# Causal Analytics for Applied Risk Analysis Louis Anthony Cox, Jr

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## Quantitative Risk Analysis Model

Equations 6.1-6.3, together with a factor for secondary cases, as derived above, can be combined into a probabilistic model for total MRSA infections in the U.S. attributable to pork. The model can be expressed as

Expected Number of Annual Infections = (Pork Handling Colonizations + Farm Worker Colonizations) x P(infection | colonization) x (1 + Secondary Case Rate) (6.4)
We implemented the simulation model in the R statistical programming environment (http://www.r-project.org/) and generated 100,000 random values for each underlying probability distribution to obtain 100,000 random values for Food Handling Colonizations (Equation 6.1), U.S. Farm Worker Colonizations (Equation 6.2), and Infection Rates (Equation 6.3). The secondary case rate of 0.0805 was determined via the separate model just discussed (c.f. Table 6.7). Equation 6.4, applied to these randomly sampled input values, yielded a distribution of U.S. annual MRSA infections attributable to pigs and pork.

## Results

The mean number of meat handler colonizations in the simulation was 358.54 [95% CI – 17.29, 1108.43]. Figure 6.1 shows its uncertainty distribution. The mean number of colonizations for pork consumers was 1042.36 [95% CI – 50.29, 3182.38], and Figure 6.2 shows its uncertainty distribution. The mean number of colonizations for pig farm workers was far larger than either of these, at 41,777.03 [95% CI – 28,967.03, 56,831.16]. Its uncertainty distribution is plotted in Figure 6.3. Thus, the number of colonizations of farm workers exceeded that of pork handlers and consumers combined by a factor of about 30. The incidence of colonization among pig farm workers constitutes 96.8% of the total risk pool.

Fig.6.1. Distribution of Annual MRSA Colonizations Attributable to Pork

Among Professional Meat Handlers

Fig.6.2. Distribution of Annual MRSA Colonizations Attributable to Pork

Among Pork Consumers

Fig.6.3. Distribution of Annual MRSA Colonizations Attributable to Pigs

Among Pig Farm Workers

Fig.6.4. Distribution of the MRSA Infection Rate for those Colonized with Pig/Pork Attributable MRSA

Fig.6.5. Distribution of Total Annual U.S. MRSA Infections Attributable to Pigs/Pork

The conditional infection rate for those colonized with pork attributable MRSA is modeled by a Beta(1, 55115) distribution as described previously. It is shown in Figure 6.4. Finally, the distribution for the total annual number of pig/pork attributable MRSA infections (Equation 4) is shown in Figure 6.5. It has a mean of 1.00 [95% CI - 0.05, 3.05]. If we allocate the mean according to the proportions of the colonization risk pools, the expected total number of annual infections in U.S. pork consumers is about 0.024/yr.; in professional meat handlers, about 0.008/yr.; and in pig farm workers, about 0.968/yr.

## Discussion and Conclusions

The size of the public health risk in the U.S. caused by MRSA from swine has not previously been quantified. Popular news stories have mentioned it in the context of 70,000 excess deaths per year from antibiotic-resistant superbugs (CBS, 2010). Our conservative quantitative risk assessment indicates that MRSA from pigs and pork should be expected to cause no more than about one infection per year in the U.S. population, almost all among pig farm workers, under current conditions. To consumers (the general public) and professional meat handlers combined, swine- and pork-associated MRSA pose a risk of not more than about one excess infection per 31 years under current conditions. This corresponds to an average per-capita risk of about one case per ten billion person-years (i.e., 1 case/(315 million people x 31 years) for the general public. Most such infections are treatable, and the excess death rate would be too small to detect. This is consistent with the historical fact that no human deaths and no serious infections have been found to have been caused among the general public or professional meat handlers by pig-associated MRSA. The fraction of all cases caused by use of antibiotics in swine is likewise undetectably small, but the finding of no statistical difference in MRSA rates between meat from hogs raised conventionally and meat from hogs raised without antibiotics (O'Brien et al., 2012) suggests that reducing antibiotic use on farms should not be expected to reduce the already small risk further.

The true risk is likely to be considerably smaller than our conservative estimates; it could be zero. We have assumed that certain events, such as invasive infection resulting from ordinary colonization (from meat handling or otherwise), can occur, even though they have not been observed. The odds of their actual occurrence have become smaller as more data has accumulated, since Bayesian conditioning on data shifts our conservative (uniform) prior distributions leftward. In addition, modeling the dynamics of MRSA in hospitals shows that ST398 MRSA risks in hospitals are unlikely to increase dramatically in future, as the ST398 type has a relatively low potential for spread (basic reproductive rate). Thus, a conservative upper-bound occupational risk of about 1 infection per pig worker per year, and a public health risk of about 1 infection per 31 years among the rest of the U.S. public, or about one excess case per 10 billion person-years, appears to be justified by current data. These estimates may continue to decline if further surveillance data accumulate showing no observed cases of ST398 infections among the general public.

The calculations in this chapter have emphasized quantitative description of the size of the human health risks from pig-derived MRSA. Similar rough upper-bound estimates of risks can also be obtained by multiplying plausible upper-bound estimates for appropriate factors in many other areas of health, safety, and environmental (HS&E) risk assessment and engineering reliability analysis. (Equation 2.11 in Chapter 2 presents a general decomposition of a probability of interest as a product of marginal and conditional probabilities in the context of Bayesian network analysis.) If the resulting upper-bound risk estimates are small enough for the risk to be safely ignored in favor of more productive risk-reducing opportunities, then such simple descriptive analyses may suffice to show that no further analyses or actions to manage these risks are currently warranted. But if the risks appear to be large enough so that it is worth considering costly interventions to manage them, then it becomes valuable to be able to predict the probable consequences of different interventions and to characterize uncertainties about them. Chapter 8 illustrates how simple calculations, together with causal attribution of observed consequences to controllable factors, can be used to accomplish such predictive modeling.

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