Statistical Meta-Analysis with Applications

Bimal K. Sinha, Joachim Hartung, Guido Knapp

• Publisher: Wiley-Interscience
• Year: 2011
• Print ISBN: 9780470290897
• eBook ISBN: 9781118210963
• Edition: 1
• Topic: Medicine
• Subtopic: Biostatistics

An accessible introduction to performing meta-analysis across various areas of research

The practice of meta-analysis allows researchers to obtain findings from various studies and compile them to verify and form one overall conclusion. Statistical Meta-Analysis with Applications presents the necessary statistical methodologies that allow readers to tackle the four main stages of meta-analysis: problem formulation, data collection, data evaluation, and data analysis and interpretation. Combining the authors' expertise on the topic with a wealth of up-to-date information, this book successfully introduces the essential statistical practices for making thorough and accurate discoveries across a wide array of diverse fields, such as business, public health, biostatistics, and environmental studies.

Two main types of statistical analysis serve as the foundation of the methods and techniques: combining tests of effect size and combining estimates of effect size. Additional topics covered include:

• Meta-analysis regression procedures

• Multiple-endpoint and multiple-treatment studies
  
  

• The Bayesian approach to meta-analysis
  
  

• Publication bias
  
  

• Vote counting procedures
  
  

• Methods for combining individual tests and combining individual estimates
  
  

• Using meta-analysis to analyze binary and ordinal categorical data
  
  

Numerous worked-out examples in each chapter provide the reader with a step-by-step understanding of the presented methods. All exercises can be computed using the R and SAS software packages, which are both available via the book's related Web site. Extensive references are also included, outlining additional sources for further study.

Requiring only a working knowledge of statistics, Statistical Meta-Analysis with Applications is a valuable supplement for courses in biostatistics, business, public health, and social research at the upper-undergraduate and graduate levels. It is also an excellent reference for applied statisticians working in industry, academia, and government.

CHAPTER 1
INTRODUCTION

Meta-analysis, a term coined by Glass (1976), is intended to provide the statistical analysis of a large collection of analysis results from individual studies for the purpose of integrating the findings.

Meta-analysis, or research synthesis, or research integration is precisely a scientific method to accomplish this goal by applying sound statistical procedures, and indeed it has a long and old history. The very invention of least squares by Legendre (1805) and Gauss (1809) is an attempt to solve just a unique problem of meta-analysis: use of astronomical observations collected at several observatories to estimate the orbit of comets and to determine meridian arcs in geodesy (Stigler, 1986). In order to determine the relationship between mortality and inoculation with a vaccine for enteric fever, Pearson (1904) used data from five small independent samples and computed a pooled estimate of correlation between mortality and inoculation in order to evaluate the efficacy of the vaccine. As an early application of meta-analysis in the physical sciences, Birge (1932) combined estimates across experiments at different laboratories to establish reference values for some fundamental constants in physics. Early works of Cochran (1937), Yates and Cochran (1938), Tippett (1931), and Fisher (1932) dealt with combining information across experiments in the agricultural sciences in order to derive estimates of treatment effects and test their significance. Likewise, there are plenty of applications of meta-analysis in the fields of education, medicine, and social sciences, some of which are briefly described below.

In the field of education, meta-analysis is useful in combining studies about coaching effectiveness to improve Scholastic Aptitude Test (SAT) scores in verbal and math (Rubin, 1981; DerSimonian and Laird, 1983), in studying the effect of open education on (i) attitude of students toward school and (ii) student independence and self-reliance, and in combining studies about the relationship between teacher indirectness and student achievement (Hedges and Olkin, 1985). In social science, there is a need to combine several studies of gender differences in separate categories of quantitative ability, verbal ability, and visual-spatial ability (Hedges and Olkin, 1985). For some novel applications of meta-analysis in the field of medicine, we refer to Pauler and Wakefield (2000) for three applications involving dentrifice data, antihypertension data, and preeclampsia data, to Berry (2000) for questions about benefits arid risks of mammography of women based on six studies, to Brophy and Joseph (2000) for meta-analysis involving three studies to compare streptokinase and tissue-plasminogen activator to reduce mortality following an acute myocardial infarction, and lastly to Dominici and Parmigiani (2000) for an application of metaanalysis involving studies in which outcomes are reported on continuous variables for some medical outcomes in some studies and on binary variables on similar medical outcomes in some other studies. Of course, there are numerous other diverse applications of meta-analysis in many other fields. We mention several applications below.

