Stochastic modelling and Bayesian inference for the effect of antimicrobial treatments on ...

318 Pages·2017·30.5 MB·English

by  Christine Middleton

Stochastic Modelling and Bayesian Inference for
the Effect of Antimicrobial Treatments on
Transmission and Carriage of
Nosocomial Pathogens
Eleni Verykouki
Thesis submitted to The University of Nottingham
for the degree of Doctor of Philosophy
July 2013
Abstract
Nosocomial pathogens are usually organisms such as fungi and bacteria that
are associated with infections caused in a hospital environment. Examples
include Clostridium difficile, Pseudomonas aeruginosa, Vancomycin-resistant
enterococcus and Methicillin-resistant Staphylococcus aureus (MRSA). MRSA,
like most of the nosocomial pathogens, is resistant to antibiotics and is one of
the most serious causes of infections. In this thesis we assess the effects of an-
tibioticsandantisepticsoncarriageandtransmissionofMRSA.Weusehighly-
detailed patient level data taken from two Intensive Care Unit (ICU) wards
in St. Guys and Thomas’s hospital in London, where patients were receiving
dailyantimicrobialtreatmentandadecolonisationprotocolwasused. Wework
in discrete time and employ three different patient-level stochastic models in a
Bayesian framework to explore the effectiveness of antimicrobial treatment on
MRSAindiscretetime. Wealsodevelopsuitablemethodsofmodelassessment.
The first two models assume that there is no transmission between patients in
the ICU wards. Initially a Markov model is used, assuming perfect swab test
specificity and sensitivity, to describe the colonisation status of an individual
onadailybasis. ResultsareobtainedusingGaussianrandomwalkMetropolis-
Hastingsalgorithms. Wefindsomeevidencethatdecolonisationtreatmentand
OxazolidinonehaveapositiveeffectinclearingMRSAcarriage.
The second model is a hidden Markov model and assumes perfect swab test
specificity but imperfect sensitivity. We obtain the results using data- aug-
mentedMarkov ChainMonte Carlo(MCMC)algorithms tomake inferencefor
the unobserved patient colonisation states. We find evidence that the Antisep-
tictreatmentusedduringthedecolonisationperiodiseffectiveintheclearance
ofMRSAcarriage.
In the third case we assume that there is MRSA transmission between the pa-
i
tientsintheICUs. Weusethreedifferentstochastictransmissionmodelswhich
overcome many of the unrealistic assumptions of other models. A data- aug-
mented MCMC algorithm is employed in order to estimate the transmission
rates of MRSA between the patients assuming imperfect swab test sensitivity.
We found no or limited evidence that antibiotic use affects the transmission
process,whereasantiseptictreatmentwasfoundtohaveaneffect.
ii
Acknowledgements
IamverygratefultomytwosupervisorsPhilipO’NeillandTheodoreKypraios,
for all their guidance, advice and support during my PhD studies. They were
alwaysthereformeandIfeelveryluckytobetheirstudent.
Many thanks to my family and especially to my parents who were extremely
supportive,notonlyduringmyPhDbutthroughoutmylifeandeducation.
Many thanks to Christos for all the encouragement, being always there for me
andforallthetimeshecametovisitmeintheUK.
IwouldalsoliketothankmyofficematesandfriendsinNottinghamformaking
mylifeenjoyableandfun.
ManythankstotheSchoolofMathematicalSciencesadministrationandITstaff
for all their assistance. Also, many thanks to Dave Parkin for the endless times
he fixed my computer, especially during the last month before the submission
ofthisthesis.
Last but not least, I would like to thank Jonathan Edgeworth and Rahul Batra
atGuy’sandSt. Thomas’HospitalTrustformakingthedatausedinthisthesis
availabletous.
