Meta-analysis: Confidence intervals and Prediction intervals

Authors

DOI: https://doi.org/10.6018/analesps.591831
Keywords: Confidence interval, Prediction interval, Meta-analysis

Abstract

Several types of intervals are usually employed in meta-analysis, a fact that has generated some confusion when interpreting them. Confidence intervals reflect the uncertainty related to a single number, the parametric mean effect size. Prediction intervals reflect the probable parametric effect size in any study of the same class as those included in a meta-analysis. Its interpretation and applications are different. In this article we explain their different nature and how they can be used to answer specific questions. Numerical examples are included, as well as their computation with the metafor R package.

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References

Blázquez‑Rincón, D., Sánchez‑Meca, J., Botella, J., & Suero, M. (2023). Heterogeneity estimation in meta‑analysis of standardized mean differences when the distribution of random effects departs from normal: A Monte Carlo simulation study. BMC Medical Research Methodology, 23(1), 19. https://doi.org/1 .1186/s12874-022-01809-0

Borenstein, M. (2019a). Common mistakes in meta-analysis. Englewood, NJ: Biostat inc.

Borenstein, M. (2019b). Heterogeneity in meta-analysis. In H. Cooper, L. V. Hedges, & J. C. Valentine (eds.), The Handbook of Research Synthesis and Meta-analysis, 3rd ed. (pp. 453-468). New York: Russell Sage Foundation.

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2017). Basics of meta-analysis: I2 is not an absolute measure of heterogeneity. Research Synthesis Methods, 8(1), 5-18. https://doi.org/1 .1002/jrsm.1230

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2021). Introduction to meta-analysis (2ª ed.). Chichester, UK: John Wiley and sons. [Chapter 17]

Botella, J., & Sánchez-Meca, J. (2015). [Meta-analysis in Social and Health Sciences] Meta-análisis en Ciencias Sociales y de la Salud. Madrid: Editorial Síntesis.

Hartung, J., & Knapp, G. (2001). On tests of the overall treatment effect in meta-analysis with normally distributed responses. Statistics in Medicine, 20(12), 1771-1782. https://doi.org/1 .1002/sim.791

Hedges, L. V., & Olkin, I. (1985). Statistical Methods for Meta-analysis. San Diego, CA: Academic Press.

Higgins, J. P. T., Thomas, J., Chandler, J., Cumpston, M., Li, T., Page, M. J., & Welch, V. A. (Eds) (2019). Cochrane handbook for systematic reviews of interventions. (2nd edition). Wiley.

Higgins, J. P., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta‐analysis. Statistics in medicine, 21(11), 1539-1558. https://doi.org/1 .1002/sim.1186

Higgins, J. P., Thompson, S. G., & Spiegelhalter, D. J. (2009). A re‐evaluation of random‐effects meta‐analysis. Journal of the Royal Statistical Society: Series A (Statistics in Society), 172(1), 137-159. https://doi.org/1 .1111/j.1467-985X.2008.00552.x

Huedo-Medina, T., Sánchez-Meca, J., Marín-Martínez, F., & Botella, J. (2006). Assessing heterogeneity in meta-analysis: Q statistics or I2 index? Psychological Methods, 11, 193–206. https://doi.org/1 .1037/1082-989X.11.2.193

Hunter, J. E., & Schmidt, F. L. (1990). Methods of meta-analysis: Correcting error and bias in research findings. Newbury Park, CA: Sage.

IntHout, J., Ioannidis, J. P., & Borm, G. F. (2014). The Hartung-Knapp-Sidik-Jonkman method for random effects meta-analysis is straightforward and considerably outperforms the standard DerSimonian-Laird method. BMC Medical Research Methodology, 14(25). http://www.biomedcentral.com/1471-2288/14/25

IntHout, J., Ioannidis, J. P., Rovers, M. M., & Goeman, J. J. (2016). Plea for routinely presenting prediction intervals in meta-analysis. BMJ open, 6(7), e010247. http://doi:1 .1136/bmjopen-2015-010247