A: Business applications. In the context of business management and administration, one often encounters several studies with a common effect, and the problem then is of drawing suitable inference about the common effect based on the information from all the studies. Here are some examples. In the context of studying price elasticity, Tellis (1988) reports results from 42 studies! Sethuraman (1995) performed meta-analysis of national brand and store brand cross-promotional price elasticities. Lodish et al. (1995) reported results of 389 real world split cable TV advertising experiments: How TV advertising works? Churchill et al. (1985) reported meta-analysis of the determinants of salesperson performance. Farley and Lehmann (1986, 2001) and Farley, Lehmann, and Sawyer (1995) emphasized the important role of meta-analysis in international research in marketing. A current major thrust in marketing has been an attempt to create global products and brands while retaining local requirements: think global, act local. Deciding which elements of which products can be produced globally and which locally requires meta-analysis of each of the elements.

B: Environmental applications. In the context of environmental problems, there are several situations where the meta-analysis methods can be successfully applied. Here is a partial list of such applications.

Evaluation of superfund cleanup technologies (Sinha, O’Brien, and Smith, 1991; Sinha and Sinha, 1995). Cleaning up of superfund waste sites (nuclear/chemical/biological) at the National Priorities List (NPL), based on an index comprising four measures, air, groundwater, soil, and surface water, often requires innova- tive/extremely expensive technology. A critical study of performance of the suggested technologies after a certain amount of time is highly desirable. If found useful, the technologies can be encouraged to continue at the same site. If otherwise, this should be determined as soon as possible so that suitable corrective measures can be taken. Towards this end, a common procedure is to study a preremediation baseline sample and an interim sample taken after a certain period of operation of the technology and test if a desirable percentage of the total contaminant has been removed. Comparison of a few such technologies can be based on several studies, and a data synthesis or pooling of evidence is very natural here in order to determine the final ranking of the technologies.

Assessment of gasoline quality (Yu, Sun, and Sinha, 2002). The U.S. Environmental Protection Agency (EPA) evaluates/regulates gasoline quality based on what is known as Reid vapor pressure (RVP). Samples of gasoline are taken from various pumps and RVPs are measured in two ways: on-site at the field level (cheap and quick) and also off-site at the laboratory level (expensive/higher precision). This usually results in two types of data: field data and lab data. Gasoline quality based on RVP can then be determined combining the evidence in both the data sets—a clear application of meta-analysis!

Water quality in Hillsdale Lake (Li, Nussbaum, and Sinha, 2000). Hillsdale Lake, a large federal reservoir located about 30 miles from the Kansas City metropolitan area, was authorized by the U.S. Congress in 1954 as part of a comprehensive flood control plan for the Osage and Missouri River Basins. The lake is a major recreational resource— over 500,000 visitors annually—and is also a significant source of drinking water. It is therefore essential that the water quality in this lake, as measured by Secchi depth, be regulated regularly. To achieve this, typically data from a survey of lake users in the various categories of swimming, fishing, boating, skiing, and water sports can be collected and analyzed in order to establish what level of water clarity users perceive as good. Again, it is quite possible that several studies are conducted for this purpose, and there is a need to pool the evidence from such studies to arrive at an overall conclusion about the water clarity level.

A comparison of CMW and DPW for groundwater monitoring (Li, 2000). Long-term monitoring of contamination of groundwater at former military land sites is performed by boring wells into the ground at predetermined locations and then assessing trace amounts of certain chemicals. There are two well-known methods for this purpose: an expensive traditional method of conventionally monitored wells (CMWs) and a relatively cheaper new methodology of direct push wells (DPWs). In order to compare these two methods, a joint study was conducted by the United States Air Force with the EPA to evaluate the assessment of pollutants. The former Hanscom Air Force Base (HAFB) located in Middlesex County, Massachusetts, and straddling the towns of Bedford, Concord, Lexington, and Lincoln was selected as the study site, and groundwater samples were collected for an assessment of long-term monitoring with both CMWs and DPWs based on 31 paired well locations. Data were collected on nine volatile organic carbons (VOCs): vinyl chloride, 1,1 -DCA, benzene, toluene, o-xylene, trans- 1,2-DCE, TCE, and 1,4-DCA—labeled as VOC1, VOC2, VOC3, VOC4, VOC5, VOC6, VOC7, VOC8, and VOC9. The site was divided into three regions, and data were collected separately in each region. It is then in the spirit of meta-analysis that we combine the results of the three regions and decide if the two methods perform equally or there is a significant difference.

