Dissertation R.C.M. van Aert
Authors: van Aert Robbie Cornelis Maria 
Published: July 2018

More and more scientific research gets published nowadays, asking for statistical methods that enable researchers to get an overview of the literature in a particular research field. For that purpose, meta-analysis methods were developed that can be used for statistically combining the effect sizes from independent primary studies on the same topic. My dissertation focuses on two issues that are crucial when conducting a meta-analysis: publication bias and heterogeneity in primary studies’ true effect sizes. Accurate estimation of both the meta-analytic effect size as well as the between-study variance in true effect size is crucial since the results of meta-analyses are often used for policy making. Publication bias distorts the results of a meta-analysis since it refers to situations where publication of a primary study depends on its results. We developed new meta-analysis methods, p-uniform and p-uniform*, which estimate effect sizes corrected for publication bias and also test for publication bias. Although the methods perform well in many conditions, these and the other existing methods are shown not to perform well when researchers use questionable research practices. Additionally, when publication bias is absent or limited, traditional methods that do not correct for publication bias outperform p¬-uniform and p-uniform*. Surprisingly, we found no strong evidence for the presence of publication bias in our pre-registered study on the presence of publication bias in a large-scale data set consisting of 83 meta-analyses and 499 systematic reviews published in the fields of psychology and medicine. We also developed two methods for meta-analyzing a statistically significant published original study and a replication of that study, which reflects a situation often encountered by researchers. One method is a frequentist whereas the other method is a Bayesian statistical method. Both methods are shown to perform better than traditional meta-analytic methods that do not take the statistical significance of the original study into account. Analytical studies of both methods also show that sometimes the original study is better discarded for optimal estimation of the true effect size. Finally, we developed a program for determining the required sample size in a replication analogous to power analysis in null hypothesis testing. Computing the required sample size with the method revealed that large sample sizes (approximately 650 participants) are required to be able to distinguish a zero from a small true effect.Finally, in the last two chapters we derived a new multi-step estimator for the between-study variance in primary studies’ true effect sizes, and examined the statistical properties of two methods (Q-profile and generalized Q-statistic method) to compute the confidence interval of the between-study variance in true effect size. We proved that the multi-step estimator converges to the Paule-Mandel estimator which is nowadays one of the recommended methods to estimate the between-study variance in true effect sizes. Two Monte-Carlo simulation studies showed that the coverage probabilities of Q-profile and generalized Q-statistic method can be substantially below the nominal coverage rate if the assumptions underlying the random-effects meta-analysis model were violated.