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Contents
ListofFigures ix
ListofTables xviii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Staphylococcusaureus-MRSA . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Theroleofantimicrobialtreatment . . . . . . . . . . . . . . 3
1.2.2 Decolonisationstrategies . . . . . . . . . . . . . . . . . . . 4
1.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.2 SummaryStatistics . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.3 AntimicrobialTreatment . . . . . . . . . . . . . . . . . . . . 12
1.4 StatisticalInference . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.5 BayesianInference-MCMC . . . . . . . . . . . . . . . . . . . . . . 21
1.5.1 Bayes’Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.5.2 MarkovChainMonteCarlo . . . . . . . . . . . . . . . . . . 23
1.6 ThesisOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2 Modelling the effect of antimicrobial treatment on carriage levels of
MRSAusingMarkovmodels 28
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
iv
CONTENTS
2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.1 Priordistributions . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.2 Updatingtheparameters . . . . . . . . . . . . . . . . . . . 36
2.6 ModelAssessmentforMarkovModels . . . . . . . . . . . . . . . . 38
2.6.1 BackgroundInformation . . . . . . . . . . . . . . . . . . . . 38
2.6.2 Model assessment of the Markov model: theoretical con-
siderations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.6.3 ModelassessmentfortheMarkovmodel . . . . . . . . . . 46
2.7 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.7.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.7.2 Usingthedayintervalsfromthep-MRSADataSet . . . . 54
2.8 ResultsusingGSTTData . . . . . . . . . . . . . . . . . . . . . . . . 57
2.8.1 p-MRSADataSet . . . . . . . . . . . . . . . . . . . . . . . . 59
2.8.2 Results from the MRSA Data Set without antimicrobial
treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.8.3 Results from the MRSA Data Set including the antiseptic
treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.8.4 p-WoundsDataSet . . . . . . . . . . . . . . . . . . . . . . . 72
2.8.5 p-RespiratoryDataSet . . . . . . . . . . . . . . . . . . . . . 73
2.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3 Modelling the effect of antimicrobial treatment on carriage levels of
MRSAusinghiddenMarkovmodels 76
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
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CONTENTS
3.3 Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4 Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.4.1 Priordistributions . . . . . . . . . . . . . . . . . . . . . . . 82
3.4.2 Updatingtheparameters . . . . . . . . . . . . . . . . . . . 83
3.5 ModelAssessment . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.5.1 BackgroundInformation . . . . . . . . . . . . . . . . . . . . 86
3.5.2 Model assessment of a HMM model: theoretical consid-
erations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.5.3 Modelassessmentusingsimulations . . . . . . . . . . . . . 91
3.6 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.6.1 SimulatedData . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.6.2 Usingthedayintervalsfromthep-MRSADataSet . . . . 93
3.7 ResultsusingGSTTData . . . . . . . . . . . . . . . . . . . . . . . . 102
3.7.1 p-MRSADataSet . . . . . . . . . . . . . . . . . . . . . . . . 102
3.7.2 ResultsfromtheMRSADataSet . . . . . . . . . . . . . . . 104
3.7.3 Results from the p-MRSA Data Set including antimicro-
bialtreatment . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7.4 p-WoundsDataSet . . . . . . . . . . . . . . . . . . . . . . . 112
3.7.5 p-RespiratoryDataSet . . . . . . . . . . . . . . . . . . . . . 113
3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4 Assessing the effect of antimicrobial treatment on MRSA transmis-
sion 116
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3 Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.4 Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.4.1 Priordistributions . . . . . . . . . . . . . . . . . . . . . . . 126
4.4.2 Updatingtheparameters . . . . . . . . . . . . . . . . . . . 127