Effect of second-hand smoking on women. This of course is a vital environmental issue with a potential for adverse health effects. Several studies were conducted in many parts of the world to determine if second-hand smoking is harmful for women, and it is absolutely essential that we carry out a meta-analysis, pooling the evidence from all the studies, in order to find out the underlying state of the matter. The relevant data set is reported in Section 18.6. We should mention that based on a suitable metaanalysis of the collected information, an advisory committee of the EPA designated environmental tobacco smoke as a carcinogen.

C: Health sciences applications. In the context of medicine or health science problems, there are several situations where the meta-analysis methods can be successfully applied. Here is a partial list of such applications.

Antiplatelet drug for patients with ischemic attacks. In 1988, the question of whether to prescribe an antiplatelet drug for patients with transient ischemic attacks to prevent stroke was controversial. At that time, many randomized trials of antiplatelet drugs to treat patients with cerebrovascular disease have been completed, but the studies were variable in question and their results were contradictory. A meta-analysis of these studies by the Antiplatelet Trialist’ Collaboration (1988) found a highly significant 22% reduction in the estimated relative risk of stroke, myocardial infarction, and vascular death in patients with cerebrovascular disease who were treated with an antiplatelet drug.

Functional dyspepsia (Allescher et al., 2001). Nonulcer dyspepsia is characterized by a variety of upper abdominal symptoms in the absence of organic disease. Within the general population, dyspepsia is very common, and as a result, empirical therapy without prior diagnostic procedures has been recommended for the management of these patients. Both acid-suppressive substances such as histamine H2-receptor antagonists (H₂-RAS) and gastroprokinetics have been suggested as first-line, empirical therapy. Clinical trials of H₂-RAS have yielded somewhat contradictory results and benefit seems largely confined to refluxlike or ulcerlike dyspepsia subgroups. All these findings came out of an appropriate meta-analysis study.

Dentifrice (Johnson, 1993). In a series of nine randomized controlled clinical trials, sodium monofluorophosphate (SMFP) was compared to sodium fluoride (NaF) dentifrice in the prevention of caries development. The data consist of treatment differences, NaF_i – SMFP_i, where NAF_i is the change from baseline in the decayed/missing (due to caries)/filled-surface dental index at three years follow-up for regular use of NaF and SMFP_i is defined similarly for i = 1,…, 9. A statistical meta-analysis is in order here.

Recovery time after aneasthesia (Whitehead, 2002). A multicenter study with nine centers was undertaken to compare two anaesthetic agents undergoing short surgical procedures, where rapid recovery is important. The response of interest is the recovery time [time from when the anaesthetic gases are turned off until the patients open their eyes (in minutes)]. A meta-analysis would be quite appropriate in this context. Incidentally, a logarithmic transformation of the underlying data produces almost normal d...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Preface
• 1 Introduction
• 2 Various Measures of Effect Size
• 3 Combining Independent Tests
• 4 Methods of Combining Effect Sizes
• 5 Inference about a Common Mean of Several Univariate Normal Populations
• 6 Tests of Homogeneity in Meta-Analysis
• 7 One-Way Random Effects Model
• 8 Combining Controlled Trials with Normal Outcomes
• 9 Combining Controlled Trials with Discrete Outcomes
• 10 Meta-Regression
• 11 Multivariate Meta-Analysis
• 12 Bayesian Meta-Analysis
• 13 Publication Bias
• 14 Recovery of Interblock Information
• 15 Combination of Polls
• 16 Vote Counting Procedures
• 17 Computational Aspects
• 18 Data Sets
• References
• Index