. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Selection Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Modeling Ozone Profiles . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Dirichlet Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4.1 Definition and properties . . . . . . . . . . . . . . . . . . . . . 5 1.4.2 Computation with Dirichlet processes . . . . . . . . . . . . . . 9 1.4.3 Applications of Dirichlet processes . . . . . . . . . . . . . . . . 10 2. SEMIPARAMETRIC BAYESIAN ANALYSIS OF SELECTION MODELS 12 2.1 Notation and models . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Some Aspects of the Model . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.1 Sampling plans . . . . . . . . . . . . . . . . . . . . . . . . . . 1...

`Publication bias' is a relatively new statistical phenomenon that only arises when one attempts through a meta-analysis to review all studies, significant or insignificant, in order to provide a total perspective on a particular issue. This has recently received some notoriety as an issue in the evaluation of the relative risk of lung cancer associated with passive smoking, following legal challenges to a 1992 EPA analysis which concluded that such exposure is associated with significant excess risk of lung cancer. We introduce a Bayesian approach which estimates and adjusts for publication bias. Estimation is based on a data augmentation principle within a hierarchical model, and the number and outcomes of unobserved studies are simulated using Gibbs sampling methods. This technique yields a quantitative adjustment for the passive smoking meta-analysis. We estimate that there may be both negative and positive but insignificant studies omitted, and that failing to allow for these woul...

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