Publication bias is a serious problem in systematic reviews and meta-analyses, which can affect the validity and generalization of conclusions. Currently, approaches to dealing with publication bias can be distinguished into two classes: selection models and funnel-plot-based methods. Selection models use weight functions to adjust the overall effect size estimate and are usually employed as sensitivity analyses to assess the potential impact of publication bias. Funnel-plot-based methods include visual examination of a funnel plot, regression and rank tests, and the nonparametric trim and fill method. Although these approaches have been widely used in applications, measures for quantifying publication bias are seldom studied in the literature. Such measures can be used as a characteristic of a meta-analysis; also, they permit comparisons of publication biases between different meta-analyses. Egger's regression intercept may be considered as a candidate measure, but it lacks an intuitive interpretation. This article introduces a new measure, the skewness of the standardized deviates, to quantify publication bias. This measure describes the asymmetry of the collected studies’ distribution. In addition, a new test for publication bias is derived based on the skewness. Large sample properties of the new measure are studied, and its performance is illustrated using simulations and three case studies.
Bibliographical noteFunding Information:
We thank the associate editor and an anonymous reviewer for many constructive comments. We also thank Professor James Hodges for helpful discussion that led to a better presentation of this article. This research was supported in part by NIAID R21 AI103012 (HC, LL), NIDCR R03 DE024750 (HC), NLM R21 LM012197 (HC), NIDDK U01 DK106786 (HC), and the Doctoral Dissertation Fellowship from the University of Minnesota Graduate School (LL).
- Publication bias
- Standardized deviate
- Statistical power