mixture modeling with applications in alzheimer's disease

208 Pages·2017·1.48 MB·English

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Theses and Dissertations--Epidemiology and
College of Public Health
Biostatistics
2017
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DDIISSEEAASSEE
Frank Appiah
University of Kentucky, [email protected]
Digital Object Identifier: https://doi.org/10.13023/ETD.2017.100
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Appiah, Frank, "MIXTURE MODELING WITH APPLICATIONS IN ALZHEIMER'S DISEASE" (2017). Theses
and Dissertations--Epidemiology and Biostatistics. 14.
https://uknowledge.uky.edu/epb_etds/14
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Frank Appiah, Student
Dr. Richard J. Charnigo, Major Professor
Dr. Steven Browning, Director of Graduate Studies
MIXTURE MODELING WITH APPLICATIONS IN ALZHEIMER’S DISEASE
ABSTRACT OF DISSERTATION
A dissertation submitted in partial
fulfillment of the requirements for
the degree of Doctor of Philosophy in
the College of Public Health at the
University of Kentucky
By
Frank Appiah
Lexington, Kentucky
Co-Directors: Dr. Richard Charnigo, Professor of Statistics and Biostatistics
and Dr. David Fardo, Associate Professor of Biostatistics
Lexington, Kentucky 2017
©
Copyright Frank Appiah 2017
ABSTRACT OF DISSERTATION
MIXTURE MODELING WITH APPLICATIONS IN ALZHEIMER’S DISEASE
This dissertation involves an application of mixture of regression models to 114 indi-
viduals who are cognitively intact (from the Alzheimer’s Disease and Neuroimaging
Initiative-ADNI, data). The correct number of components in the model were esti-
mated with the Singular BIC (SBIC), marking the first time it has been applied to
such a problem. The smallest true model in conjunction with the approximation of
SBIC was fixed at 1. The resulting posterior probabilities from the model were used
to estimate the probability of a person transitioning and risk plots were obtained
that could in principle be used by clinicians to identify patients at risk. This work
also proposed a model selection criterion for mixture of regression models with ap-
plication to the ADNI data. Finally simulation studies were conducted to compare
the performance of the novel model selection and existing criteria.
KEYWORDS: Mixture models, cognitively intact, Alzheimer’s disease, model com-
plexity/component, selection criteria
Frank Appiah
Author’s signature
April 25, 2017
Date
MIXTURE MODELING WITH APPLICATIONS IN ALZHEIMER’S DISEASE
By
Frank Appiah
Richard Charnigo
Co-Director of Dissertation
David Fardo
Co-Director of Dissertation
Steven Browning
Director of Graduate Studies
April 25, 2017
Date
This work is entirely dedicated to the memory of my late mother Paulina Appiah,
my wife Leslie and my children Aiden and Naomi.
ACKNOWLEDGMENTS
I am indebted to my wife Leslie A. Appiah and my children Aiden O. Appiah and
Naomi A. Appiah for their unwavering support and love throughout the years of my
graduate education. I am also very appreciative of my advisor, Dr. Charnigo and co-
chair Dr. Fardo, for providing great insights and motivation for this work. A similar
heartfelt thanks go to my advising committee members Drs. Abner and Mays, for
their patience, directions and thought provoking questions. This acknowledgement
will be incomplete without giving a special thanks to the woman who with the help
of God made this day a possibility. This woman is none but my late mother Mrs.
Paulina Appiah, who passed away on March 19, 2014. I am very thankful for all
the work and ’painful sacrifices’ she made for me. Mom, I dedicate this work in its
entirety to your memory. God bless.
