A bound for publication bias based on the fraction of unpublished studies

Publication bias in meta-analysis is usually modeled in terms of an accept/reject selection procedure in which the selected studies are the "published" studies and the rejected studies are the "unpublished" studies. One possible selection mechanism is to suppose that only studies that report an estimated treatment effect exceeding (or falling short of) some threshold are accepted. We show that, with appropriate choice of thresholds, this attains the maximum bias among all selection mechanisms in which the probability of selection increases with study size. It is impossible to estimate the selection mechanism from the observed studies alone: this result leads to a "worst-case" sensitivity analysis for publication bias, which is remarkably easy to implement in practice. The method is illustrated using data on the effectiveness of prophylactic corticosteroids.     

Assessing the implications of publication bias for two popular estimates of between-study variance in meta-analysis

Perhaps the greatest threat to the validity of a meta-analysis is the possibility of publication bias, where studies with interesting or statistically significant results are more likely to be published. This obviously impacts on inference concerning the treatment effect but also has implications for estimates of between-study variance. Two popular and established estimation methods are considered and formulae for assessing the implications of the bias are provided in terms of a general process for selecting studies. Meta-analysts, concerned that publication bias may be present, can use these as part of a sensitivity analysis to assess the robustness of their estimates of between-study variance using any selection process that is likely to be used in practice. The procedure is illustrated using a meta-analysis of clinical trials concerning the effectiveness of endoscopic sclerotherapy for preventing death in patients with cirrhosis and oesophagogastric varices.     

Confidence intervals and P-values for meta-analysis with publication bias

We study publication bias in meta-analysis by supposing there is a population (y, sigma) of studies which give treatment effect estimates y approximately N(theta, sigma(2)). A selection function describes the probability that each study is selected for review. The overall estimate of theta depends on the studies selected, and hence on the (unknown) selection function. Our previous paper, Copas and Jackson (2004, Biometrics 60, 146-153), studied the maximum bias over all possible selection functions which satisfy the weak condition that large studies (small sigma) are as likely, or more likely, to be selected than small studies (large sigma). This led to a worst-case sensitivity analysis, controlling for the overall fraction of studies selected. However, no account was taken of the effect of selection on the uncertainty in estimation. This article extends the previous work by finding corresponding confidence intervals and P-values, and hence a new sensitivity analysis for publication bias. Two examples are discussed.     

The file-drawer problem revisited: a general weighted method for calculating fail-safe numbers in meta-analysis

Quantitative literature reviews such as meta-analysis are becoming common in evolutionary biology but may be strongly affected by publication biases. Using fail-safe numbers is a quick way to estimate whether publication bias is likely to be a problem for a specific study. However, previously suggested fail-safe calculations are unweighted and are not based on the framework in which most meta-analyses are performed. A general, weighted fail-safe calculation, grounded in the meta-analysis framework, applicable to both fixed- and random-effects models, is proposed. Recent meta-analyses published in Evolution are used for illustration.     

A simple and accurate method for generating co-dominant markers: an application of conformation-sensitive gel electrophoresis to linkage analysis in the silkworm

A simple and sensitive method for linkage analysis is described, which is based on conformation-sensitive gel electrophoresis (CSGE). Using urea-containing agarose gels or a commercially available polyacrylamide-derived matrix, 13 polymorphic markers were newly identified for known genes of the silkworm, Bombyx mori, which had been scored as monomorphic by PCR-RFLP analysis. This method for detecting polymorphisms is quite sensitive, and can be performed with inexpensive reagents and apparatus that is available in most molecular biology laboratories. Received: 19 November 1998 / Accepted: 2 March 1999