Modeling Hierarchical Data, Allowing for Overdispersion and Zero Inflation, in Particular Excess ...

201 Pages·2014·2.05 MB·English

Modeling Hierarchical Data,
Allowing for Overdispersion
and Zero Inflation,
in Particular Excess Zeros
Wondwosen Kassahun Yimer
Promotor: Prof. dr. Geert Molenberghs
Co-Promotor: Prof. dr. Christel Faes

Acknowledgements
Itisapleasuretothankmanypeoplewhomadethisthesispossible. Thisworkwould
not have been possible without the support and help of them.
First and foremost I would like to express my heartfelt gratitude to my PhD
promotors Prof. dr. Geert Molenberghs and Prof. dr. Christel Faes. I am very
grateful to Geertfor his enthusiasm,his inspiration,his guidance, his encouragement
andunderstandingme. Geert,ithasbeenapleasureandagreatopportunitytowork
with you. I would also like to express my sincere thanks to Christel, for her great
ideas,suggestionsandinvaluable help. Christel,youhavebeenalwayswilling to help
me, I thank you so much.
I would like to thank Prof. dr. Geert Verbeke for his invaluable contributions,
commentsandsuggestions,asco-author. Iamalsoverymuchthankfultomycolleague
Thomas Neyens for working together with me from the start, and for the useful
discussions that we had together. Thomas, I thank you so much for your friendship
and help in many ways.
IamindebtedtotheVLIRIUC-JUprojectforfundingmyPhD.Iamverygrateful
to Prof. dr. Paul Janssen (Modeling Project Leader, North) for his help to get me
first incontactwith my promoters,andhis continuoussupport inmy visitat Hasselt
University. I wouldlike to thank Prof. dr. Luc Duchateau(ProgrammeCoordinator,
North) and Mr. Kora Tushune (Programme Coordinator, South) for their contribu-
tion and continuous support in the course of my PhD. My thanks go to Prof. dr.
Ziv Shkedy for his support in various ways, specially during my visits at CENSTAT.
I am grateful to all staff members of the program support and administrative units
at Jimma, Hasselt and Ghent Universities, specially: Mr. Kasahun Eba, Mr. Boka
Assefa, Mr. Jemal Abafita, Mr. Marc Thoelen, Ms. Martine Machiels, Ms. Heleke
ii
Bayens, Ms. Mira Jasheri and Ms. Annick Verheylezoon for assisting me in many
different ways.
I am indebted to many colleagues at Jimma University for the permission to use
several data sets resulting from our joint research or their own. In this line, I would
like to thank Prof. Tefera Belachew and other research team members of the Jimma
Longitudinal Family Survey of Youth for the kind permission to use the data, and
colleagues in the malaria incidence study of under ten years old children around the
Gilgel-Gibe hydroelectric dam: Dr. Delenasaw Yewhalaw, Prof. Kifle W/Michael,
Mr. Kora Tushune, and Prof. dr. Luc Duchateau. I would also like to thank Mr.
Fasil Tessema and Prof. MakonenAssefa for the permissionto use the Jimma Infant
Growth Data. Support from WHO Special Programme for Researchand Training in
TropicalDiseases(TDR)andIAPresearchNetworkP7/06oftheBelgianGovernment
(Belgian Science Policy) is gratefully acknowledge.
I am indebted to my many colleagues at CENSTAT for providing me different
support. IwouldliketothankYehenew,Girma,Birhanu,Bedilu,AkliluandAbelfor
their friendship and advice they provided.
I would also like to thank my entire extended family members for their uncondi-
tionalloveandsupportsandencouragement. MybelovedmotherTerengoH/Mariam,
my lovely sisters and brother were particularly supportive.
Finally, and most importantly, I am forever indebted to my family, specially my
wife, MeseretW/Cherkos,who have alwaysencouragedme to pursue my studies and
taken full responsibility of family issues in the course of my absence. To whom I
dedicate this thesis.
Thank you everyone that I could not mention here, who have encouraged and
helped me in different ways.
Wondwosen KassahunYimer
04 April 2014
Diepenbeek
List of Publications
Kassahun,W.,Neyens,T.,Molenberghs,G.,Faes,C.,andVerbeke,G.(2012).
•
ModelingOverdispersedLongitudinalBinaryDataUsingaCombinedBetaand
Normal Random Effects Model. Archives of Public Health, DOI: 10.1186/0778-
7367-70-7.
Kassahun, W., Neyens, T., Molenberghs, G., Faes, C., and Verbeke, G.
•
(2013). A Joint Model for Hierarchical Continuous and Zero-inflated Overdis-
persed Count Data. Journal of Statistical Computation and Simulation, DOI:
10.1080/00949655.2013.829058.
Kassahun,W.,Neyens,T.,Molenberghs,G.,Faes,C.,andVerbeke,G.(2014).
•
AZero-InflatedOverdispersedandHierarchicalPoissonModel. StatisticalMod-
elling, accepted for publication.
Kassahun,W.,Neyens,T.,Molenberghs,G.,Faes,C.,andVerbeke,G.(2014).
•
MarginalizedMultilevelHurdleandZero-InflatedModelsforOverdispersedand
Correlated Count Data with Excess Zeros. Statistics in Medicine, revised and
resubmitted.

