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).

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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 Our previous paper, Copas and Jackson (2004, A bound for publication bias based on the fraction of unpublished studies, Biometrics 60, 146-153), studied the maximum bias over all possible selection functions which satisfy the weak condition that large studies (small σ)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
Date:	2006
Volume:	Vol.2006
Number:	No.1
Number of Pages:	26
Status:	Not Peer Reviewed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 A bound for publication bias based on the fraction of unpublished studies.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.
URI:	http://wrap.warwick.ac.uk/id/eprint/35560

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