Statistical Methods for Meta-Analyses with Different Types of Outcome Measures

In meta-analysis practice, effect measures from individual studies are synthesized to produce an overall result. Researchers frequently face studies that report the same outcome differently. The first scenario is that continuous outcomes are measured on different scales. In this situation, the mean difference (MD) may not be pooled in the same meta-analysis. For transforming the outcomes on the same scale, the standardized mean difference (SMD) is commonly used to ensure the unit is uniform across studies. The first part of this dissertation investigates the performance of standardized mean differences when the continuous measures follow different types of distributions. We conducted simulation studies to compare the performance of standardized mean difference and mean second scenario is that some studies report a continuous variable (e.g., scores for rating depression), while others report a binary variable (e.g., counts of patients with depression dichotomized by certain latent, unreported depression scores). For combining these two types of studies in the same analysis, a simple conversion method has been widely used to handle standardized mean differences and odds ratios (ORs). This conventional method uses a linear function connecting the standardized mean difference and log odds ratio; it assumes logistic distributions for (latent) continuous measures. However, the normality assumption is more commonly used for continuous measures, and the conventional method may be inaccurate when effect sizes are large, or cutoff values for dichotomizing binary events are extreme (leading to rare events). The second part of this dissertation proposes a Bayesian hierarchical model to synthesize standardized mean differences and odds ratios without using the conventional conversion method. This model assumes exact likelihoods for continuous and binary outcome measures, which account for full uncertainties in the synthesized results. We performed simulation studies to compare the performance of the conventional and Bayesian methods in various settings. The Bayesian method generally produced less biased results with smaller mean squared errors and higher coverage probabilities than the conventional method in most cases. Two case studies were used to illustrate the proposed Bayesian meth-od in real-world settings.