Topics in Meta-analysis with Few Studies

Zejnullahi, Rrita

doi:https://doi.org/10.21985/n2-bbcy-fz41

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Topics in Meta-analysis with Few Studies

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This dissertation consists of three papers on methods for meta-analysis with few studies. These papers are concerned with proper inference from meta-analysis models that combine data from a small number of studies using fixed and random-effects models. Chapter 1 provides an introduction to meta-analysis, the motivation for this work and an overview of each substantive paper. Chapters 2 to 4 contain the substantive papers. The title and a brief summary of each follow. Chapter 2. Fixed and random-effects meta-analysis of randomized trials when the outcome is continuous and the number of studies is small. In this chapter, I begin with a review of the technical and conceptual components of fixed-effect and random-effects models. Although a fixed-effect model is not directly the focus, it nevertheless plays an important role in motivating the random-effects model. I explore the feasibility of applying commonly-used random-effects methods to a small collection of studies (i.e. k<10) under various configurations of unbalancedness that are of interest to empirical practice. The focus of this chapter is the Standardized Mean Difference effect size, which is the most frequently used effect size when the outcome in a study is continuous. Good statistical methods will produce unbiased and precise estimates, and the construction of confidence intervals will give proper coverage of the summary treatment effect. I demonstrate that commonly used random-effects procedures, however, can result in confidence intervals that may be too narrow, depending on the configuration of the within-study sample sizes, amount of heterogeneity and number of studies. The chapter considers the application of robust standard errors to the meta-analytic context and shows that these serve as good alternatives to estimate the variance of the summary estimate. It further provides adjusted degrees of freedom for the t-test statistics that make these methods more suitable for small meta-analyses. Chapter 3. Random-effects meta-analysis of randomized clinical trials when the outcome is binary and the number of studies is small. In this chapter, I extend the results from Chapter 2 to effect sizes based on binary data, i.e. risk difference, log odds ratio and log risk ratio. The results from this chapter provide some empirical evidence about the accuracy of various random-effects methods - including ones that are common practice - and methods that utilize robust standard errors. The study reveals that methods that use robust standard errors are indeed promising under the scenarios I investigated. It is further demonstrated that one variant of robust standard errors leads to generally proper coverage across all scenarios considered. Chapter 4. Considerations in heterogeneity variance estimation in small meta-analysis. The challenges that arise from applying a random-effects model to a small number of studies is primarily due to the difficulty in obtaining an unbiased and efficient estimate of the heterogeneity variance parameter. In chapter 4, I investigate the properties of five heterogeneity variance estimators in terms of bias and efficiency. Bias and variance of the estimators are derived analytically, where possible to do so, and investigated empirically through Monte Carlo simulations. Recommendations for which estimator to use in practice depend on the goal of meta-analysis. If the goal is to quantify heterogeneity, then a point estimate should be provided along with its standard error. Guidance for choosing an estimator is primarily based on bias. It turns out that no one estimator is superior to the alternatives considered across all scenarios. Despite this fact, some generalizations are credible and presented in chapter 4.

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