In our simple model, the number of CRS cases prevented by rubella vaccination in the United States during the ten-year period from 2001 through 2010 (X ) is given by

(1)

and the corresponding number of prevented ASD cases (Y ) is given by

(2)

where α and β are vaccine era and pre-vaccine era CRS incidence in the US, respectively, and γ is average number of live births per year. The percentage of CRS cases presenting with an ASD is denoted by δ . This model was chosen as a parsimonious representation of the relationship between a reduction in CRS incidence resulting from rubella vaccination and the incidence of ASD.

Table 1 defines the parameters used to calculate the numbers of CRS and ASD cases prevented by rubella vaccination in the United States from 2001 through 2010. The estimate of vaccine era CRS annual incidence (α ) was obtained by averaging CRS incidence in the United States from 2001 to 2008 (most recent data) [8]. The number of live births was obtained from National Vital Statistics Reports [9, 10]. Data on the number of live births per year (γ ) were averaged over 2001-2009 (most recent data) and rounded to the nearest thousand. Average values were used for vaccine era CRS incidence and the number of live births because the annual values changed very little over the respective time periods of interest. Although vaccine era CRS incidence and live birth data were only available through 2008 and 2009, respectively, it was assumed that these data would remain relatively constant through 2010.

Table 1 Model parameters, estimates, and lower and upper limits Full size table

Explicit data on pre-vaccine era CRS incidence in the US are limited. The estimate of CRS incidence (β ) and lower and upper limits of this parameter were taken from a study by Stray-Pedersen [11], which modeled pre-vaccine era CRS incidence in Norway. In general, the values of pre-vaccine era CRS incidence reported by Stray-Pedersen are supported by research from other countries, although individual estimates of CRS incidence vary. Compared to the Norway study, CRS surveillance in Jamaica returned the same overall estimate of CRS incidence (4.0 cases per 10,000 births) [12]. A slightly higher estimate of approximately 5 CRS cases per 10,000 live births was reported from mathematical modeling of pre-vaccine era CRS incidence in Australia [13]. Mathematical modeling by Cutts and Vynnycky [14] yielded overall estimates of CRS incidence in the range of 17 cases per 10,000 live births in some developing regions. These estimates had very wide ranges [14], however, and other studies have only reported such high incidence rates during outbreaks [15]. Therefore, taking a conservative approach, we chose to use the value reported from Norway and Jamaica. The Norway and Jamaica studies also obtained the same estimate of endemic CRS incidence (2.0 cases per 10,000 live births) [11, 12]. This value is similar to the estimated 0.81 to 1.27 CRS cases per 10,000 live births derived from a retrospective review of medical records in Morocco [16] and to the estimated 1 case per 10,000 live births obtained from active surveillance in Yangon, Myanmar [17]. In addition, a review by Cutts, et al. [15], summarized estimates of epidemic CRS incidence from several countries, ranging from 6 CRS cases per 10,000 live births in Trinidad and Tobago to 22 cases per 10,000 live births in Panama. Within this range fell the Stray-Pedersen estimate of 15 CRS cases per 10,000 live births [11], and we included this value in our calculations.

The percentage of CRS cases presenting with an ASD (δ ) was obtained from the Chess study of 243 preschool children with CRS [7]. In the Chess study, eighteen children had either the "full" syndrome (meeting all diagnostic criteria) or "partial" syndrome (meeting some but not all diagnostic criteria) of autism, for a total prevalence of 7.4% [7]. Autism diagnosis was based on Kanner's original description of the disorder, published in 1943 [7]. According to Chess, Kanner's classical criteria for autism included "extreme autistic aloneness," language abnormalities, stereotypic relations to the environment, and a lack of affective human contact [7]. In our model, the value of 7.4% was set as the overall estimate of the percentage of CRS cases presenting with an ASD, and lower and upper limits were set at 3.0% and 10.0%, respectively. These limits are designed to be conservative, considering that 1) quantitative data on the CRS-ASD association are limited and 2) current ASD diagnostic criteria are broader and more inclusive than Kanner's classical criteria [18–20].

The estimates in Table 1 were used to calculate the numbers of CRS and ASD cases prevented by rubella vaccination from 2001 through 2010. A one-way sensitivity analysis of the number of CRS cases prevented was performed by varying pre-vaccine era CRS incidence. It is somewhat unreasonable to extend an "endemic" or "epidemic" estimate over a ten-year period because rubella epidemics typically occur every six to ten years in an unvaccinated population [21]. Nevertheless, we decided to employ the endemic estimate to represent the "most conservative scenario," in which CRS incidence remains low in spite of a lack of rubella vaccination. In contrast, extension of the epidemic estimate represents the "least conservative scenario," in which rubella transmission is sustained at high levels in an unvaccinated population. A two-way sensitivity analysis of the number of ASD cases prevented was performed by simultaneously varying pre-vaccine era CRS incidence and the percentage of CRS cases presenting with an ASD.