iii
TABLE OF CONTENTS
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Definition of Mixture Models and Examples . . . . . . . . . . . . . . 1
1.2 Review of Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Review of Mixture Model Applications to Alzheimer’s Disease . . . . 15
1.4 Review of Existing Model Selection Criteria and Mixture of Regression 19
Chapter 2 An Application of A Bivariate Normal Mixture Model . . . . . . . 22
2.1 Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Methodologies, Cognitive Assessment and Review of Related Concepts 27
2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4 Limitations and Future Directions . . . . . . . . . . . . . . . . . . . . 47
2.5 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Chapter 3 Application of Mixture of Linear Regressions Models And the Ap-
proximate Singular Bayesian Information Criterion . . . . . . . . 76
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2 General Overview of Mixture of Regression Models With An Illustration 77
3.3 Overview of Primary Objectives . . . . . . . . . . . . . . . . . . . . . 82
3.4 Methodologies and Overview of AIC . . . . . . . . . . . . . . . . . . 84
3.5 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.6 Limitations and Future Directions . . . . . . . . . . . . . . . . . . . . 104
3.7 Illustrative Computations for A1-A3 in Drton and Plummer(2016) for
Mixture of Regression Models . . . . . . . . . . . . . . . . . . . . . . 135
Chapter 4 A Singular Flexible Information Criterion From A Mixture of Lin-
ear Regressions Perspective . . . . . . . . . . . . . . . . . . . . . 158
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
iv
4.2 Deduction of Within and Between Covariance Matrices . . . . . . . . 159
4.3 Definition and Derivation of SFLIC . . . . . . . . . . . . . . . . . . . 163
4.4 Consistency of SFLIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.5 Application of SFLIC to the ADNI data . . . . . . . . . . . . . . . . 169
Chapter 5 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 170
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
5.2 Overview of Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 170
5.3 Simulation Design and Results . . . . . . . . . . . . . . . . . . . . . . 172
Chapter 6 Supplementary Chapter . . . . . . . . . . . . . . . . . . . . . . . 178
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
6.2 Review of Other Comparable Models Fitted As Part of This Work . . 178
Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Oral Presentations (Delivered by First author) . . . . . . . . . . . . . . . . 188
Poster Presentations (Delivered by First author) . . . . . . . . . . . . . . 189
External Funding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Professional Organizations . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Leadership Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
v
LIST OF FIGURES
2.1 Original Biomarkers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Derived Biomarker Histogram . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 BNM Component Membership Probability Distribution . . . . . . . . . . 53
2.4 BNM Predicted Components Scatterplot . . . . . . . . . . . . . . . . . . 54
2.5 BNM Component Kaplan Meier Plots . . . . . . . . . . . . . . . . . . . 55
2.6 Component contour plots . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.7 The empty circles identify potential outliers among the eight participants 57
2.8 Joint Biomarker contour plot . . . . . . . . . . . . . . . . . . . . . . . . 58
2.9 Joint Biomarker density plot . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.10 ROC plot. AUC: Area under the curve . . . . . . . . . . . . . . . . . . . 60
2.11 Risk Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.12 Risk Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.13 Risk Differentiation Boundaries . . . . . . . . . . . . . . . . . . . . . . . 63
2.14 BNM Four Component Membership Probability Distribution . . . . . . . 64
2.15 BNM Four Component Kaplan Meier Plots . . . . . . . . . . . . . . . . 65
2.16 BNM Predicted Four Component Plots . . . . . . . . . . . . . . . . . . . 66
2.17 Comparison of rtaubeta between CN and MCI/AD groups . . . . . . . . 67
2.18 Comparison of rptaubeta between CN and MCI/AD groups . . . . . . . 68
2.19 Contours embedded on risk components . . . . . . . . . . . . . . . . . . 69
3.1 Relationship between biomarkers ratios and race. + represents the grand
mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.2 Relationship between biomarker ratios and Apoe4 + represents the grand
mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.3 Relationship between biomarkers, race and Apoe4. + is grand mean. . . 108
3.4 Joint Distribution of rtaubeta and rptaubeta Given Race . . . . . . . . 109
3.5 Posterior probability plot with race as predictor in the mixture regression
model indicates that the model is well separated . . . . . . . . . . . . . 110
3.6 Individual biomarker ratios grouped into different risk regions. Here race
is the predictor variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.7 The survivability of the two groups over time given in weeks. Here race
is the predictor variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.8 Risk strata for Blacks from the posterior probabilities obtained from the
mixture of linear regression with race as covariate . . . . . . . . . . . . . 113
vi