Causal Analytics for Applied Risk Analysis Louis Anthony Cox, Jr

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Congenital Toxoplasmosis

Congenital cases (where infection is transferred vertically from the pregnant mother to the fetus) were estimated from historical case rates and current populations. The provisional count of births in the United States for the 12-month period ending June 2012 was 3,942,000 (Hamilton & Sutton, 2012). Some fraction of these infants was born with congenital toxoplasmosis. However, the only available survey data regarding the prevalence of congenital toxoplasmosis in the U.S. is largely outdated. Two prospective studies in the 1970s both reported rates of congenital toxoplasmosis of approximately 10 per 10,000 live births. More recent data regarding the rate of congenital toxoplasmosis are available from the New England Regional Newborn Screening Program (Guerina et al., 1994). All infants born in the catchment area of this program are tested for evidence of congenital toxoplasmosis; infected infants undergo clinical evaluation and treatment for 1 year. Of 635,000 infants who underwent serologic testing in 1986-1992, 52 were infected, representing an infection rate of approximately 0.8 per 10,000 live births.

Jones et al. (2007) found that the T. gondii prevalence in U.S. females ages 12-49 declined from 13.4% [95% CI - 11.6, 15.1] during 1988-1994 (the approximate time frame of the Guerina et al. study) to 8.2% [95% CI – 6.6, 9.8] during 1999-2004, or approximately 38.8%. It has also been shown that prevalence tends to be highest in the Northeast U.S. (the area of the Guerina et al. study). For the period 1988-1994, Jones et al.(2001) estimated a prevalence of 29.2% for the Northeast, 22.8% for the South, 20.5% for the Midwest, and 17.5% for the West. Given these data, and assuming that the rate of congenital toxoplasmosis is approximately proportional to the prevalence of T. gondii in adult women, it seems plausible that 0.8 per 10,000 live births from the 1994 Guerina et al. study is an upper bound on the 2012 nationwide average rate. Using the observed prevalence reduction, we will assume that the mean prevalence is now 0.8 x (1-.388) ≈ 0.5 per 10,000 births. Correspondingly, the low estimate (accounting for regional differences and potential further reductions) is assumed to be 0.2 per 10,000 live births. Using a total number of births of 3,942,000 (Hamilton & Sutton, 2012), the mean estimate for congenital toxoplasmosis in 2012 is then 197 cases with a range of 79 to 315. The mean pork-attributable count is 40.4. More precise estimates are presented and discussed in the Results section.

Congenital Cases = (3,942,000/10,000) x Congenital Rate x Proportion Foodborne x Proportion from Pork (7.6)

QALYs Lost Assignment

Data provided by Hoffman et al.(2012) can be used to derive an average Quality Adjusted Life Year (QALY) loss per incident of Illness, hospitalization, and death due to T. gondii for both adult and congenital cases. QALYs combine into one metric a measure of the relative impacts of health conditions on mortality, comfort, and the ability to engage in normal activities. A loss of one QALY is equivalent to the loss of one healthy human life-year, while a value of zero equates to zero loss of health. Fractional values can be used to quantify both shorter periods of time and intermediate levels of impairment. The metric has the desirable effect of placing greater weight on death or injury occurring earlier in life. QALYs were originally developed to assess alternative medical treatment options, and are increasingly used in policy and risk analysis. The averaged QALY values are shown in bold in Table 3. The total pork-attributable QALYs lost due to toxoplasmosis is distributed as:

Total QALY loss = 1.3373e-4 x (Total Cases - Hospitalizations) + 0.0565 x Hospitalizations

+ 27.71 x Deaths + 2.2086 x Congenital Cases (7.7)


This section assesses the excess risk associated with a shift in the proportion of swine from total confinement to open/free range production, with the size of the shifted fraction of swine ranging from 0 to 0.001 (0.1 %). It is useful to compare the size of the shift to the current levels of pigs in the open/free range category. The number of USDA certified “organic” swine in 2006 was 7,508, growing to 12,373 in 2011 (USDA-ERS, 2012). The USDA organic seal verifies that producers met animal health and welfare standards, did not use antibiotics or growth hormones, used 100% organic feed, and provided animals with access to the outdoors. It does not include other labeling types such as “natural” or “free-range”, however, it does provide an idea of the magnitude versus conventionally raised swine. In contrast, for the same year, the USDA estimated the total U.S. farm hog population at 64,925,000 head (USDA-NASS, 2012). Therefore, about 1 out of every 5,200 pigs was raised organically in 2011, corresponding to a production shift, ΔC of approximately 1/5,200 = 0.00019. To measure the impact of a range of possible future values, we varied ΔC from 0 to 0.001 in 10 increments of 0.0001 (approximately 6,500 pigs each). Each successive value of ΔC was supplied as an input to a probabilistic simulation model developed in the R (version 2.15) statistical programming environment (, using the mc2d (Tools for Two-Dimensional Monte Carlo Simulations) add-in package for its 4-parameter Beta distribution random number generator. We generated 10,000 random values for each underlying probability distribution to obtain 10,000 random values for each relative risk factor (equation 7.2) and each level of health outcome (equations 7.3 to 7.7). Multiplying these numbers yielded the distribution of excess risk results for each outcome:

rk ~ r(ΔC) * Hk (7.8),
is the excess risk of human toxoplasmosis associated with a production shift ΔCin swine from total confinement to open/free range production, where Hkdenotes the random variable measuring annual loss for health outcome measure k, for k = total cases, hospitalizations, deaths, or total QALYs. A conceptual diagram of the simulation model is depicted in Figure 2 below.

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