Statistical Methods for Correlated Count Data Pubblico

Abstract

Current biomedical research has generated large datasets with complexities requiring new or improved methods of analysis. In this dissertation, I propose various statistical methods for analyzing correlated count datasets motivated by different scientific questions.

 

Meta-analysis of functional neuroimaging data has become increasingly important. Much attention has been paid to detect consistent activation regions or locations across independently performed studies, while very limited works have focused on co-activation pattern identifications. We propose a Bayesian Poisson-Gamma graphical model for which we introduce a sparsity indicator for the co-activation strength. We develop efficient posterior inference for estimating the co-activation patterns and the associated brain network. We illustrate our methods via simulation studies and a meta-analysis of functional neuroimaging data for emotion state studies. As a results, we are able to create a statistical framework that allows us to make inference about functional co-activation in the brain for coordinate-based meta-analysis data and reproduce general findings in literature.

 

Influenza, one of the most common transmissible infectious diseases of the respiratory tract, affects populations worldwide. Influenza-associated excess mortality is commonly estimated from time-series of death counts. Presence of temporal autocorrelation in death counts is a well-recognized analytic challenge. We used United States weekly vital records, viral surveillance of 4 influenza subtypes, and population data from 1981 to 2014 to evaluate two methods for addressing temporal autocorrelation. We examined (1) a parametric bootstrap method for generalized linear models that incorporates autocorrelation in the residuals and (2) a Bayesian hierarchical model that incorporates autocorrelation within the mean. Age-specific seasonal influenza-associated excess deaths were estimated from respiratory-coded deaths.

 

The aforementioned methods, provided unexpected results. The Bayesian method consistently estimated lower influenza-associated mortality compared to the bootstrap method, and often smaller standard error. The smaller estimates may be attributed to better control of temporal residual confounding of viral proxy association. To explore the presence and effect of temporal residual confounding in the model, we examine a methods for adjusting for long-term and seasonal trends using flexible splines. Via simulation study, we evaluate the timescale of the confounding between the outcome and predictors time-series as well as the relationship strength between influenza proxies and trend. As a results, we note how seasonal trend is accounted for and a tightly correlated timescale of confounding have the greatest impact on influenza-related mortality estimation.

Table of Contents

1 Introduction 1

1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Introduction to Influenza . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Motivating Influenza Mortality Dataset . . . . . . . . . . . . . 4

1.3 An Introduction to the Human Brain . . . . . . . . . . . . . . . . . . 4

1.3.1 Functional Neuroimaging . . . . . . . . . . . . . . . . . . . . . 5

1.3.2 Meta-Analysis of Functional Neuroimaging . . . . . . . . . . . 6

1.3.3 Motivating Neuroimaging Dataset . . . . . . . . . . . . . . . . 6

1.4 Count Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Correlated Response Data . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Bayesian Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.6.1 Impact of Bayesian Method on Biomedical Research . . . . . . 10

1.6.2 Bayesian Tools . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.7 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Bayesian analysis of multivariate sparse count data with application

to meta-analysis of functional neuroimaging data 12

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Neuroimaging . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.2 Preprocessing Pipeline . . . . . . . . . . . . . . . . . . . . . . 14

2.1.3 fMRI from single-subject studies . . . . . . . . . . . . . . . . . 15

2.1.4 Meta-Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.1.1 Poisson-Gamma Model . . . . . . . . . . . . . . . . . 21

2.2.1.2 Sparse Poisson-Gamma Model . . . . . . . . . . . . . 22

2.3 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.0.1 Simulation Results . . . . . . . . . . . . . . . . . . . 24

2.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3 Estimation of United States (US) Influenza-Associated Mortality

Model 36

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1.1 Global Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1.2 USA Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.1 History of Influenza Mortality Models and Current Methods . 42

3.2.2 US National Mortality, Population, and Influenza Surveillance

Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2.3 Time-Series Model for Estimating Influenza-Associated Deaths 45

3.2.4 Accounting for Temporal Correlation Using Residuals . . . . . 46

3.2.5 Accounting for the Temporal Correlation Using the Mean . . . 48

3.2.6 Application to US Mortality Data . . . . . . . . . . . . . . . . 49

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4 Addressing Long-term and Seasonal Trends in Influenza-Associated

Mortality Model 57

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.2 Application to US Mortality Data . . . . . . . . . . . . . . . . . . . . 64

4.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

A Appendix for Chapter 2 79

B Appendix for Chapter 3 81

C Appendix for Chapter 4 94

Bibliography 123

About this Dissertation

Rights statement

• Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.

School	Laney Graduate School
Department	Biostatistics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Biology, Biostatistics
Parola chiave	correlated data, count data
Committee Chair / Thesis Advisor	Kang, Jian, Emory University Chang, Howard, Emory University
Committee Members	Haber, Michael, Emory University Iuliano, Danielle, Centers for Disease Control and Prevention

Ultima modifica

Primary PDF

Thumbnail	Title	Date Uploaded	Actions
	Statistical Methods for Correlated Count Data ()	2018-04-05 10:33:24 -0400	Press to Select an action Download

Supplemental Files

Thumbnail	Title	Date Uploaded	Actions