Summary 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.

When reporting the results of clinical studies, some researchers may choose the five‐number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation (SD), particularly for skewed data. For these studies, when included in a meta‐analysis, it is often desired to convert the five‐number summary back to the sample mean and SD. For this purpose, several methods have been proposed in the recent literature and they are increasingly used nowadays. In this article, we propose to further advance the literature by developing a smoothly weighted estimator for the sample SD that fully utilizes the sample size information. For ease of implementation, we also derive an approximation formula for the optimal weight, as well as a shortcut formula for the sample SD. Numerical results show that our new estimator provides a more accurate estimate for normal data and also performs favorably for non‐normal data. Together with the optimal sample mean estimator in Luo et al., our new methods have dramatically improved the existing methods for data transformation, and they are capable to serve as “rules of thumb” in meta‐analysis for studies reported with the five‐number summary. Finally for practical use, an Excel spreadsheet and an online calculator are also provided for implementing our optimal estimators.

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Given the relatively low agreement between many publication bias tests, meta-analysts should not rely on a single test and may apply multiple tests with various assumptions. Non-statistical approaches to evaluating publication bias (e.g., searching clinical trials registries, records of drug approving agencies, and scientific conference proceedings) remain essential.

Epidemiologic research often involves meta-analyses of proportions. Conventional two-step methods first transform each study’s proportion and subsequently perform a meta-analysis on the transformed scale. They suffer from several important limitations: the log and logit transformations impractically treat within-study variances as fixed, known values and require ad hoc corrections for zero counts; the results from arcsine-based transformations may lack interpretability. Generalized linear mixed models (GLMMs) have been recommended in meta-analyses as a one-step approach to fully accounting for within-study uncertainties. However, they are seldom used in current practice to synthesize proportions. This article summarizes various methods for meta-analyses of proportions, illustrates their implementations, and explores their performance using real and simulated datasets. In general, GLMMs led to smaller biases and mean squared errors and higher coverage probabilities than two-step methods. Many software programs are readily available to implement these methods.