Statistical methods to evaluate disease outcome diagnostic accuracy of multiple biomarkers with

231 Pages·2016·1.09 MB·English

Statistical methods to evaluate disease outcome diagnostic
accuracy of multiple biomarkers with application to HIV and
TB research
By
Muna Balla Elshareef Mohammed
[email protected]
Supervisor : Professor Henry G. Mwambi
[email protected]
School of Mathematics, Statistics and Computer Science
University of KwaZulu-Natal
Pietermaritzburg, South Africa
A thesis submitted for the fulfillment of the requirements for
Doctor of Philosophy at the
School of Mathematics, Statistics and Computer Sciences, University of
KwaZulu-Natal, Pietermaritzburg
October 2015
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Abstract
Onechallengeinclinicalmedicineisthatofthecorrectdiagnosisofdisease. Medicalresearchers
invest considerable time and effort to improving accurate disease diagnosis and following from
this diagnostic tests are important components in modern medical practice. The receiver oper-
ating characteristic (ROC)isastatisticaltoolcommonlyusedfordescribingthediscriminatory
accuracy and performance of a diagnostic test. A popular summary index of discriminatory
accuracy is the area under ROC curve (AUC). In the medical research data, scientists are
simultaneously evaluating hundreds of biomarkers. A critical challenge is the combination
of biomarkers into models that give insight into disease. In infectious disease, biomarkers
are often evaluated as well as in the micro organism or virus causing infection, adding more
complexity to the analysis. In addition to providing an improved understanding of factors
associated with infection and disease development, combinations of relevant markers are im-
portant to the diagnosis and treatment of disease. Taken together, this extends the role of, the
statistical analyst and presents many novel and major challenges. This thesis discusses some
of the various strategies and issues in using statistical data analysis to address the diagnosis
problem, of selecting and combining multiple markers to estimate the predictive accuracy of
test results. We also consider different methodologies to address missing data and to improve
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the predictive accuracy in the presence of incomplete data.
The thesis is divided into five parts. The first part is an introduction to the theory behind
the methods that we used in this work. The second part places emphasis on the so called
classic ROC analysis, which is applied to cross sectional data. The main aim of this chap-
ter is to address the problem of how to select and combine multiple markers and evaluate
the appropriateness of certain techniques used in estimating the area under the ROC curve
(AUC). Logistic regression models offer a simple method for combining markers. We applied
resampling methods to adjust for over-fitting associated with model selection. We simulated
several multivariate models to evaluate the performance of the resampling approaches in this
setting. We applied these methods to data collected from a study of tuberculosis immune
reconstitution inflammatory syndrome (TB-IRIS) in Cape Town, South Africa. Baseline levels
of five biomarkers were evaluated and we used this dataset to evaluate whether a combination
ofthesebiomarkerscouldaccuratelydiscriminatebetweenTB-IRISandnonTB-IRISpatients,
by applying AUC analysis and resampling methods.
The third part is concerned with a time dependent ROC analysis with event-time outcome
and comparative analysis of the techniques applied to incomplete covariates. Three different
methods are assessed and investigated, namely mean imputation, nearest neighbor hot deck
imputation and multivariate imputation by chain equations (MICE). These methods were used
together with bootstrap and cross-validation to estimate the time dependent AUC using a
non-parametric approach and a Cox model. We simulated several models to evaluate the
performance of the resampling approaches and imputation methods. We applied the above
methods to a real data set.
Thefourthpartisconcernedwithapplyingmoreadvancedvariableselectionmethodstopredict
the survival of patients using time dependent ROC analysis. The least absolute shrinkage and
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selectionoperator(LASSO)Coxmodelisappliedtoestimatethebootstrapcross-validated,632
and 632+ bootstrap AUCs for TBM/HIV data set from KwaZulu-Natal in South Africa. We
also suggest the use of ridge-Cox regression to estimate the AUC and two level bootstrapping
to estimate the variances for AUC, in addition to evaluating these suggested methods.
The last part of the research is an application study using genetic HIV data from rural
KwaZulu-Natal to evaluate the sequence of ambiguities as a biomarker to predict recent infec-
tion in HIV patients.
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Preface
The work described in this thesis was carried out from March 2013 to October 2015, under the
supervision and direction of Professor Henry G. Mwambi, School of Mathematics, Statistics
and Computer Science, University of KwaZulu-Natal, Pietermaritzburg.
The thesis represent original work of the author and has not been otherwise been submitted in
any form for any degree or diploma to any University. Where use has been made of the work
of others it is duly acknowledged in the text.
Signature (Student) Date: 31st of March 2016
Signature (Supervisor) Date: 31st of March 2016
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Dedication
TO MY LOVELY PARENTS DR BALLA AND HANAN, MY DEAR HUSBAND AYOUB, MY LOVELY
DAUGHTER FATIMA, MY BROTHERS MUGTABA, AHMED AND TO THE SOUL OF MY SISTER
FATIMA (TOTA), I DEDICATE THIS WORK.
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Acknowledgements
First of all, I thank ALLAH for his Grace and Mercy showered upon me. I heartily express my
profound gratitude to my supervisor, Professor Henry G. Mwambi, for his invaluable learned
guidance, advises, encouragement, understanding and continued support he has provided me
throughout the duration of my studies which led to the compilation of this thesis. I will be
always indebted to him for introducing me to this fascinating area of application in health
research and creating my interest in Biostatistics.
I lovingly thank my dear husband Ayoub, who supported me each step of the way and without
his help and encouragement it simply never would have been possible to finish this work. I
also would like to thank my lovely parents Hanan and Dr Balla for their continuous support
and best wishes.
Also I would like to thank Mr Rob Ettershank, for his kindness and valuable corrections,
comments and suggestions through the editing and proofreading process.
I am grateful for the facilities made available to me by the School of Mathematics, Statistics
and Computer Science of the University of KwaZulu-Natal (UKZN), Pietermaritzburg. I am
also grateful for the financial support that I have received from UKZN and the South African
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CenterforEpidemiologicalModellingandAnalysis(SACEMA).MythanksextendtoProfessor
Robert Wilkinson, Dr Suzaan Marais and Professor Tulio de Oliveira for supporting us with
real datasets.
Finally I sincerely thank my entire extended family represented by Balla, Hanan, Mohammed
Elmojutaba, Ahmed, Fatima (tota), Basheer, Suaad, Eihab, Adeeb and Nada.
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Table of contents
Abstract ii
Preface v
Dedication vi
Acknowledgements vii
Table of contents ix
List of notations xvi
List of figures xix
List of tables xxi
1 Introduction 1
ix