Causal Analytics for Applied Risk Analysis Louis Anthony Cox, Jr

Estimating the Annual Probability of MRSA Infection for Those Colonized

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Estimating the Annual Probability of MRSA Infection for Those Colonized

Transient colonization of the human nasal passages (and other mammals) with Staphylococcus aureus is common in the U.S., and is usually harmless. Gorwitz et al.(2008) estimated a prevalence of 28.6% in the U.S. in 2004. A fraction of these are methicillin-resistant, approximately 1.5% of the U.S. population. Fortunately, only a small fraction of those colonized with MRSA at any moment develop active MRSA infections. Although the relationship between colonization and infection is not fully understood, in one instance researchers have shown that more than 80% of bloodstream infections caused by S.aureus in hospitalized adults were preceded by colonization of the anterior nares with the same strain (Graham et al., 2006). For initial approximation purposes, we assume that the relationship of infected to colonized can be expressed as a fraction, that is, the number of infected/year is a given fraction of those colonized.

An approximate infection rate can be estimated from a MRSA surveillance program conducted in Iowa during and following the initial detection of ST398 MRSA in swine. In a comprehensive study of 1166 MRSA isolate submissions from this program (invasive cases only) from 1999-2006, no ST398 strains were found (Van De Griend et al., 2009). 343 isolates were from the latest year, 2006. According to a report from the same laboratory (IARTF, 2011), in the years 2007-2009, the following additional numbers of MRSA isolates were submitted to the Iowa University Hygienic Lab by year: 445, 447, and 455. The report states: “To date, MRSA CC398 [i.e. ST398] has not been identified among the invasive MRSA isolates submitted to SHL [State Hygienic Laboratory] from Iowa residents.” (Surveillance ended 1/1/2011 and data after 2009 was not provided.) Thus, while ST398 appears likely to be not uncommon among Iowa swine, there are no reported cases of invasive or even soft-tissue infection cases of ST398 in Iowa through the time of the most recent studies. Iowa accounts for 28% of U.S. pork production (USDA, 2008). This finding is replicated at the national level. The CDC has collected over 12,000 MRSA isolates over recent years that include colonization isolates, infecting isolates, and isolates from animals and from food.  The vast majority were collected through the Active Bacterial Core surveillance (ABCs) system ( However, no ST398 strains have been detected (Limbago, 2010).

Probability Model for Infection given Colonization

If ST398 MRSA was widespread among Iowa hogs by 2006 (Smith, TC. et al., 2008), then for a period of four years, 2006-2009, and likely longer, there were no detected invasive ST398 MRSA cases in Iowa despite the simultaneous significant prevalence among Iowa swine herds and pig farm workers. To put an upper bound on the probable human health risk that is consistent with these observations, we first estimate the mean number of human colonizations of ST398 MRSA in Iowa from 2006-2009 as:

Iowa Colonization Years = 4 years x 0.28 of U.S. pigs in Iowa x

U.S. Farm Worker Colonizations (from Equation 2) (6.3)

To obtain a distribution of results corresponding to equation 3, we generated 100,000 random samples from the previously described distributions of uncertain inputs. The mean of the distribution was 55,114. If an estimated 55,114 ST398 MRSA colonization-years in Iowa produced 0 invasive cases, then, using a conservative Bayesian analysis similar to that described earlier, we can estimate a plausible upper bound for the annual posterior probability of infection given colonization as belonging to a beta(1; 55,115) distribution with mean 1/55,116 = 1.81E-5.

Estimating Secondary Cases

While transmission of MRSA among hospital patients is a significant health concern worldwide, the secondary case rate for ST398 MRSA appears to be much lower than that for other types of MRSA. This may be due to the relatively transient nature of ST398 colonizations (van Cleef B. et al., 2009; Graveland et al., 2011; Frana et al., 2013).

