Causal Analytics for Applied Risk Analysis Louis Anthony Cox, Jr

The mean value for the equation is approximately (9.45E-4)*382000 + (0.8.6E-6)*122,093,000 = 361 occupational cases of colonization + 1050 consumer cases of colonization ≈ 1411 total cases of ST398 MRSA colonization from pork meat per year in the U.S.

ST398 MRSA Colonizes Pig Farm Workers

ST398 MRSA in pigs can transiently colonize pig farm workers. Cases of ST398 MRSA transient colonization, with occasional cases of infection (the latter observed only in Europe), occur mostly in individuals having direct contact with livestock, especially pigs. Table 6.3 summarizes the available worldwide data on the proportion of colonized pig farm workers on farms where pigs have been colonized.
Table 6.3. ST398 MRSA Colonization Among Pig Farm Workers

Location	# Positive	# Farm Workers Tested	Reference
Ontario, Canada	5	9	(Khanna et al., 2008)
Germany	97	113	(Cuny et al., 2009)
Belgium	47	94	(Denis et al., 2009)
Iowa and Illinois	9	14	(Smith, T. C. et al., 2009)
Iowa and Illinois	27	51	(Smith, Tara C. et al., 2013)
Total	185	281

Pooling these samples for workers on MRSA-positive farms yields an empirical ratio of 185/281. To approximate uncertainty regarding the true proportion, we again use a Bayesian updating of a uniform prior distribution as described earlier. Accordingly, the probability that a pig farm worker in direct contact with pigs is colonized with MRSA is estimated by a Beta(s + 1, n - s +1) = Beta(186, 97) posterior distribution, with a mean of (s+1)/(n+2) = 186/283 = 0.66 and a standard deviation of 0.028. This mean and standard deviation make a normal approximation applicable, as the endpoints (0 and 1) are many standard deviations away from the mean.

Estimating the Number of U.S. Pig Farm Workers

To estimate the number of individuals in the U.S. in close contact with pigs, it is necessary to consider the number of pig farms by herd size, since the average number of workers per pig is known to decrease with herd size. Otto et al. (1998) performed an economic analysis of Iowa hog production that estimated direct workers required (for farrow-to-finish operations) as a function of herd size as follows: 150 pigs - 1.4 workers, 300 pigs - 3 workers, 1200 pigs - 10 workers, and 3400 pigs - 21 workers. We obtained the latest available values for the number of herds by size from the National Agricultural Statistical Services (USDA-NASS, 2009). Using approximation and interpolation, we set the labor requirements within the USDA herd size breakouts as shown in column 2 of Table 6.4. Subsequent calculations shown in the table determine the estimate for total workers on pig farms in the U.S.

Table 6.4.Computation of Total Pig Farm Workers in the U.S.

Herd Size	Workers/Herd	Percent of Herds	Number of Herds	Total Workers^1
1-199	1.4	73.05	55110	77155
200-499	3	6.00	4524	13572
500-999	6.5	4.76	3588	23322
1000-1999	10	5.32	4013	40130
2000-4999	21	7.10	5356	113476
5000+	21	3.78	2850	59850
Total		100.0	75,442	326,505

To model uncertainty, we assume that this estimate of 326,505 for the risk population may be off by as much as 20% (approx. 65,301) in either direction. This subjective uncertainty is expressed as a uniform probability distribution ranging from 261,204 to 391,806.This range is admittedly subjective – other ranges could be considered –but it suffices to explore the sensitivity of results to uncertainty in the size of the heavily exposed worker population.

Estimating the Proportion of Farms with MRSA

No wide-scale survey of MRSA prevalence on farms has been performed in the U.S. However, Table 6.5 summarizes recent relevant data points for the U.S. and Canada. (ABF farms were not included).

Table 6.5. MRSA Positive Farms in the U.S. and Canada

Location	# Farms MRSA Positive	# Farms Tested	Reference
Ontario, Canada	9	20	(Khanna et al., 2008)
Canada	2	28	(Weese, J. S. et al., 2009)
Canada	5	46	(Weese, J Scott et al., 2011)
Midwestern U.S.	12	40	(Frana et al., 2013)
Iowa/Illinois	4	9	(Smith, Tara C. et al., 2013)
Minnesota	0	9	(Davies, 2010)
Ohio/N. Carolina	0	6	(Smith, Tara C. et al., 2013)
Total	30 (19%)	158

The overall proportion of farms in the U.S. and Canada positive for ST398 MRSA is 30/158 = 19%. To approximate uncertainty regarding the true proportion, we again use Bayesian updating of a uniform prior distribution, yielding a Beta(31, 129) distribution, with a mean of (s+1)/(n+2) = 31/160 ≈ 0.19, fornthe distribution of the fraction of MRSA positive farms.

Probability Model for ST398 MRSA Colonization

Table 6.6 assembles the probability distributions derived above into a product-form probability model for the number of annual ST398 MRSA colonizations among U.S. pig farm workers.

Table 6.6. MRSA Colonization Model Parameters

Parameter	Distribution	Mean Value
Number of U.S. Pig Farm Workers	Uniform(261,204 to 391,806)	326,505
Fraction of MRSA Positive Farms	Beta(38, 126)	0.19
P(Colonization|MRSA Positive Farm)	Normal(0.65, 0.028)	0.66
Estimated U.S. Colonizations	Product of above	40,944

The equation for the model is:

Farm Worker Colonizations = No. Pig farm workers x Fraction MRSA positive farms x P(Colonization|MRSA positive) (6.2)