Meta-analysis collects and synthesizes results from individual studies to estimate an overall effect size. If published studies are chosen, say through a literature review, an inherent selection bias may arise, since for example, studies may tend to be published more readily if they are statistically significant, or deemed to be more `interesting' in terms of the impact of their outcomes. We develop a simple rank-based data augmentation technique, formalizing the use of funnel plots, to estimate and adjust for the numbers and outcomes of missing studies. Several non-parametric estimators are proposed for the number of missing studies, and their properties are developed analytically and through simulations. We apply the method to simulated and epidemiological data sets, and show it is both effective and consistent with other criteria in the literature. Corresponding author's email address: tweedie@stat.colostate.edu Key words: Meta-analysis; Publication bias; Missing studies; File dra...

this paper we extend a Bayesian method described in Givens, Smith and Tweedie (1997), which covers the situation where publication is due solely to significance levels, to a stratified model which allows for other aspects to be taken into account. Estimation uses the data augmentation principle (Tanner, 1991); specifically, we construct an algorithm which imputes latent sets of missing studies into a meta-analysis, in accordance with the probabilities that they are missing in given significance ranges, or quality ranges, or the like. We then apply this model to a set of studies collected by Delgado-Rodriguez et al. (1992), who examine studies on the association between the use of oral contraceptives and cervical cancer. We investigated the effect of publication bias due to significance levels alone in LaFleur et al., (1996). Here we are able to consider the effect of the quality assessments made by Delgado-Rodriguez et al. (1992), and show that this makes a considerable difference in the final evaluation of the data set. Specifically, after allowing for these biases the estimated relative risk of cervical cancer from oral contraceptive use is reduced considerably, indicating that a suppression bias against studies of insignificance or poor quality may seriously distort the results of an ordinary meta-analysis of these data. 2 Adjusting for Publication Bias

this paper we present a new technique, the `Trim and Fill' method developed in [16,17], for estimating and adjusting for the numbers and outcomes of such missing studies. It has the advantage of being computationally simple, and in practical situations seems to perform better than existing methods. To illustrate this new approach, in this article we apply the trim and fill method to an existing meta-analysis of the effect of using gangliosides in reducing case fatality in acute stroke. The data are taken from the 1998 Cochrane Database of Systematic Reviews, which contains several hundred overviews of clinical trials which can be assessed using meta-analyses.

this paper we restrict comment to the following specific issues, although there are many more to which similar approaches will apply: (i) the problem of comparability of data and study design, since for the meta-analysis to be meaningfully interpreted, we must not combine "apples and oranges"; (ii) the effect of "publication bias", recognising that failure to obtain all relevant studies, both published and unpublished, may result in a quite distorted meta-analysis; (iii) the possible existence of systematic errors in individual studies, since these flow to bias in the overall analysis, and some account must be taken of them. Clearly all of these (and many other problems) are of concern in principle in any metaanalysis, but it is not obvious whether they will cause real problems in any one specific application. Our theme in this paper is that, by using sensitivity analyses based on the collection of real data and comparison of more and less sophisticated models, one can develop useful information on the extent and effect of such problems, rather than merely expressing concern about their existence. We shall see that for each of (i)--(iii), we can develop approaches based on data which describe the best and worst case scenarios (and the intermediate ones also), and use these to quantify whether further steps must be taken to protect the meta-analysis from incorrect inferences. Although other measures of relationship are possible, in epidemiology it is common to consider the effect of the relationship to be measured by the relative risk (RR), given conceptually as the ratio

this paper we investigate three properties of this approach: (a) We consider which of the estimators have the better mean square error (MSE) properties: we show in Section 3 that the estimators R 0 and L 0 are both better than Q 0 , but that there are values of the number of observed and missing studies for which each is better than the other; (b) We use the distributional properties of the estimators to formulate tests for the existence of publication bias, and compare these with recent methods of Begg (1994) and Egger et al (1997): the resulting tests, in Section 5, appear to be quite powerful if there are more than 5-6 missing studies; (c) We compare the properties of the iterated version of the algorithm (used in practice) with those of the analytic versions in Taylor and Tweedie (1998): using simulations, we see in Section 4.2 that the iteration does not adversely affect accuracy in general, and so the analytic descriptions of the tests and estimators can be used in the iteration. We then apply the iterative algorithm and the test methods, in Section 6, to a number of sets of studies, and show that they are consistent with the Begg (1994) and Egger et al (1997) approaches, and also to the more complex Bayesian method in Givens et al (1997). These data sets include meta-analyses of the risk of Chlamydia trachomatis from oral contraceptive (OC) use, described by Cottingham and Hunter (1992) and analyzed by Begg (1994); studies of the association between lung cancer and passive smoking, collected and analyzed in Tweedie et al (1996); and a psychometric meta-analysis of IQ scores and teacher expectancy, collected by Raudenbush (1984), and analyzed by Begg (1994) and Gleser and Olkin (1996). 1.2 Funnel plots and quantitative methods

ather higher than this. The conclusion was subsequently challenged in the courts by the tobacco manufacturers, suppliers and growers, and the EPA lost the case (which is currently under appeal with a final ruling pending). Although some of the reasons for this judgment were procedural, the courts ruled in effect that the EPA had not established causality, and had not used appropriate statistical methods in reaching its evaluation. The intense nature of this and other debates on ETS worldwide (another example being the Australian NH&MRC review of ETS and its relationship to a variety of diseases [9]) has focused attention on some interesting and possibly unique statistical or environmetrical aspects of the arguments used. These include: (a) To what degree can statistics be used in supporting causal assertions? In particular, is a relative risk of 1.20 strong enough for such a conclusion (especially when, for example, effects of exposures to electromagnetic fields from powerlines hav

It is human nature for “the affirmative or active to effect more than the negative or privative. So that a few times hitting, or presence, countervails oft-times failing or absence.”