New methods for meta-analysis under a fixed effects framework, with frequentist and Bayesian estimation.

Abstract

Meta-analysis, as a pivotal component of systematic reviews, has been used extensively in recent years to synthesize the increasing amount of evidence produced in medical and health care research. The two main approaches to meta-analysis are based either on the assumption that all studies estimate a single common effect or on the assumption that the effects are sampled from an unknown distribution. In this dissertation, we propose and develop methods for an alternative approach to meta-analysis, based on the assumption that the effects estimated in the different studies are unknown, but fixed and not necessarily identical. In Chapter 1 we present a brief introduction and review of current methods for meta-analysis. In Chapter 2, we provide a novel yet simple justification for the precision weighted average estimator, commonly used in meta-analysis. Unlike standard arguments that require a homogeneity assumption on the study effects, our justification is based on an optimality property of this particular weighted average of the effect-size parameters, among the class of all affine combinations. We also propose a parameter to quantify the heterogeneity observed in the studies at hand, as an alternative to the classical between-studies variance in a random effects approach. We propose frequentist estimators of these parameters, illustrating their properties through an applied example and evaluating their performance in a simulation study. In Chapter 3, we propose Bayesian methods for estimation of the location and dispersion parameters. We discuss how different prior beliefs like homogeneity, exchangeability or correlation, can be incorporated through a variety of prior distributions that may or may not involve the use of hyper parameters. Important properties of the estimators obtained from a conjugate prior are derived analytically and then illustrated in an example. In Chapter 4, we explore methods to improve on the estimation of the individual effects themselves, rather than a summary of them. We discuss some ideas on shrinkage estimation and convex clustering adapted to meta-analysis, with particular attention to penalized estimation. We propose a loss function which takes into account the precision of the effect estimates, and can be seen either as a weighted version of the Fused Lasso Signal Approximator (FLSA) or a specific case of a Convex Cluster criterion. We derive some important properties of the solutions to the loss function, which allow us to construct an efficient algorithm to obtain the complete solution path. We also propose a novel procedure based on the parametric bootstrap for the estimation of the tuning parameter, and present results from a simulation study evaluating the proposed shrinkage estimation method. Finally, we conclude with a discussion and conclusions in Chapter 5.