Errors in Table
Authors: Maimuna Majumder, Jane Huston, John Brownstein
Journal: JAMA Pediatrics (2015)

ality, as all models are.We agree that this is an important consideration and we were pleased to see that Blumberg et al 1 incorporated heterogeneity in their own analysis of the Disneyland measles outbreak.However, we believe that the results obtained from the IDEA model are valuable in that they effectively highlight the pervasiveness of vaccine hesitancy clusters in the United States, a phenomenon that directly contributes to increased risk of disease transmission.Leung and Munoz assert that the IDEA model has not been applied to relatively small-magnitude outbreaks; this is simply not the case.The IDEA method was used estimate the basic reproductive number (R 0 ) of the 2014 Middle East respiratory syndrome outbreak in Saudi Arabia, where the total number of cumulative cases used in the model was approximately 115. 2 Given that the total number of cases used to model the effective reproductive number (R E ) of the 2015 measles outbreak was approximately 100, we believe that the application of the IDEA method in this particular context is mathematically sound. 3e used well-accepted historical values of R 0 alongside our modeled estimates of R E to ascertain vaccination rates among the exposed population. 4Bogardus and Blumberg et al 1 note that perhaps contact rates are unusually high in Disneyland; for this very reason, we used a range of R 0 instead of treating it as a constant, allowing us to account for variability in both contact rates and the probability of infection given contact.Conversely, in their approximation of vaccination rates among the exposed population, Leung and Munoz erroneously treated the probability of infection given contact as a constant.In reality, this parameter is subject to a great deal of uncertainty, which we took into account by considering a wide range of historic R 0 values.It is worth noting that the authors' estimate of 89% is quite similar to our upper-end estimate of 86%; perhaps their lower-end estimate would have also been similar to ours had they included confidence intervals in their calculations.Given that all authors expressed disbelief regarding our lower-end estimate of 50%, we clarify that the estimated vaccination rate range (50%-86%) applies only to the exposed population, that is, individuals who were exposed to cases epidemiologically linked to Disneyland, regardless of whether they themselves traveled to Disneyland.We did not estimate measles, mumps, and rubella vaccination rates for the state of California or any county therein.Thus, contrary to claims by Leung and Munoz, our study does not aim to invalidate national survey data of state vaccination rates; instead, it attempts to estimate vaccination rates at a more granular level, namely, for the exposed population.Although we too found our results to be deeply disturbing, such low measles, mumps, and rubella vaccination rates are not without precedence.If the authors closely inspect the California Department of Public Health kindergarten immunization data, they will find that school vaccination rates are extremely heterogeneous, ranging from 100% coverage to as low as 9%. 5Given these pockets of extremely low vaccination in the United States, it is hardly surprising that almost 75% of imported measles cases in 2010 were US residents returning from international travel. 6Thus, requiring proof of immunization on entry to the United States, as proposed by Leung and Munoz, is unlikely to prevent future measles outbreaks on its own.