Hospital Cases

Wulf et al. reported an instance of an apparent outbreak of ST398 MRSA in a Dutch hospital (Wulf et al., 2007). Bootsma et al.(2011) identified cases of ST398 transmission from patient to health care workers (2 “outbreaks” involving colonization of 1 and 2 workers) in an examination of two large datasets from Dutch hospitals. This and other anecdotal instances reported in Europe indicate that secondary infections are possible.

Van Rijen et. al (van Rijen et al., 2008) compared the secondary transmission rates for typable MRSA versus non-typable MRSA (presumably ST398) in a Dutch hospital. They reported that “Sixteen patients who carried typable MRSA stayed in the hospital without precautions, for a total of 138 days. Twenty-two of 2139 persons exposed to these 16 patients were shown to be colonized with the index strain. For non-typable MRSA, during 37 exposure days for 8 patients, 0 of the 408 exposed patients and health care workers were colonized….. Only recently, in 2007, 1 health care worker was colonized with non-typable MRSA, acquired from a patient who had not been treated in isolation.”

Hospital Estimation Model

Based on these data, a conservative upper bound on the secondary case rate, using Bayesian analysis again, would be that the transmission rate of ST398 MRSA within the hospital is approximately (1/410) /(22/2139) = 0.238 that of non-ST398 strains. A similar result was reported in Wassenberg et al.(2011) who computed a relative transmission risk of 0.28. A somewhat lower relative risk was obtain by (Bootsma et al., 2011), with 0.169. The Van Rijen et al. data further implies that the average length of stay for ST398 MRSA was (37/8) = 4.625 days versus (138/16) = 8.625 days for non ST398 MRSA, a reduction ratio of 4.625/8.625 = 0.536. Wassenberg et al. obtained values of 7 days for ST398 infections and 8 days for non ST398 (.875 reduction ratio). As discussed in the previous section, the Van Rijen et al. results also imply a rate of conversion from colonization to infection in ST398 strains that is approximately (1/4.83) = 0.207 that of non ST398 strains. Wassenberg et al. obtained values of 13 days of exposure before transmission for ST398 cases and 3 days of exposure for non ST398 case, implying a ratio of 3/13 = 0.231 between the two.

We used this data on hospitalization infection dynamics and the mathematical framework of Webb et al. (2009), who developed a set of differential equations describing the epidemiological dynamics of MRSA in U.S. hospitals. Their motivation was to determine the conditions under which community acquired MRSA (CA-MRSA) would displace hospital acquired MRSA (HA-MRSA) as the dominant infection. They derived a basic reproduction number, R0, which corresponds to the steady state number of secondary infections per initial infection. Using baseline empirical parameter values, they computed an R0 for community associated MRSA () of approximately 0.66, and 0.69 for hospital-associated MRSA . To model the hospital dynamics of swine-associated (ST398) MRSA, we modified the Webb et al. baseline model for community-associated MRSA based on averages of the parameters discussed above, as summarized in Table 6.7. To account for uncertainty, we created a stochastic simulation version of the hospital dynamics model. This assumed that input parameters follow log-normal distributions (µ = avg. value, σ = µ/2) with the exception of the hand hygiene compliance fraction, which was distributed uniformly between 0.40 and 0.80 versus an original baseline value of 0.60.
Table 6.7. Adjustment factors (right column) applied to a community-acquired MRSA hospital dynamics model to obtain parameters for ST398 MRSA hospital dynamics

Parameter Group

Derived from Van Rijen et al.

Wassenberg et al.

Bootsma et al.


βxy – transmission rates





φxy – infection rates



NA (colonization only)


γ xy – discharge rates (1/length of stay)



NA (no distinction made)


100,000 iterations of the simulation model yielded a median reproductive rate for community-associated ST398 MRSA, , of approximately 0.0787 (probability > 1 = .0016), and a median value (hospital associated) of approximately 0.0823 (probability > 1 = .0019) These are less than 1/8 of the corresponding values for non ST398 MRSA when using the same model with the original baseline values. Our QRA model uses a midpoint value of 0.0805 to capture the secondary hospital case rate.

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