Model-based Assessment of the Effect of Contact Precautions Applied to Surveillance-detected Carriers of Carbapenemase-producing Enterobacteriaceae in Long-term Acute Care Hospitals

Abstract Background An intervention that successfully reduced colonization and infection with carbapenemase-producing Enterobacteriaceae (CPE) in Chicago-area long-term acute-care hospitals included active surveillance and contact precautions. However, the specific effects of contact precautions applied to surveillance-detected carriers on patient-to-patient transmission are unknown, as other, concurrent intervention components or changes in facility patient dynamics also could have affected the observed outcomes. Methods Using previously published data from before and after the CPE intervention, we designed a mathematical model with an explicit representation of postintervention surveillance. We estimated preintervention to postintervention changes of 3 parameters: β, the baseline transmission rate excluding contact precaution effects; δb, the rate of a CPE carrier progressing to bacteremia; and δc, the progression rate to nonbacteremia clinical detection. Results Assuming that CPE carriers under contact precautions transmit carriage to other patients at half the rate of undetected carriers, the model produced no convincing evidence for a postintervention change in the baseline transmission rate β (+2.1% [95% confidence interval {CI}, −18% to +28%]). The model did find evidence of a postintervention decrease for δb (−41% [95% CI, −60% to −18%]), but not for δc (−7% [95% CI, −28% to +19%]). Conclusions Our results suggest that contact precautions for surveillance-detected CPE carriers could potentially explain the observed decrease in colonization by itself, even under conservative assumptions for the effectiveness of those precautions for reducing cross-transmission. Other intervention components such as daily chlorhexidine gluconate bathing of all patients and hand-hygiene education and adherence monitoring may have contributed primarily to reducing rates of colonized patients progressing to bacteremia.

Using integration by parts we can rewrite this as Where is the moment-generating function of the live-discharge length of stay distribution.
We are also given the mean and 25 th , 50 th , and 75 th percentiles of the overall length of stay distribution ( , 25 , 50 , 75 ), which encompasses stays ending in either death or live discharge. Under the above assumptions we have the following cumulative distribution function all for overall length of stay: Using integration by parts we get The mean is therefore: Noting the result above that = 1 − (− ), we can solve for independently of the live-discharge stay distribution: We assume a mixed exponential-gamma distribution for the live-discharge stay distribution, with a portion of patients following an exponential distribution with mean and the rest following a gamma distribution with mean and shape parameter . For this distribution: We apply these two functions to the four equations above and numerically solve for the four unknown parameters , , , and k.
Pre-intervention, we have = 0.215, = 33.8 days, 25 = 16 days, 50 = 28 days, and 75 = 43 days, which leads to: Patient state dynamics Where governs during-stay state transitions and death rates, a is the distribution of states at admission, and the live-discharge length of stay distribution has cumulative distribution function ( ), the equilibrium cross-sectional state distribution * is: To evaluate the integral in this expression, we must consider the integral ∫ ( )(1 − ( )) ∞ 0 for the eigenfunctions that comprise the elements of the matrix exponential . Assuming the death hazard for any patient is nonzero, the eigenvalues of W are negative and real, so the eigenfunctions take the form ( ) = . We use integration by parts: Here, and are the probability density function and moment-generating function of the live-discharge length of stay distribution, respectively.
Pre-intervention dynamics: Our constraints are * + cd * + b * = pre ( c + b ) * = pre b ( * + cd * ) = pre In the above equations, the values of a , , , and are fixed from the pre-intervention results from the reported data (Table 1 main text), with a and scaled by an assumed surveillance test sensitivity (Table 2 main text). The values of and are assumed ( Table 2 main text). The value of the death rate and the length of stay distribution formula F are fixed at the pre-intervention values described above. Then we solve for , c , b , and the equilibrium * = ( * , * , cd * , b * ) by simultaneously solving the above equation * with = pre and the three above constraint equations. Finally, we solve for using the remaining equation above for .
Post-intervention dynamics:  Our constraints are * + sd * + cd * + b * = post ( c + b )( * + sd * ) = post b ( * + sd * + cd * ) = post In the above equations, the values of a , , , , a , and s are fixed from the post-intervention results from the reported data (Table 1 main text), with a , , a , and s scaled by an assumed surveillance test sensitivity (Table 2 main text). The values of and are assumed ( Table 2 main text). The value of the death rate and the length of stay distribution formula F are fixed at the post-intervention values described above. Then we solve for , c , b , and the equilibrium * = ( * , sd * , * , sd * , cd * , b * ) by simultaneously solving the above equation * with = post and the three above constraint equations. Finally, we solve for using the remaining equation above for .