### Data Collection

We collected detailed census and microbiologic data from eight adult 10-bed intensive care units (ICUs) in a tertiary academic medical center in Boston, Massachusetts where routine admission and weekly bilateral nares screening for MRSA was occurring with high compliance (90%). Types of ICUs included medical, cardiac, general surgery (2), neurosurgery, thoracic surgery, and cardiac surgery (2). One of the two general surgery wards also received burn and trauma patients. Dates of MRSA-positive clinical cultures (all sources), as well as positive and negative MRSA nares screening cultures were collected during a 17-month period from September 2003 through January 2005. Negative clinical cultures were not assessed. All specimens were processed by routine bacterial culturing techniques. This study was approved by the Institutional Review Board at Brigham and Women's Hospital with a waiver of informed consent.

Newly-identified and previously known MRSA-positive patients were placed under contact precautions consisting of gown and glove use as well as use of single rooms (all ICU rooms were single occupant). Once identified as MRSA-positive, contact precautions were applied on that admission and all subsequent admissions. No nurse cohorting was utilized. Dates of each ICU admission and discharge were obtained, along with the date on which contact precautions were initially applied (for MRSA or other highly antibiotic resistant pathogens). The first institutional date of a MRSA-positive culture was also recorded, even if it preceded the study period.

### Data analysis

#### Stochastic model

Our baseline analysis used a previously described dynamic stochastic single-ward transmission model to analyse the data [1]. At any point in time, each patient is assumed by this model to be in one of two states, colonized (defined here as the presence of MRSA at any body site, regardless of symptoms) or uncolonized. Each patient entering the ward has a probability ϕ of being already colonized, unless they are already known to be so (i.e. having already had a previous positive test).

During a stay on the ward, an initially uncolonized patient is assumed to have a risk of becoming colonized that can be described by a Poisson process: this means that the probability of a patient becoming colonized between time *t* and time *t*+*τ* can be approximated by *λ (t) τ* (where *τ* is a small interval of time, the approximation becoming exact as *τ* approaches zero). Consequently, a patient's chances of becoming colonized increase with length of stay on the ward. The rate λ *(t)* can vary through time; since we are interested in comparing different potential sources of colonization we assume that λ *(t) = β*
_{
0
}
*+ C(t)β*
_{
1
}
*+ I(t)β*
_{
2
}. Here, *β*
_{0} is the rate of background transmission, *β*
_{1} is the rate of transmission due to colonized but nonisolated patients, *β*
_{2} is the rate of transmission due to colonized and isolated patients, and *C(t)* and *I(t)* are the numbers of nonisolated and isolated colonized patients at time *t*, respectively. We thus assume that the "colonization pressure" on an uncolonized individual increases linearly with the number of colonized patients who are isolated and nonisolated. Although it is common practice to use a scaling such as *β*
_{1}/*N* instead of *β*
_{1}, with *N* the typical number of patients on the ward, this did not seem necessary since there was very little variation in ward occupancy both between wards and between different times during the study period. The inclusion of the background rate *β*
_{0} models the assumption of a constant risk of colonization irrespective of the presence of colonized patients. Such background transmission could, for example, result from environmental contamination or contact with staff carriers of MRSA [2–4]. Note that the model takes no explicit account of HCW compliance with barrier precautions.

Once a patient is colonized, we assumed that he or she remains so for a three month period. Thus, a patient colonized on discharge is assumed to still be colonized if readmitted within three months. This assumption was not critical: the results presented below were virtually unchanged when different periods of colonization were assumed (e.g. 6 months, 9 months). We assumed that the nares culture had a specificity of 100% and a sensitivity of *p* × 100%, where *p* (the sensitivity of a nasal swab for detecting MRSA carriage at any site) was estimated from the data.

