Model structure

A discrete-time Markov chain model was implemented in MATLAB to simulate patients moving through different patient classes. We defined 4 classes: patients with a central line, patients with a Foley catheter, and patients with both, and patients with neither. Patients with central lines may acquire CLABSIs, and patients with Foley catheters may acquire CAUTIs. The distribution of patients depends on the class they were in previously. The next day’s distribution was calculated using the following formula:

$$X\left( {t + 1} \right) = B\cdot\;I\cdot\;P\cdot\;D\cdot\;X\left( t \right),$$

where B is a transition matrix that represents the probability of getting CHG bathed or obtaining a SCLBK, I is a transition matrix that represents the probability of getting an infection, P is a transition matrix that represents the probability of obtaining a catheter or central line, and D is a transition matrix that represents the probability of being discharged. Patients with CLABSI or CAUTI may develop a secondary infection of the other type. Each day, if a patient does not acquire an infection or an intervention, the patient moves to the i + 1 version of the same class.

The patient’s average length of stay, 1/δ_k, differs for each class k. The daily probability of getting an intervention p, ρ _p , was calculated using the following formula:

$${\rho _p}\; = \;1\; - \;{\left( {1\; - \;K} \right)^{{\delta _k}}},$$

where K represents the percentage of hospitalized patients with intervention p.

The infection rate, r, was calculated based on a compliance rate of 60% for CHG bathing and by number of days since last intervention. Here, η and κ are the reduction of incidence of CAUTI and CLABSI due to CHG bathing and CLABSI due to SCLBK, respectively, and were pre- to postintervention incidence.

Model inputs

Virginia Commonwealth University Health System is an 865-bed academic medical center with 65,000 patient discharges estimated annually. Prior to SCLBK and CHG bathing interventions, there were 80 CLABSIs and 39 CAUTIs annually. The daily number of patients used in the simulations was 850 patients.^{Reference Reagan, Chan and Vanhoozer3} The probability of a patient developing a CAUTI was 0.1257 per 1,000 patient days and 0.2579 per 1,000 patient days for a CLABSI. Simulation results were calculated at steady state. Parameter values are listed in Table 1.

Table 1.

Parameters Used in the Simulations

One CHG bath costs $8.47. Patients who do not receive a CHG bath on a given day are assumed to receive a bath with non-CHG wipes that cost $2.47 per bath. The noncentralized central-line bundle costs $0.04 more due to the compilation of necessary supplies needed to insert a central line compared to the SCLBK. On average, a CAUTI infection costs $13,793⁴ and a CLABSI infection costs $70,696.⁵ The total cost calculation included costs related to CHG bathing materials for CAUTI, the SCLBK for CLABSI, and the costs associated with HAIs.