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What works?: selectivity models and meta‐analysis

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  • J. Copas

Abstract

What works seeks to identify rehabilitative treatments which are successful in reducing the likelihood that offenders will reoffend. A large number of small case–control studies have been reported in the literature, but with conflicting results. Meta‐analysis has been used to reconcile these findings, but again with conflicting results. We reanalyse one of the published meta‐analyses in the corrections literature and argue the importance of specifically modelling heterogeneity and selection bias. A sensitivity approach is advocated, suggesting lower average effects and substantially increased measures of uncertainty. The method is tested on a medical example where independent confirmation from a large controlled trial is also available.

Suggested Citation

  • J. Copas, 1999. "What works?: selectivity models and meta‐analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 95-109.
    • Handle: RePEc:bla:jorssa:v:162:y:1999:i:1:p:95-109
    DOI: 10.1111/1467-985X.00123
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    Cited by:

    1. Zuzana Irsova & Pedro R. D. Bom & Tomas Havranek & Heiko Rachinger, 2023. "Spurious Precision in Meta-Analysis," Working Papers IES 2023/05, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Feb 2023.
    2. Mengke Li & Yukun Liu & Pengfei Li & Jing Qin, 2022. "Empirical likelihood meta-analysis with publication bias correction under Copas-like selection model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 93-112, February.
    3. Ying Yuan & Roderick J. A. Little, 2009. "Meta-Analysis of Studies with Missing Data," Biometrics, The International Biometric Society, vol. 65(2), pages 487-496, June.
    4. Sander Greenland, 2005. "Multiple‐bias modelling for analysis of observational data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 267-306, March.
    5. van Aert, Robbie Cornelis Maria & van Assen, Marcel A. L. M., 2018. "P-uniform," MetaArXiv zqjr9, Center for Open Science.
    6. van Aert, Robbie Cornelis Maria, 2018. "Dissertation R.C.M. van Aert," MetaArXiv eqhjd, Center for Open Science.
    7. Ao Huang & Kosuke Morikawa & Tim Friede & Satoshi Hattori, 2023. "Adjusting for publication bias in meta‐analysis via inverse probability weighting using clinical trial registries," Biometrics, The International Biometric Society, vol. 79(3), pages 2089-2102, September.
    8. Costa-Font, Joan & McGuire, Alistair & Stanley, Tom, 2013. "Publication selection in health policy research: The winner's curse hypothesis," Health Policy, Elsevier, vol. 109(1), pages 78-87.
    9. Sanghyun Hong & W. Robert Reed, 2020. "Using Monte Carlo Experiments to Select Meta-Analytic Estimators," Working Papers in Economics 20/10, University of Canterbury, Department of Economics and Finance.
    10. Jaime L. Peters & Alex J. Sutton & David R. Jones & Keith R. Abrams & Lesley Rushton & Santiago G. Moreno, 2010. "Assessing publication bias in meta‐analyses in the presence of between‐study heterogeneity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(3), pages 575-591, July.
    11. Robbie C M van Aert & Jelte M Wicherts & Marcel A L M van Assen, 2019. "Publication bias examined in meta-analyses from psychology and medicine: A meta-meta-analysis," PLOS ONE, Public Library of Science, vol. 14(4), pages 1-32, April.
    12. Alan S. Gerber & Neil Malhotra, 2008. "Publication Bias in Empirical Sociological Research," Sociological Methods & Research, , vol. 37(1), pages 3-30, August.
    13. Jian Qing Shi & John Copas, 2002. "Publication bias and meta‐analysis for 2×2 tables: an average Markov chain Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 221-236, May.
    14. Mengke Li & Yan Fan & Yang Liu & Yukun Liu, 2021. "Diagnostic test meta-analysis by empirical likelihood under a Copas-like selection model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 927-947, August.
    15. Stanley, T. D. & Doucouliagos, Hristos, 2011. "Meta-regression approximations to reduce publication selection bias," Working Papers eco_2011_4, Deakin University, Department of Economics.
    16. Guanqun Cao & David Todem & Lijian Yang & Jason P. Fine, 2013. "Evaluating Statistical Hypotheses Using Weakly-Identifiable Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 256-273, June.
    17. Christopher H. Schmid, 2018. "Discussion of “quantifying publication bias in meta‐analysis” by Lin et al," Biometrics, The International Biometric Society, vol. 74(3), pages 797-799, September.

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