#### Statistical inference

The above model has five main parameters, namely ϕ, *p, β*
_{0},*β*
_{1}, and *β*
_{2}. We wish to estimate these from the data, which consist of admission times, discharge times, and the times and outcomes of tests. Since our approach involves estimating unseen colonization times, we can also estimate quantities such as the duration of carriage prior to a positive test result. Assessment of the effectiveness of isolation is performed by comparing estimates of *β*
_{1} and *β*
_{2}: evidence that *β*
_{1} > *β*
_{2}would support the hypothesis that isolation is effective in reducing transmission. Specifically, we estimate P(*β*
_{1} > *β*
_{2}) and the ratio *β*
_{1}/*β*
_{2} . Estimation was carried out within a Bayesian statistical framework using Markov chain Monte Carlo (MCMC) methods [5].

The five model parameters were assigned uninformative and independent prior distributions: Uniform(0,1) distributions for ϕ and *p*; and exponential distributions with rate 10^{-6} for each of the *β* parameters. Since the likelihood of the observed data (dates and outcomes) given the model parameters is computationally intractable, we used a data augmentation method in which the unobserved colonization times were included as additional parameters. This yields an augmented posterior density that is known up to proportionality, which we explored using an MCMC algorithm. Within the algorithm, infection rate parameters were updated using Metropolis-Hastings steps, while both ϕ and *p* were updated using Gibbs steps [6].

Our methods enable us to estimate the percent of patient days that are attributed to patients who are colonized but not yet detected (*p*
_{
hidden
}), and the percent of patient days attributed to patients who are colonized and have been tested, but who are awaiting test results (*p*
_{
wait
}). Note that *p*
_{
hidden
}> *p*
_{
wait
}since all "waiting" patients are also "hidden".

Some of the parameter estimates were combined using a random effects model with inverse variance weights [[7], Sec. 5.2] to derive pooled estimates and corresponding standard errors. These computations were carried out using the rmeta package for R http://www.r-project.org. All other analysis, such as the implementation of the MCMC algorithms, was performed using programs we wrote in C.

#### Sensitivity analysis

We refer to the model described above as the *full model*. To assess the impact of our assumptions, we repeated the analyses using two alternative models. In the first (the *no-background model*), *β*
_{0} is assumed to be zero with high probability (specifically, *β*
_{0} was assigned an exponential prior distribution with mean 10^{-4} so P(*β*
_{0} < 0.001) > 0.99). This corresponds to the assumption that virtually all of the MRSA acquisitions result from patient-to-patient transmission (much of which is presumably mediated by transiently colonized healthcare workers, though this is not explicitly modeled). Background transmission unrelated to colonization pressure, e.g. environmental contamination, is assumed to be of negligible importance. In the second (the *non-linear model*), the assumption of linearly increasing colonization pressure is relaxed, and it is instead assumed that colonization pressure due to both isolated and nonisolated individuals remains constant provided at least one colonized individual is present. Although biologically less plausible than the full model, this model represents an extreme case and by fitting it we obtain insights into the impact of the assumptions underlying the full model. For both the non-linear and no-background models, assessment of the effect of isolation is measured via comparison of the two rates *β*
_{1} and *β*
_{2} as described above.

#### Test sensitivity

We consider two definitions of swab sensitivity: swab sensitivity in detecting colonization of the nares, and swab sensitivity for detecting colonization at any body site. The former is calculated from a subset of the data (without making use of the model) by comparing subsequent swabs in patients who have a first positive swab. Precisely, the sensitivity is estimated by the ratio TP/(TP+FN) using serial nares cultures alone, where TP and FN denote total numbers of true positive and false negative tests on a ward excluding the first positive swab from each patient. Since patients, once colonized, are assumed to remain so throughout their ICU stay, TP is simply the number of positive swabs excluding the first for each patient episode, and FN the number of negative swabs that follow an earlier positive for the same patient. The second reported sensitivity is the parameter *p* estimated from the model making use of cultures from all sites (this is necessarily lower than the sensitivity for detecting nares carriage).

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