrich 1930

So one might think, if reports of measles cases over different ages up to 15 don’t add up to 95%, they’re incomplete, and one can calculate a correction factor from that! But one thing this doesn't take into account is the children that have died before reaching age 15, either from measles or from other causes. The 95% figure is based on surveys of living children. So Hedrich looked at some data to see what measles mortality was and if it could affect the correction factor.

He found that in Baltimore from 1906 to 1915, measles killed about 4 out of every 1000 children under 15. The deadliest age was around 1 year old, with about 14 in 10000 dying from measles. This isn't necessarily indicating severity at these ages; it could be that the longer one lived, the more likely one had already survived measles.

Figure 3: Data from paper, figure I made. Deaths from measles per million people in Baltimore at a given age.

But anyway, this allowed calculation of the correction factor, and it turned out that fatal cases of measles didn't really affect it much. Though this wouldn't be the case with diseases that had higher mortality, or even sometimes measles epidemics that were especially deadly (like in Aberdeen, Scotland from 1883 to 1902, where the estimated death rate from measles was 2 of every 100 people; pretty scary).

Using this correction factor, Hedrich calculated with remarkable consistency that on average, 6.5% of city children under 15 get measles each year. He discusses a number of potential confounding factors that could introduce error but decides they don’t change the results significantly. So this could be useful for further study of measles epidemiology.

A number of later papers cite this one as important for later epidemiology, but I think some may have confused this paper with another of Hedrich's, since I didn't find what they say is there in it. Still, it’s interesting:

"Hedrick [sic] demonstrated, in Baltimore, that measles epidemics did not develop when the level of immunity was above 55 per cent. Though all the figures do not necessarily apply to urban areas, his findings do point out that considerably less than 100 per cent of the population need become immune before an epidemic is prevented or halted."³

"Based on the study of Hedrich (1930), Sencer et al. (1967) estimated that in Baltimore during the period 1897-1927 a level of immunity of 55 per cent was sufficient to prevent the development of epidemics."⁴

"The meticulous studies by A.W. Hedrich of measles diffusion in Baltimore from 1897 to 1927 formed the basis for epidemiological studies of measles for nearly 35 years. By carefully tabulating monthly measles rates and correlating them with the proportion of the population under fifteen years of age, Hedrich was able to develop a ratio of susceptible to immune children and thus account for fluctuations in the incidence of measles. It was determined that when the level of natural immunity exceeded 55 percent, the diffusion rate decreased. However, children escaping epidemics were still susceptible, and as more children were born, the number of susceptibles was augmented. Increased numbers of susceptibles led, in turn, to further epidemic fluctuations in measles."⁵

Citations:

1. Hedrich, A. W. The Corrected Average Attack Rate from Measles Among City Children. Am. J. Epidemiol. 11, 576–600 (1930).

2. Panum, P. Observations made during the epidemic of measles on the Faroe Islands in the year 1846. Bibiliothek for Laeger, Copenhagen 3R, 270–344 (1847).

3. Kogan, B. A. et al. Mass measles immunization in Los Angeles County. Am J Public Health Nations Health 58, 1883–1890 (1968).

4. Griffiths, D. A. The Effect of Measles Vaccination on the Incidence of Measles in the Community. Journal of the Royal Statistical Society. Series A (General) 136, 441–449 (1973).

5. Pyle, G. F. Measles as an Urban Health Problem: The Akron Example. Economic Geography 49, 344–356 (1973).