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Confidence intervals and P-valves for meta analysis with publication bias

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Henmi, Masayuki, Copas, John B. and Eguchi, Shinto (2006) Confidence intervals and P-valves for meta analysis with publication bias. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2006 (No.1).

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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...

Abstract

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, σ2). 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, A bound for publication bias based on the
fraction of unpublished studies, Biometrics 60, 146-153), studied the maximum bias over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 worstcase
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 paper
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.

Item Type:

Working or Discussion Paper (Working Paper)

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Meta-analysis, Confidence intervals

Series Name:

Working papers

Publisher:

University of Warwick. Centre for Research in Statistical Methodology

Place of Publication:

Coventry

Official Date:

2006

Dates:

Date	Event
2006	Published

Volume:

Vol.2006

Number:

No.1

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

Funder:

Engineering and Physical Sciences Research Council (EPSRC)

References:

Copas, J. B. and Jackson, D. (2004). A bound for publication bias based on the fraction
of unpublished studies. Biometrics 60, 146-153.
Copas, J. B. and Li, H. G. (1997). Inference for non-random samples (with discussion).
Journal of the Royal Statistical Society B 59, 55-95.
Copas, J. B. and Shi, J. Q. (2000a). Reanalysis of epidemiological evidence on lung cancer
and passive smoking. British Medical Journal 320, 417-418.
Copas, J. B. and Shi, J. Q. (2000b). Meta-analysis, funnel plots and sensitivity analysis.
Biostatistics 1, 247-262.
Copas, J. B. and Shi, J. Q. (2001). A sensitivity analysis for publication bias in systematic
reviews. Statistical Methods in Medical Research 10, 251-265.
DerSimonian, R. and Laird, N. (1986). Meta-analysis in clinical trials. Controlled Clinical
Trials 7, 177-188.
Givens, G. H., Smith, D. D. and Tweedie, R. L. (1997). Publication bias in meta-analysis:
a Bayesian data-augmentation approach to account for issues exemplified in the passive
smoking debate. Statistical Science 12, 221-250.
Greenhouse, J. and Iyengar, S. (1994). Sensitivity analysis and diagnostics. In The Handbook
of Research Synthesis, H. Cooper and L. V. Hedges (eds), New York: Sage.
Hackshaw, A. K., Law, M. R. and Wald, N. J. (1997). The accumulated evidence on lung
cancer and environmental tobacco smoke. British Medical Journal 315, 980-988.
Hedges, L. V. (1984). Estimation of effect size under non random sampling: The effects
of censoring studies yielding statistically insignificant mean differences. Journal of
Education Statistics 9, 61-85.
Lane, D. M. and Dunlap, W. P. (1978). Estimating effect size: Bias resulting from the
significance criterion in editorial decisions. British Journal of Mathematical and Statistical
Psychology 31, 107-112.
Poswillo, D. et al. (1998). Report of the Scientific Committee on Tobacco and Health.
London: The Stationery Office.
Rothstein, H. R., Sutton, A. J. and Borenstein, M. (eds) (2005). Publication Bias in
Meta-Analysis. Chichester: Wiley.
Shao, J. (2003). Mathematical Statistics, second edition. New York: Springer-Verlag,
Sutton, A. J., Abrams, K. R., Jones, D. R. and Sheldon, T. A. (2000). Methods for
meta-analysis in medical research. Chichester: Wiley.