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CONTENTS
4.5 ModelAssessment . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.6 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.7 ResultsusingtheGSTTData . . . . . . . . . . . . . . . . . . . . . . 137
4.7.1 MRSADataSet . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.7.2 WoundsDataSet . . . . . . . . . . . . . . . . . . . . . . . . 147
4.7.3 RespiratoryDataSet . . . . . . . . . . . . . . . . . . . . . . 148
4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5 ConclusionsandFuturework 153
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
References 158
A AppendixfortheMarkovModel 168
A.1 p-MRSADataSet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
A.1.1 Modelfitexample . . . . . . . . . . . . . . . . . . . . . . . 173
A.1.2 Afterfirstpositivetest . . . . . . . . . . . . . . . . . . . . . 174
A.2 p-WoundsDataSet . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
A.2.1 Afterfirstpositivetest . . . . . . . . . . . . . . . . . . . . . 182
A.3 p-RespiratoryDataSet . . . . . . . . . . . . . . . . . . . . . . . . . 186
A.3.1 Afterfirstpositivetest . . . . . . . . . . . . . . . . . . . . . 190
B AppendixfortheHiddenMarkovModel 194
B.1 p-MRSADataSet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
B.1.1 Afterfirstpositivetest . . . . . . . . . . . . . . . . . . . . . 199
B.2 p-WoundsDataSet . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
B.2.1 Afterfirstpositivetest . . . . . . . . . . . . . . . . . . . . . 209
B.3 p-RespiratoryDataSet . . . . . . . . . . . . . . . . . . . . . . . . . 214
vii
CONTENTS
B.3.1 Afterfirstpositivetest . . . . . . . . . . . . . . . . . . . . . 219
C AppendixTransmissionModels 224
C.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
C.2 MRSADataSet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
C.2.1 SusceptibilityModel . . . . . . . . . . . . . . . . . . . . . . . 228
C.2.2 InfectivityModel . . . . . . . . . . . . . . . . . . . . . . . . . 234
C.2.3 FullModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
C.3 WoundsDataSet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
C.3.1 SusceptibilityModel . . . . . . . . . . . . . . . . . . . . . . . 253
C.3.2 InfectivityModel . . . . . . . . . . . . . . . . . . . . . . . . . 259
C.3.3 FullModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
C.4 RespiratoryDataSet . . . . . . . . . . . . . . . . . . . . . . . . . . 272
C.4.1 SusceptibilityModel . . . . . . . . . . . . . . . . . . . . . . . 272
C.4.2 InfectivityModel . . . . . . . . . . . . . . . . . . . . . . . . . 278
C.4.3 FullModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
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List of Figures
1.1 NumberoftestsfortheMRSADataSet. . . . . . . . . . . . . . . . 9
1.2 NumberoftestsfortheWoundsDataSet. . . . . . . . . . . . . . . 10
1.3 NumberoftestsfortheRespiratoryDataSet. . . . . . . . . . . . . 11
1.4 AntimicrobialtreatmentusefortheMRSADataSet,ward1 . . . 15
1.5 AntimicrobialtreatmentusefortheMRSADataSet,ward2 . . . 16
1.6 AntimicrobialtreatmentusefortheWoundsDataSet,ward1 . . 17
1.7 AntimicrobialtreatmentusefortheWoundsDataSet,ward2 . . 18
1.8 AntimicrobialtreatmentusefortheRespiratoryDataSet,ward1 19
1.9 AntimicrobialtreatmentusefortheRespiratoryDataSet,ward2 20
2.1 Trace plots for p and q using simulated data and assuming that we
0 0
havedailytransitions. . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.2 Kerneldensityplotsfor p and q fromthesimulateddata . . . . 52
0 0
2.3 Kernel density plots for p and q for the simulated transitions
0 0
usingthedayintervalsfromthep-MRSADataSet . . . . . . . . . 56
2.4 Scatterplot for the correlation between p and q for the simu-
0 0
lated transitions with the day intervals from the p-MRSA Data
Set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.5 Kerneldensityplotsfor p andq fromthep-MRSADataSetassuming
0 0
noantimicrobialtreatment. . . . . . . . . . . . . . . . . . . . . . . . . 60
2.6 Posterior correlations between p , q , α and β using the p-MRSA Data
0 0
Setincludingantimicrobialtreatment. . . . . . . . . . . . . . . . . . . 62
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