Factors Associated With Measles Transmission in the United States During the Postelimination Era

Key Points Question What are the factors causing the transmission of measles in long-standing measles control programs? Findings This cross-sectional study found that lack of vaccination and birth on or after 1957, as well assortative transmission by age (particularly among school-aged children), are the primary factors associated with measles transmission in the United States. Although current measles vaccines are known to be highly effective in decreasing susceptibility to measles, these analyses shed light on the degree by which vaccination also limits measles transmission. Meaning The findings underscore the importance of maintaining homogenous, high, 2-dose measles vaccine coverage, especially among school-aged children, to sustain elimination of measles in the United States.

The probability, , that case was infected by case is where the sum in the denominator is over all potential infectors k of case j.
The expected value of the case reproduction number for case is = ∑ . The expected value of the case reproduction number for a set, , of cases is = ∑ ∈ ⁄ .
Higher moments of the reproduction number for a set of cases may be easily estimated from a generating function, as follows. The probability that case was infected by one of the cases in is = ∑ ∈ . Define the generating function (2) The coefficient of in ( ) is the probability that the cases in infected exactly cases in the set . (The sets and need not be mutually exclusive.) Numerical evaluation of the polynomial coefficients in ( ) is straightforward. Let ( ) = ∑ . Then, and var( ) = 1 ∑ 2 − ( ) 2 .
The cumulative probability distribution is = ∑ ≤ . The -th quantile of the reproduction number is the smallest value of where ≥ .
A likelihood based estimation of the reproduction number and its credible bounds proceeds as follows. If the number of transmissions due to a case is assumed to follow a Poisson distribution with mean , and cases are observed to result in transmissions, then the normalized likelihood of follows Γ( + 1, ), a gamma distribution with shape + 1 and rate . It follows that follows the distribution ∑ Γ( + 1, )/ . Credible intervals of are given by appropriate quantiles of the distribution.
Although we identified four explanatory variables to be independently associated to measles transmission, incorporating them into the weighting procedure required some consideration. Some of these characteristics are expected to be related more to contact patterns than to an intrinsic capacity to transmit the virus, e.g., age-specific transmission might be more influenced by social contacts, while being vaccinated might also affect communicability by conferring some level of protection against symptoms. Because the procedure weights transmissibility by the characteristic of the infector and does not account for levels of susceptibility among contacts, the adjustment might not be applicable to factors that impact transmission as a result of a person's interactions. For this reason, due to concerns for collinearity, and because initial unadjusted results indicated differences in transmissibility were more marked based on vaccination and birth pre-vaccination, we chose to adjust our base analyses by these two factors. However, sensitivity analyses performed including more of these characteristics in the weighting procedure showed that patterns of transmissibility in more fully adjusted models were similar to those seen with our base analyses (eTables [4][5][6].

Adjustment of transmissibility based on characteristics of cases
The weights of cases with certain transmissibility characteristics α are assumed to be of the form = where is a transmissivity coefficient determined by the characteristics α of the primary cases (e.g., vaccination status, etc.), and are unknown. A self-consistent method to estimate the relative values of these coefficients is as follows. Assuming that the expected reproduction number for a case or a set of cases is proportional to the transmissivity coefficient for the case or set of cases, the relative values of the transmissibility coefficients may be estimated by solving where is number of cases with a given characteristic or set of characteristics α, is their transmissivity coefficient, and the sum is over all cases with these characteristics, and all cases that they could have infected.
Since only the relative values of the matter, one of them, say may be arbitrarily set to 1. Initiate all the to 1; in the next iteration, estimate replace the estimated on the right hand side and iterate until the estimates converge.

eResults. Comparison of Unadjusted and Adjusted Estimates of R
To investigate the effect of the weighting procedure that adjusts the relative transmissibility of cases presenting in a single day based on certain characteristics of these cases, we compared unadjusted estimates, to adjusted estimates including an increasing number of covariates in the weighting procedure. Results are shown in eTable 4-6.

