Bayesian Hierarchical Models for Meta-Analysis

Abstract

Meta-analysis is an important and widely used tool for synthesizing information from multiple independent but related studies. While many meta-analyses, such as those of randomized controlled trials, focus on the synthesis of treatment effects across studies, this dissertation will focus on the meta-analysis of prevalence and normative data. The first part of this thesis concerns the multivariate meta-analysis of prevalence data. When conducting a meta‐analysis involving prevalence data for an outcome with several subtypes, each of them is typically analyzed separately using a univariate meta‐analysis model. Recently, multivariate meta‐analysis models have been shown to correspond to a decrease in bias and variance for multiple correlated outcomes compared with univariate meta‐analysis, when some studies only report a subset of the outcomes. Chapter 2 of this thesis proposes a novel Bayesian multivariate random effects model to account for the natural constraint that the prevalence of any given subtype cannot be larger than that of the overall prevalence. Extensive simulation studies show that this new model can reduce bias and variance when estimating subtype prevalences in the presence of missing data, compared with standard univariate and multivariate random effects models. The data from a rapid review on occupation and lower urinary tract symptoms by the Prevention of Lower Urinary Tract Symptoms Research Consortium are analyzed as a case study to estimate the prevalence of urinary incontinence and several incontinence subtypes among women in suspected high risk work environments. The second part of this thesis concerns estimating a reference range from a meta-analysis. Clinicians frequently must decide whether a patient’s measurement reflects that of a healthy ``normal” individual. Thus, the reference range is defined as the interval in which some proportion (frequently 95\%) of measurements from a healthy population is expected to fall. One can estimate it from a single study, or preferably from a meta-analysis of multiple studies to increase generalizability. This range differs from the confidence interval for the pooled mean or the prediction interval for a new study mean in a meta-analysis, which do not capture natural variation across healthy individuals. Chapter 3 proposes three methods for estimating the reference range from a meta-analysis of aggregate data that incorporate both within and between-study variations. The results of a simulation study are presented demonstrating that the methods perform well under a variety of scenarios, though users should be cautious when the number of studies is small and between‐study heterogeneity is large. These methods are applied to two examples: pediatric time spent awake after sleep onset and frontal subjective postural vertical measurements. Chapter 4 provides a guide for clinicians and epidemiologists explaining the three approaches for estimating the reference range presented in Chapter 3: a frequentist, a Bayesian, and an empirical method. Each method is also extended to individual participant data (IPD) meta-analysis, with the latter being the gold standard when available. These approaches are illustrated using a clinical scenario about the normal range of a liver stiffness test.