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**Modelling Healthcare Associated Infections: A case study in MRSA.**

Theodore Kypraios (University of Nottingham) Philip D. O’Neill (University of Nottingham) Ben Cooper (Health Protection Agency) Nottingham November 2007

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**Outline Introduction Project Overview. Mathematical Modelling**

A Case Study in MRSA A Transmission Model Methodology Applications Discussion and Future Work Nottingham November 2007

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**Project Overview Wellcome Trust: Methods:**

Funding for 3 years ( ). Aim: To address a range of scientific questions via analyses of detailed data sets taken from observational studies on hospital wards. Methods: Use appropriate state-of-the-art modelling and statistical techniques (standard statistical methods not appropriate). Nottingham November 2007

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**Mathematical Modelling: What is it?**

A description of the mechanism of the spread of the pathogen between individuals within the wards. Incorporates stochasticity (i.e. randomness). Available data enable estimation of the unknown model parameters (e.g. rates, probabilities, etc). Can investigate scientific hypotheses by comparing different models. November 2007

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**Mathematical Modelling: The Benefits**

Overcomes unrealistic assumptions of standard statistical methods. Highly flexible, can include any real-life features. Provides quantitative assessment of various control measures. Permits exploration of proposed control measures etc. November 2007

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Project Details Typical data sets contain anonymised ward - level information on: Dates of patient admission and discharge Dates of swab tests (e.g. for MRSA, VRE) Outcomes of tests Patient location (e.g. in isolation) Details of antibiotics administered to patients Typing data November 2007

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**Assessing effectiveness of isolation of MRSA-colonised patients.**

A Case Study Ward Adm. Isol. 1 1165 146 2 650 88 3 1205 63 4 1077 65 5 868 67 6 193 50 7 732 142 8 1136 152 9 909 109 Assessing effectiveness of isolation of MRSA-colonised patients. Data from a hospital in Boston. 9 different wards (7 surgical, 2 medical). Study Period: 17 months. Total number of patients in the study: 7935 720 patients known to be colonised with MRSA. Regular swabbing was carried out. Age, sex etc. recorded November 2007

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**A Transmission Model Admitted Uncolonised Colonised Colonised**

and Isolated Discharged November 2007

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**A Transmission Model Admitted Uncolonised Colonised Colonised**

and Isolated Discharged November 2007

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**A Transmission Model Admitted 1-φ φ: importation probability**

Uncolonised Colonised Colonised and Isolated Discharged November 2007

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**A Transmission Model λ: Admitted Uncolonised Colonised and Isolated**

Discharged φ: importation probability λ: colonisation rate 1-φ November 2007

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**A Transmission Model λ: Admitted Uncolonised Colonised and Isolated**

Discharged φ: importation probability λ: colonisation rate p: sensitivity 1-φ November 2007

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**λ = β0 + β1×C + β2×I A Transmission Model (cont.) Assume that:**

β0: Background transmission rate β1: Rate due to colonised (but non-isolated) individuals β2: Rate due to isolated (and colonised) individuals β1 > β2 suggests that isolation is effective. November 2007

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**Methodology Inference for the unknown parameters { β0, β1, β2, φ, p }**

is very challenging: Complex model with several unknown parameters; Problems arise with unobserved events such as colonisations; Standard methods (eg. regression) inappropriate. Therefore: Use state-of-the-art computational techniques such as Markov Chain Monte Carlo (MCMC) are used. Often need problem-specific methods November 2007

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Results: Ward 1 Nares swab test’s sensitivity November 2007

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**Results: Ward 1 Results Importation probability (φ)**

Nares Swab Test’s Sensitivity (p) November 2007

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**Pr [β1>β2|data] Results: Across Wards Ward Probability 1 0.94 2**

0.71 3 0.75 4 0.58 5 6 0.70 7 8 0.37 9 0.83 For each ward we evaluate: Pr [β1>β2|data] November 2007

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A Case Study (cont.) Investigate how transmission within the ward is related to “colonisation pressure”. Within our framework we can investigate scientific hypotheses by comparing different models, i.e.: Model 1: Assumes that transmission is not related to colonisation pressure (i.e. only background transmission) Model 2: Assumes that colonisation pressure is related to colonisation pressure. (Ongoing Work) November 2007

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**A Case Study (cont.) Model 1: λ = β0 Model 2: λ = β0 + β1×(C+Ι)**

In mathematical terms, the total pressure (λ) that an uncolonised individual is subject to just prior to colonisation is: Model 1: λ = β0 Model 2: λ = β0 + β1×(C+Ι) November 2007

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Model Choice Our principal interest lies in observing the extent to which the data support the scientific hypothesis that transmission is related with colonisation pressure. We consider the aforementioned models denoted by M1 and M2. Using computational intensive methods we can compute model probabilities: Pr(M1 | data) Pr(M2 | data) = 1 - Pr(M1 | data) November 2007

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**Pr [M2|data] Model Choice (cont). Ward Probability 1 0.048 2 0.074 3**

0.037 4 0.217 5 0.031 6 0.032 7 0.026 8 0.339 9 0.263 For each ward we evaluate: Pr [M2|data] November 2007

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Discussion “Standard” statistical methods are usually inappropriate for communicable disease data (e.g. dependence). Models seek to describe process of actual transmission and are biologically meaningful (e.g. imperfect sensitivity). Scientific hypotheses can be quantitatively assessed. Able to check that conclusions are robust to particular choices of models. Methods are very flexible but still contain implementation challenges. November 2007

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**Ongoing and Future Work**

Consider more than two different models and see which of them is mostly supported by the data. What effects do antibiotics play? How do strains interact? Is it of material benefit to increase or decrease the frequency of the swab tests? November 2007

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**Acknowledgments (for funding us) Harvard Medical School**

Dr Susan Dept. of Medicine, University of California, Irvine (data + help) Harvard Medical School November 2007

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