Contents
Table of Contents v
List of Abbreviations x
List of Tables xiii
List of Figures xix
1 Introduction 1
2 Motivating Examples 7
2.1 The Jimma Infant Growth Study . . . . . . . . . . . . . . . . . . . . 7
2.2 Anopheles Mosquito Data . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Indoor Resting Collection (IRC) . . . . . . . . . . . . . . . . . 11
2.2.2 CDC Light Trap Catches (CDC) . . . . . . . . . . . . . . . . . 14
2.3 Jimma Longitudinal Family Survey of Youth . . . . . . . . . . . . . . 15
2.4 A Clinical Trial in Epileptic Patients . . . . . . . . . . . . . . . . . . . 18
3 Basic Concepts and Models 21
3.1 Generalized Linear Models . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Binary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.2 Count Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 OverdispersionModels . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 A Model for Longitudinal Continuous Data . . . . . . . . . . . . . . . 25
3.4 Generalized Linear Mixed Models . . . . . . . . . . . . . . . . . . . . 26
3.5 Models Combining Overdispersionwith Normal Random-Effects . . . 27
v
vi Table of Contents
3.6 MarginalizedMultilevel Models . . . . . . . . . . . . . . . . . . . . . 29
3.7 Models for Excessive Zero Observations . . . . . . . . . . . . . . . . . 30
3.8 Generalized Estimating Equations . . . . . . . . . . . . . . . . . . . . 31
3.9 HierarchicalBayesianModel . . . . . . . . . . . . . . . . . . . . . . . 32
4 Modeling Overdispersed and Correlated Binary Data 35
4.1 Models Combining Conjugate and Normal Random Effects . . . . . . 36
4.2 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3.1 The Jimma Infant Growth Study . . . . . . . . . . . . . . . . . 40
4.3.2 Jimma Longitudinal Family Survey of Youth . . . . . . . . . . 41
4.3.3 Comparison Between Estimation Methods . . . . . . . . . . . . 44
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5 A Zero-Inflated Overdispersed Hierarchical Poisson Model 53
5.1 Zero-inflatedModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.1 The Jimma Infant Growth Study . . . . . . . . . . . . . . . . . 56
5.3.2 Epilepsy Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.4 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.4.1 Simulation Setting . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6 MarginalizedMultilevelHurdleandZero-InflatedModelsforOverdis-
persed and Correlated Count Data with Excess Zeros 69
6.1 MarginalizedHurdle Combined Model . . . . . . . . . . . . . . . . . . 71
6.2 MarginalizedZero-Inflated Combined Model . . . . . . . . . . . . . . 72
6.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.4.1 IRC Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.4.2 CDC Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.4.3 Jimma Longitudinal Family Survey of Youth . . . . . . . . . . 87
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Table of Contents vii
7 AJointModelforHierarchicalContinuousandZeroInflatedOverdis-
persed Count Data 99
7.1 A Joint Combined Model for Continuous and Zero-inflatedCount Data 100
7.2 MarginalizedJoint H(NN)(PNG) and
ZI(NN-)(PNG) Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.4 Analysis of the Jimma Infant Growth Study . . . . . . . . . . . . . . . 104
7.5 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.5.1 Simulation Settings. . . . . . . . . . . . . . . . . . . . . . . . . 109
7.5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8 General Conclusions 117
9 Nederlandse samenvatting 125
Bibliography 129
A SAS and WinBugs Codes for Overdispersed Hierarchical Binary
Data 135
A.1 A SAS Program. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.2 WinBugs Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 137
B A SAS Program for the Zero-Inflated Models (Epilepsy Study) 143
B.1 (P--), ZI(P--) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.2 (PN-), ZI(PN-) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.3 (P-G), ZI(P-G) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
B.4 (PNG), ZI(PNG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
C A SAS Program for Marginalized Models (IRC Dataset) 149
C.1 ZI(PNG) and MZI(PNG) Implementaion. . . . . . . . . . . . . . . . . 149
C.2 H(PNG) and MH(PNG) Implementaion . . . . . . . . . . . . . . . . . 154
C.3 M(PNG) and M(PN-) Implementaion . . . . . . . . . . . . . . . . . . 158
D A SAS Program for the Joint Model 159
D.1 ZI(NN-)(PNG), H(NN-)(PNG) and
special cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
D.2 Test of Zero-inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
D.3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
viii Table of Contents
E Posterior Densities 175