Journal of Official Statistics, Vol.15, No.4, 1999. pp. 477494

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Bayesian Estimation of the Number of Unseen Studies in a Meta-Analysis

Public policies based on science today are often formed with the help of a meta-analysis, a combining of those experiments testing the hypothesis of interest. For example, a nation's drug regulatory body may combine clinical trial results from public health clinics, university research clinics, and pharmaceutical companies to determine if a drug under study is efficacious and safe. However, a parameter estimate from a meta-analysis is biased when the experiments to be combined are a non-random sample from the population of all experiments done on the hypothesis of interest. In particular, publication bias occurs when studies with significant results are more likely to be published than studies with non-significant results. We develop a model for the distribution of the total number of studies carried out, both published and unpublished, dependent on the probability of publication. We assume a selection model where all studies significant at level are published, while non-significant studies are published with probability . Using a Bayesian hierarchical model with Metropolis simulation and Gibbs sampling techniques, we study how the distribution of the total number of studies changes as changes. An application on lead exposure and IQ level in children is presented and the results interpreted. Comparisons are made with Rosenthal's fail-safe N estimators and with the recent frequentist estimation method of Gleser and Olkin.

Hierarchical models; file-drawer problem; Gibbs sampling; publication

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