Random Estimating Functions to Accommodate Heterogeneity in Meta-Analysis Open Access

Abstract

Introduction: Meta-analysis is defined here as the statistical analysis of a collection of analytic results for the purpose of integrating the findings (DerSimonian & Laird, 1986). A major concern in meta-analysis is heterogeneity among the studies contributing analytic findings. Failure to account for heterogeneity could lead to misleading conclusions in a meta-analysis. The aim is to use statistical approaches to derive a common estimated odds ratio that represents the common truth behind multiple similar studies.

Methods: To accommodate heterogeneity, we propose to add a random perturbation to each component estimating function. The advantages of this proposal over a random-effects model are that, under reparametrization, the random estimating function remains unbiased, remains subject to an additive perturbation, and has a variance that is well-governed and easy to evaluate.

Results: Our new method can capture between- table heterogeneity and produces a valid estimate of the log odds ratio. An advantage of our new method is that it can be applied to further meta-analysis studies under reparametrization, by simply applying the Delta Method.

Discussion: A major advantage of our random estimating equation method over existing random-effects methods is that our new method can be implemented into meta-analyses for any 1-1 transformation of the odds ratio. Unlike a random-effects model, however, our approach does not easily suggest a data generation mechanism, which makes it challenging to conduct a simulation study. The ways of generating random observations under our model of a randomly perturbed Mantel-Haenszel estimating function need to be explored further.

Table of Contents

1. Introduction........................................................................................1

1.1 Background.......................................................................................1

1.2 Problem Statement.............................................................................1

1.3 Purpose Statement.............................................................................2

1.4 Dataset Description............................................................................3

2. Literature Review.................................................................................5

2.1 Meta-analysis....................................................................................5

2.2 Mantel-Haenszel Estimate(MH).............................................................5

2.3 DerSimonian & Laird Estimate(DSL)......................................................8

3.Methodology........................................................................................11

3.1 Study Design....................................................................................11

3.2 Log Odds Ratio Estimation and Between Table Variance Estimation...........12

3.3 Variance Estimation of Log Odds Ratio..................................................15

4. Results...............................................................................................17

4.1 Case 2 Results: Independent Binomials with large row totals mi1, mi2.......17

4.2 Case 3 Results: Independent Binomials with small row totals mi1, mi2...... 18

5. Discussion...........................................................................................20

5.1 Strengths..........................................................................................20

5.2 Limitations.........................................................................................20

References..............................................................................................22

About this Master's Thesis

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School	Rollins School of Public Health
Department	Biostatistics and Bioinformatics
Subfield / Discipline	Biostatistics - MPH & MSPH
Degree	MSPH
Submission	Master's Thesis
Language	English
Research Field	Biology, Biostatistics
Keyword	Meta-Analysis Random Estimating Equation Between-Table Heterogeneity
Committee Chair / Thesis Advisor	Hanfelt, John, Emory University
Committee Members	Zhang, Rebecca, Emory University
Partnering Agencies	Does not apply (no collaborating organization)

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