Jackson, D., Law, M., Rücker, G., & Schwarzer, G. (2017). The Hartung-Knapp modification for random-effects meta-analysis: A useful refinement but are there any residual concerns? Statistics in Medicine, 36, 3923–3934. https://doi.org/1 .1002/sim.7411

Langan, D., Higgins, J. P., & Simmonds, M. (2017). Comparative performance of heterogeneity variance estimators in meta‐analysis: a review of simulation studies. Research Synthesis Methods, 8(2), 181-198. https://doi.org/1 .1002/jrsm.1198

Langan, D., Higgins, J. P., Jackson, D., Bowden, J., Veroniki, A. A., Kontopantelis, E., ... & Simmonds, M. (2019). A comparison of heterogeneity variance estimators in simulated random‐effects meta‐analyses. Research Synthesis Methods, 10(1), 83-98. https://doi.org/1 .1002/jrsm.1316

Partlett, C., & Riley, R.D. (2017). Random effects meta-analysis: Coverage performance of 95% confidence and prediction intervals following REML estimation. Statistics in Medicine, 36, 301-317. https://doi.org/1 .1002/sim.7140

Riley, R. D., Higgins, J. P., & Deeks, J. J. (2011). Interpretation of random effects meta-analyses. BMJ, 342. https://doi.org/1 .1136/bmj.d549

Sánchez-Meca, J., & Marín-Martínez, F. (2008). Confidence intervals for the overall effect size in random-effects meta-analysis. Psychological Methods, 13, 31-48. https://doi.org/1 .1037/1082-989X.13.1.31

Schmid, C. H., Stijnen, T., & White, I. (Eds.). (2021). Handbook of Meta-analysis. CRC Press.

Schmid, C. H, Carlin, B. P., & Welton, N. J. (2021). Bayesian Methods for Meta-analysis. En Handbook of Meta-Analysis (pp. 41-64). Chapman and Hall/CRC.

Sidik, K., & Jonkman, J. N. (2002). A simple confidence interval for meta-analysis. Statistics in Medicine, 21(21), 3153–3159. https://doi.org/1 .1002/sim.1262

Stijnen, T., White, I. R., & Schmid, C. H. (2021). Analysis of univariate study-level summary data using normal models. In Handbook of Meta-Analysis (pp. 41-64). Chapman and Hall/CRC. [Section 4.4.4.2]

Suero, M., Botella, J., & Durán, J. I. (2023). Methods for estimating the sampling variance of the standardized mean difference. Psychological Methods, 28(4), 895-904. https://doi.org/1 .1037/met0000446

Suero, M., Botella, J., Durán, J. I., & Blázquez-Rincón, D. (2023, September 12). Reformulating the meta-analytical random effects model as a mixture model. https://doi.org/1 .17605/OSF.IO/V2FDE

Veroniki, A. A., Jackson, D., Viechtbauer, W., Bender, R., Bowden, J., Knapp, G., ... & Salanti, G. (2016). Methods to estimate the between‐study variance and its uncertainty in meta‐analysis. Research Synthesis Methods, 7(1), 55-79. https://doi.org/1 .1002/jrsm.1164

Viechtbauer W. (2005). Bias and efficiency of meta-analytic variance estimators in the random-effects Model. Journal of Educational and Behavioral Statistics, 30, 261–293. https://doi.org/1 .3102/10769986030003261

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1-48. https://doi.org/1 .18637/jss.v036.i03

Viechtbauer, W. (2023). Package ‘metafor’. Unpublished document. University de Maastricht.

Viechtbauer, W., López-López, J. A., Sánchez-Meca, J., & Marín-Martínez, F. (2015). A comparison of procedures to test for moderators in mixed-effects meta-regression models. Psychological Methods, 20, 360-374. https://doi.org/1 .1037/met0000023

Published
03-04-2024
How to Cite
Botella, J., & Sánchez-Meca, J. (2024). Meta-analysis: Confidence intervals and Prediction intervals. Anales de Psicología / Annals of Psychology, 40(2), 344–354. https://doi.org/10.6018/analesps.591831
Issue
Section
Methodology

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