In this chapter we presented some information about Staphylococcus aureus and MRSA and some background information about the previous work that has been done considering the control strategies and the use of antimicrobial treat-ment for this pathogen. We also gave a description of the data analysed in this thesis and gave the fundamentals of Bayesian inference and MCMC that are going to be used in the following chapters.
The remaining chapters of this thesis are organised as follows:
In Chapter 2 we use a discrete time Markov Model to look at the effects of antimicrobial treatment on carriage levels of MRSA, ignoring patient-to-patient transmission. Swab test sensitivity and specificity are assumed to be perfect.
Maximum likelihood and MCMC techniques are used to obtain the parameter estimates followed by an investigation of model assessment. Lastly, we present some simulation results as well as the results obtained form the three datasets used.
In Chapter 3 a discrete time hidden Markov model is used to investigate the effect of antimicrobials on MRSA carriage, again without taking into account patient-to-patient transmission. We still assume perfect swab test specificity but imperfect sensitivity. Thus, to obtain our parameter estimates we use a data augmentation MCMC algorithm. We then discuss model assessment and display the results from the simulations and from the three datasets used.
In Chapter 4 we use three discrete time stochastic transmission models to ex-plore the effect of antimicrobial treatment on MRSA transmission. We assume imperfect swab test sensitivity and perfect specificity. Results are obtained us-ing a data-augmented MCMC algorithm to infer the unobserved patient coloni-sation times. Then we describe the model assessment and lastly we present the results from simulations and the GSTT datasets for the three models.
In Chapter 5 we conclude discussing the main results drawn for this research and any model limitations. We also present possible future work.
All results and graphics for this thesis have been obtained using the C program-ming language and the R statistical software.
Modelling the effect of
antimicrobial treatment on carriage levels of MRSA using Markov
models
2.1 Introduction
In this chapter we look at the effects of antibiotics and antiseptic treatment on MRSA carriage levels of colonised patients. Throughout this chapter we as-sume that there is perfect swab test sensitivity and specificity. Moreover, we make the assumption that there is no person-to-person transmission so we use only a within-patient modelling approach. We will include only the patients who have at least one positive test. The reason we do this is because we have ignored patient-to-patient transmission and thus we cannot draw any conclu-sions about the effect of antimicrobial treatment when a patient has only nega-tive tests.
We will use a discrete-time Markov chain to model the colonisation status of an individual on a daily basis taking into account daily antimicrobial treatment.
The data we are going to use come from the two 15-bed ICUs from St. Guy’s and Thomas’ hospital in London as described in section 1.3.
Earlier work using Markov Models to analyse whether antimicrobial treatment
can influence carriage levels of MRSA has been done by Kypraios et al. in [Kypraios et al., 2011]. In their work they use discrete time Markov models to assess the effects of antimicrobial treatment considering three models: one using a 1-day timescale, and two using a 1-week timescale considering either one antimicrobial at a time or multiple antimicrobial use. For the weekly tran-sition models, they included only tests that took place at weekly intervals and assumed that an antimicrobial had been received that week only if the patient was receiving it for four or more days that week. There was strong evidence that antiseptic treatment had an effect on reducing MRSA carriage while an-tibiotic treatment was not associated with changes in MRSA carriage. One lim-itation of this work is that there is no discussion about assessing model fit.
The work in this chapter uses a similar model as the model for daily transitions used in [Kypraios et al., 2011]. The MRSA Data Set that includes only the pa-tients with at least one positive test is also the same as the one used in [Kypraios et al., 2011]. However, here we will obtain results from two more data sets: the Wounds Data Set and the Respiratory Data Set for which we will also consider only patients with at least on positive test. Furthermore, this chapter includes a detailed analysis of model assessment which has not been done in any previous works.
For the model’s parameter estimation, a Frequentist and a Bayesian approach are used utilising maximum likelihood estimation and Markov Chain Monte Carlo (MCMC) methods respectively. We initially validate our methods using simulated data and then, using the GSTT data, we obtain results making several different assumptions for the three different data sets; MRSA Data Set, Wounds Data Set and Respiratory Data Set. We then assess the model fit using two different methods discussed in Section 2.6.
We find that antiseptic treatment has an effect on the clearance of MRSA car-riage for the MRSA Data Set. Moreover, Oxazolidinone seems to be effective in reducing MRSA carriage for all the three data sets while Macrolide and Cephalosporin seem to have the opposite effect. These results are in agreement with the findings in [Kypraios et al., 2011]. Finally, it was not always clear that the model fit was adequate.
In Section 2.2 we present some summary statistics of the data we are going to use in this chapter. In Section 2.3 we describe the model, in Section 2.4 the
Likelihood, in Section 2.5 we discuss the inference methods and in Section 2.6 the model assessment methods. In Sections 2.7 and 2.8 we validate our methods using simulated data and present the results from the three data sets (MRSA Data Set, Wounds Data Set and Respiratory Data Set). Finally, Section 2.9 gives an overview of the methods and the results discussed in the previous sections as well as model’s limitations and suggestions for possible improvements.
2.2 Data
In this chapter we perform our analysis by including only patients that have at least one positive test. The reason we do this is that, since we are interested in the effects of antimicrobial treatment on MRSA carriage levels, it is better to include in our study those patients who had acquired the infection. Another reason is that including all patients is computationally demanding. However, for comparison, in Section 2.8 we have a case where we include the results for patients with no positive tests, to show that these results do not differ much from the those that include only the positive patients.
The data sets we use for our main study in this chapter will be subsets of the MRSA, Wounds and Respiratory Data Sets described in the previous chapter 1. We are going to refer to them as p-MRSA Data Set, p-Wounds Data Set and p-Respiratory Data Set to distinguish them from the original and complete data sets.
Tables 2.1 and 2.2 give some basic statistics of the three data sets.
Statistic p-MRSA p-Wounds p-Respiratory
number of patients 545 351 302
average stay/patient (days) 18.510 26.603 26.473
median stay/patient (days) 12 17 19
average no. of tests/patient 3.121 6.752 2.884
no. of tests 1701 2370 871
no. of positive tests 910 736 480
proportion of positive tests 0.5349 0.3105 0.5510
days of study 1574 1566 1547
total no. of days in ICU 10088 9338 7995
total no. of days antimicrobials prescribed 7322 6773 5863 Table 2.1:Summary statistics for the p-MRSA, p-Wounds and p-Respiratory
Data Sets.
Antimicrobial p-MRSA p-Wounds p-Respiratory
Aminoglycoside 1119 1058 908
Antiseptic 3715 3752 2902
Cephalosporin 1327 1014 892
Glycopeptide 2900 2691 2404
Macrolide 1278 1096 1099
Nitroimidazole 1136 941 760
Oxazolidinone 118 129 89
Penicillin 639 625 450
Polymyxin 161 173 136
Quinolone 549 397 468
Rifamycin 128 80 108
Table 2.2:Number of days each antimicrobial group was prescribed for the p-MRSA, p-Wounds and p-Respiratory Data Sets.