Publication Bias

1. Publication Bias Emily E. Tanner-Smith Associate Editor, Methods Coordinating Group Research Assistant Professor, Vanderbilt University Campbell Collaboration Colloquium Copenhagen, Denmark May 29th, 2012

2. Outline • What is publication bias • Avoiding publication bias • Methods for detecting publication bias • Detecting publication bias in Stata • Summary & recommendations

3. Publication Bias • Publication bias refers to bias that occurs when research found in the published literature is systematically unrepresentative of the population of studies (Rothstein et al., 2005) • Publication bias is often referred to as the file drawer problem where: “…journals are filled with the 5% of studies that show Type I errors, while the file drawers back at the lab are filled with the 95% of the studies that show non-significant (e.g. p < 0.05) results” (Rosenthal, 1979)

4. Reporting Biases Source: Sterne et al. (Eds.) (2008: 298)

5. Why Publication Bias Matters • Systematic reviews and meta-analyses are often used to inform policy and practice • Omitting unpublished studies from a review could yield a biased estimate of an intervention effect • Biased results could lead decision-makers to adopt practices that may ultimately cause harm, increase adverse events, or prevent treatment of life-threatening diseases or disorders

6. Avoiding Publication Bias As Primary Researchers: • Ethical imperative for primary researchers to publish null/negative findings • Prospective registration of trials As Systematic Reviewers/Meta-analysts: • Prospective meta-analysis of studies identified prior to reporting of study results • Extensive grey literature searching • Transparent assessment of possible bias

7. Avoiding Publication Bias: Grey Literature Searching • An ounce of prevention is worth a pound of cure… • Conference proceedings • Technical reports (research, governmental agencies) • Organization websites • Dissertations, theses • Contact with primary researchers

8. Avoiding Publication Bias: Grey Literature Searching

9. Detecting Publication Bias Methods for detecting publication bias assume: • Large n studies are likely to get published regardless of results due to time and money investments • Small n studies with the largest effects are most likely to be reported, many will never be published or will be difficult to locate • Medium n studies will have some modest significant effects that are reported, others may never be published

10. Funnel Plots • Exploratory tool used to visually assess the possibility of publication bias in a meta-analysis • Scatter plot of effect size (x-axis) against some measure of study size (y-axis) • x-axis: use logged values of effect sizes for binary data, e.g., ln(OR), ln(RR) • y-axis: the standard error of the effect size is generally recommended (see Sterne et al., 2005 for a review of additional y-axis options) • Not recommended in very small meta-analyses (e.g., n < 10)

11. Funnel Plots • Precision of estimates increases as the sample size of a study increases • Estimates from small n studies (i.e., less precise, larger standard errors) will show more variability in the effect size estimates, thus a wider scatter on the plot • Estimates from larger n studies will show less variability in effect size estimates, thus have a narrower scatter on the plot • If publication bias is present, we would expect null or ‘negative’ findings from small n studies to be suppressed (i.e., missing from the plot)

12. Note x & y axes • Centered around FE mean • Pseudo 95% confidence limits Asymmetry in small n studies provides evidence of possible bias

13. Symmetric funnel plots indicate a possible absence of bias

14. Symmetry difficult to assess with <10 studies

15. Interpreting Funnel Plots • Asymmetry could be due to factors other than publication bias, e.g., • poor methodological quality (smaller studies with lower quality may have exaggerated treatment effects) • Other reporting biases • Artefactual variation • Chance • True heterogeneity • Assessing funnel plot symmetry relies entirely on subjective visual judgment

16. Contour Enhanced Funnel Plots • Funnel plot with additional contour lines associated with ‘milestones’ of statistical significance: p = .001, .01, .05, etc. • If studies are missing in areas of statistical non-significance, publication bias may be present • If studies are missing in areas of statistical significance, asymmetry may be due to factors other than publication bias • If there are no studies in areas of statistical significance, publication bias may be present • Can help distinguish funnel plot asymmetry due to publication bias versus other factors (Peters et al., 2008)

18. Asymmetry may be due to factors other than publication bias

19. Tests for Funnel Plot Asymmetry • Several regression tests are available to test for funnel plot asymmetry • Attempt to overcome subjectivity of visual funnel plot inspection • Framed as tests for “small study effects”, or the tendency for smaller n studies to show greater effects than larger n studies; i.e., effects aren’t necessarily a result of bias

20. Egger Test • Recommended test for mean difference effect sizes (d, g) • Weighted regression of the effect size on standard error • β0 = 0 indicates a symmetric funnel plot • β0> 0 shows less precise (i.e., smaller n) studies yield bigger effects • Can be extended to include p predictors hypothesized to potentially explain funnel plot asymmetry (see Sterne et al., 2001)

22. Fail to reject the null hypothesis of no small study effects (b = -1.14; p = .667) No evidence of “small study bias”

23. Egger Test • Limitations • Low power unless there is severe bias and large n • Inflated Type I error with large treatment effects, rare event data, or equal sample sizes across studies • Inflated Type I error with log odds ratio effect sizes

24. Peters Test • Modified Egger test that for use with log odds ratio effect sizes • Weighted regression of ES on 1/total sample size

26. Reject the null hypothesis of no small study effects (b=-118.21;p=.002) Possible evidence of “small study bias”

27. Tests for Funnel Plot Asymmetry • Other recommended tests for use with the log odds ratio effect size: • Harbord test (Harbord et al., 2006) if τ2 < .10 • Rücker test (Rücker et al., 2008) • Numerous other tests available (see Sterne et al., 2008 for a review)