Choice of the measles serial interval
Estimates of the measles case reproduction number, R, were derived from an existing algorithm 3,4 that uses the case incidence time series data (epidemic curves) and the distribution of the serial interval (the time between the onset of symptoms in primary cases and the secondary cases they generate). Our base analyses used a serial interval for measles derived from household transmission studies with a gamma probability distribution and a mean of 11·1 days and standard deviation of 2·47 days. 5 We also ran the analyses using two other (lower and higher) serial interval estimates reported in the literature. 9 Results are shown in eTables 7-9; base analyses results are shown for comparison.

Width of the time window for allowable connections to be made between consecutive cases.
When two consecutive cases in a chain of transmission are reported to be too near or distant from each other in regards to the number of days expected by the known distribution of the serial interval, this could be the result of either an unidentified common ancestor to these two cases, or an unidentified case between these two cases. In these scenarios, the algorithm might assign these cases as a transmission pair even though it might have been an issue of underreporting. To account for this, we excluded putative transmissions outside the observed range of reported serial intervals (approximately from 6 through 18 days), 9 which was also equivalent to the central 95% confidence interval (CI) profile of the serial interval we used. Here we examine results including all putative connections (no restriction analyses). Results are shown in eTables 10-12; the base analyses results are shown for comparison. The median age is based on 2215 measles case-patients. c Measles vaccine was first licensed in the United States in 1963; persons born before 1957 are likely to have been infected naturally and are thus considered to have acceptable presumptive evidence of measles immunity in the United States. d Internationally imported cases are persons who acquired measles outside of the United States and brought their infection into the United States; i.e., they were outside the United States during their exposure period (7-21 days before rash onset), had rash onset within 21 days of entry into the United States, and had no known exposure to measles in the United States during that time. e U.S.-acquired are persons who had not been outside the United States during the 21 days before rash onset or who were known to have been exposed to measles within the United States. f Categorized as either U.S.-resident or foreign visitor (e.g., international tourists and students, new international adoptees, recent immigrants). g Of a measles-containing vaccine; doses were counted if given at least one maximum incubation period (21 days) prior to the onset of rash. h Ten measles case-patients were reported to have received three doses, two to have received four doses, and one to have received five doses of a measles-containing vaccine. i Previous studies indicate reduced antibody responses and increased susceptibility to measles when the first dose is given before 15 months of age (as opposed to when given at 15 months of age or older); the age at first dose was 6-8 months for 8 cases, 9-11 months for 6 cases, 12-14 months for 37 cases, 15-23 months for 21 cases, and 24-71 months for 19 cases. j Time since last documented dose of a measles-containing vaccine; twelve years was the median value of time since vaccination. k E.g., otitis media, diarrhea, vomiting, dehydration, pneumonia, thrombocytopenia, encephalitis, and death. l Cases in a single chain of measles transmission that were not genotyped were assigned the same genotype as other cases in the chain. The duration of a chain of transmission was calculated as the difference between the dates of rash onset of the first and last cases. c Seventeen or 74% of the 23 superspreading events occurred either in the first or second day of the outbreak. d Other reported primary settings: Workplace (1), airplane (1), childcare (2), church (3), community (4)

eFigure. Outbreak Transmission Matrix
A representation of the transmission matrix for a single outbreak showing the day of rash onset of primary cases in the horizontal axis, and the day of rash onset of secondary cases in the vertical axis. The squares represent all possible secondary cases arising from the primary case presenting that day; the probability of each primary case infecting (i.e., being the ancestor to) the secondary case are shown as squares in a gray-scale, with darker squares being the more likely ancestor. The dashed lines indicate the time lag corresponding to the central 95% confidence interval of the serial interval distribution, based on the rash onset of each primary case; thus darker squares (likely primary-secondary pairings) fall within these limits. The circles represent the reproduction number, R, assigned to each primary case, calculated as the sum of probabilities of it being the ancestor (over all secondary cases). As an example, the first case in the outbreak is assigned a R=7·9, equal to the sum of probabilities of the first case being the ancestor, over all secondary cases.