A sensitivity analysis allowing for all possible selection processes of studies in meta analysis

1
A sensitivity analysis allowing for all possible
selection processes of studies in meta analysis

• Masayuki Henmi, John B. Copas
• and Shinto Eguchi
• Institute of Statistical Mathematics, Tokyo,
  Japan
• University of Warwick, Coventry, UK

2
Introduction

• In most cases of meta analysis, studies are not
  randomly
• selected to review. (unpublished negative
  results,
• unselected studies of poor quality, etc.)

• Adjustment of publication bias requires a strong
  and
• untestable assumption for processes of study
  selection.

• We propose a method of sensitivity analysis
  under as
• weak assumption as possible by deriving
  confidence
• intervals and P-values which allow for all
  selection
• processes satisfying that assumption.

3
Passive smoking lung cancer data
37 studies
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Selection model

• Individually estimated treatment effect

( within-, between-study variance)

• Selection function

5
Assumption for selection
is
a non-increasing function of
i.e. smaller studies with larger are
not more likely selected than larger
studies with smaller
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Confidence interval allowingfor selection
Theorem 1. Suppose that is a
non-increasing function of Then for given
a confidence interval for with
asymptotic significance level (in the
sense that
for sufficiently large ) is given by

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Confidence interval allowingfor selection
(no unpublished studies)
reduces to the conventional confidence interval
8
Sensitivity analysis 1(passive smoking lung
cancer data)
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Bound for the P-value
Distribution for a selected study
two-sided asymptotic P-value for
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Sensitivity analysis 2(passive smoking lung
cancer data)
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Consistency between the two methods
12
Parametric sensitivity analysis(Copas and Shi,
2000)
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Summary

• Adjustment for publication bias requires a
  strong and
• untestable assumption for selection processes.

• We proposed a method of sensitivity analysis
  avoiding
• such a strong assumption. It is based on a
  confidence
• interval and P-value allowing for all possible
  selection
• mechanisms under a sufficiently weak assumption.

• We reanalyzed the passive smoking data using our
  method.
• The result shows the significant evidence for
  the risk
• seems to be still valid under possible
  processes of selection.

14
References
Henmi, M., Copas, J. B. and Eguchi, S.
(2007). Confidence Intervals and P-values for
Meta-Analysis with Publication Bias. Biometrics
63, 475-482.
Copas, J. B. and Shi, J. Q. (2000). Meta-analysis,
funnel plots and sensitivity analysis. Biostatist
ics 1, 247-262.
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.