28. Other Methods • Selection modeling (Hedges & Vevea, 2005) • Incorporate biasing selection mechanism into your model to get an adjusted mean effect size estimate • Selection model is rarely known; do sensitivity analysis with alternative selection models • Relatively complex to implement, performs poorly with small number of studies

29. Other Methods • Trim and fill analysis (Duval & Tweedie, 2000) • Iteratively trims (removes) smaller studies causing asymmetry • Uses trimmed plot to re-estimate the mean effect size • Fills (replaces) omitted studies and mirror-images • Provides an estimate of the number of missing (filled) studies and a new estimate of the mean effect size • Major limitations include: misinterpretation of results, assumption of a symmetric funnel plot, poor performance in the presence of heterogeneity

30. Other Methods • Sensitivity testing • Comparing fixed- and random-effects estimates • Cumulative meta-analysis • Typically used to update pooled effect size estimate with each new study cumulatively over time • Can use as an alternative to update pooled effect size estimate with each study in order of largest to smallest sample size • If pooled effect size does not shift with the addition of small n studies, provides some evidence against publication bias

31. Other Methods • Failsafe N (Rosenthal 1979) • Number of additional null studies that would be needed to increase the p-value to above .05 • Ad hoc rule of thumb that failsafe N less than 5n + 10, results may not be robust to publication bias • Several variations of the failsafe N • Numerous limitations (not recommended for use); see Becker (2005)

32. Detecting Publication Bias in Stata • Several user-written commands are available that automate the most commonly used methods to detect publication bias

33. Summary & Recommendations • Publication bias deserves careful consideration in systematic reviews and meta-analyses, given their potentially large impact on policy and practice • Narrative and non-systematic reviews are subject to all the same potential biases as systematic reviews and meta-analyses • Yet publication bias is rarely if ever acknowledged in narrative reviews • Meta-analyses have the benefit of being able to empirically assess the possibility of publication bias and its potential impact on review findings

34. Summary & Recommendations • Reporting biases occur when the nature and direction of research findings influence their dissemination and availability • The reality of reporting biases means systematic reviewers must conduct comprehensive literature searches in attempt to locate all eligible studies • Protocols and reviews should be explicit and transparent about methods used to assess publication bias

35. Summary & Recommendations • Funnel plots • Always examine & report funnel plots when you have 10 or more studies with some variability in standard errors across studies • Always consider publication bias as only one possible source of funnel plot asymmetry

36. Summary & Recommendations • Regression tests • For continuously measured intervention effects (d, g): Egger test • For log odds ratio effect sizes: Peters, Harbord, or Rücker test if τ2 < .10 • For log odds ratio effect sizes: Rücker test ifτ2> .10 • Acknowledge low power of statistical tests • Other sensitivity tests • Comparing FE vs. RE estimates, trim & fill analysis, cumulative meta-analysis, selection modeling

37. Summary & Recommendations • What if you find possible evidence of publication or small study bias? • “Solution” will vary; requires thoughtful consideration by the reviewers • Reconsider search strategy, grey literature inclusion • Identify plausible explanations (e.g., study quality, other study characteristics) • Explore potential explanations with subgroup and moderator analyses • Explicitly acknowledge all potential biases when discussing the findings of the review

38. Recommended Reading • Duval, S. J., & Tweedie, R. L. (2000). A non-parametric ‘trim and fill’ method of accounting for publication bias in meta-analysis. Journal of the American Statistical Association, 95, 89-98. • Egger, M., Davey Smith, G., Schneider, M., & Minder, C. (1997). Bias in meta-analysis detected by a simple, graphical test. British Medical Journal, 315, 629-634. • Hammerstrøm, K., Wade, A., Jørgensen, A. K. (2010). Searching for studies: A guide to information retrieval for Campbell systematic reviews. Campbell Systematic Review, Supplement 1. • Harbord, R. M., Egger, M., & Sterne, J. A. C. (2006). A modified test for small-study effects in meta-analyses of controlled trials with binary endpoints. Statistics in Medicine, 25, 3443-3457. • Peters, J. L., Sutton, A. J., Jones, D. R., Abrams, K. R., & Rushton, L. (2008). Contour-enhanced meta-analysis funnel plots help distinguish publication bias from other causes of asymmetry. Journal of Clinical Epidemiology, 61, 991-996.

39. Recommended Reading • Rosenthal, R. (1979). The ‘file-drawer problem’ and tolerance for null results. Psychological Bulletin, 86, 638-641. • Rothstein, H. R., Sutton, A. J., & Borenstein, M. L. (Eds). (2005). Publication bias in meta-analysis: Prevention, assessment and adjustments. Hoboken, NJ: Wiley. • Rücker, G., Schwarzer, G., & Carpenter, J. (2008). Arcsine test for publication bias in meta-analyses with binary outcomes. Statistics in Medicine, 27, 746-763 • Sterne, J. A., & Egger, M. (2001). Funnel plots for detecting bias in meta-analysis: Guidelines on choice of axis. Journal of Clinical Epidemiology, 54, 1046-1055. • Sterne, J. A. C., Egger, M., & Moher, D. (Eds.) (2008). Chapter 10: Addressing reporting biases. In J. P. T. Higgins & S. Green (Eds.), Cochrane handbook for systematic reviews of interventions, pp. 297 – 333. Chichester, UK: Wiley. • Sterne, J. A. C., et al. (2011). Recommendations for examining and interpreting funnel plot asymmetry in meta-analyses of randomised controlled trials. BMJ, 343, d4002.

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