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Confidence Intervals and P‐Values for Meta‐Analysis with Publication Bias
Author(s) -
Henmi Masayuki,
Copas John B.,
Eguchi Shinto
Publication year - 2007
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2006.00705.x
Subject(s) - publication bias , confidence interval , statistics , meta analysis , sigma , sensitivity (control systems) , selection (genetic algorithm) , selection bias , function (biology) , mathematics , econometrics , population , computer science , physics , biology , medicine , artificial intelligence , environmental health , quantum mechanics , electronic engineering , evolutionary biology , engineering
Summary We study publication bias in meta‐analysis by supposing there is a population ( y , σ) of studies which give treatment effect estimates y ∼ N (θ, σ 2 ) . A selection function describes the probability that each study is selected for review. The overall estimate of θ 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 σ) are as likely, or more likely, to be selected than small studies (large σ). 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.