Confidence Intervals and P-Values for Meta-Analysis with Publication Bias

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We study publication bias in meta-analysis by supposing there is a population (y, ) of studies which give treatment effect estimates yN(, 2) . A selection function describes the probability that each study is selected for review. The overall estimate of  depends on the studies selected, and hence on the (unknown) selection function. Our previous paper, Copas and Jackson (2004, Biometrics60, 146–153), studied the maximum bias over all possible selection functions which satisfy the weak condition that large studies (small ) are as likely, or more likely, to be selected than small studies (large ). 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.

Keywords: Publication bias; Selection model; Sensitivity analysis; Unpublished studies

Document Type: Research Article


Affiliations: Institute of Statistical Mathematics and Department of Statistical Science, The Graduate University for Advanced Studies, Minami-azabu, Tokyo 106-8569, Japan, Email:

Publication date: June 1, 2007

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