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Multiple test procedures and smile plots

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  • Roger Newson

    () (Guy's Hospital)

Abstract

Scientists often have good reasons for wanting to calculate multiple confidence intervals and/or p-values, especially when scanning a genome. However, if we do this, then the probability of not observing at least one "significant" difference tends to fall, even if all null hypotheses are true. A skeptical public will rightly ask whether a difference is "significant" when considered as one of a large number of parameters estimated. This presentation demonstrates some solutions to this problem, using the unofficial Stata packages parmest and smileplot. The parmest package allows the calculation of Bonferroni-corrected or Sidak-corrected confidence intervals for multiple estimated parameters. The smileplot package contains two programs, multproc (which carries out multiple test procedures) and smileplot (which presents their results graphically by plotting the p-value on a reverse log scale on the vertical axis against the parameter estimate on the horizontal axis). A multiple test procedure takes, as input, a set of estimates and p-values, and rejects a subset (possibly empty) of the null hypotheses corresponding to these p-values. Multiple test procedures have traditionally controlled the family-wise error rate (FWER), typically enabling the user to be 95% confident that all the rejected null hypotheses are false, and that all the corresponding "discoveries" are real. The price of this confidence is that the power to detect a difference of a given size tends to zero as the number of measured parameters become large. Therefore, recent work has concentrated on procedures that control the false disco very rate (FDR), such as the Simes procedure and the Yekutieli-Benjamini procedure. FDR-controlling procedures attempt to control the number of false discoveries as a proportion of the number of true discoveries, typically enabling the user to be 95% confident that some of the discoveries are real, or 90% confident that most of the discoveries are real. This less stringent requirement causes power to "bottom out" at a non-zero level as the number of tests becomes large. The smileplot package offers a selection of multiple test procedures of both kinds.

Suggested Citation

  • Roger Newson, 2003. "Multiple test procedures and smile plots," United Kingdom Stata Users' Group Meetings 2003 16, Stata Users Group.
  • Handle: RePEc:boc:usug03:16
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    1. Roger Newson, 2000. "A program for saving a model fit as a dataset," Stata Technical Bulletin, StataCorp LP, vol. 9(49).
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    1. repec:ucp:jlabec:doi:10.1086/690652 is not listed on IDEAS
    2. Günther Fink & Margaret McConnell & Sebastian Vollmer, 2014. "Testing for heterogeneous treatment effects in experimental data: false discovery risks and correction procedures," Journal of Development Effectiveness, Taylor & Francis Journals, vol. 6(1), pages 44-57, January.
    3. Dunsch, Felipe A. & Evans, David K. & Eze-Ajoku, Ezinne & Macis, Mario, 2017. "Management, Supervision, and Health Care: A Field Experiment," IZA Discussion Papers 10967, Institute for the Study of Labor (IZA).
    4. Cubi-Molla, P. & Shah, K.K & Garside, J. & Herdman, M. & Devlin, N., 2017. "Age and Utilities: Issues for HTA," Research Papers 001830, Office of Health Economics.
    5. Michael J. Kottelenberg & Steven F. Lehrer, 2017. "Targeted or Universal Coverage? Assessing Heterogeneity in the Effects of Universal Child Care," Journal of Labor Economics, University of Chicago Press, vol. 35(3), pages 609-653.
    6. Böhme, Marcus H. & Persian, Ruth & Stöhr, Tobias, 2015. "Alone but better off? Adult child migration and health of elderly parents in Moldova," Journal of Health Economics, Elsevier, vol. 39(C), pages 211-227.
    7. Roger B. Newson, 2010. "Frequentist q-values for multiple-test procedures," Stata Journal, StataCorp LP, vol. 10(4), pages 568-584, December.
    8. repec:eee:joepsy:v:64:y:2018:i:c:p:18-48 is not listed on IDEAS
    9. Bell, Suzanne & Prata, Ndola & Lahiff, Maureen & Eskenazi, Brenda, 2012. "Civil unrest and birthweight: An exploratory analysis of the 2007/2008 Kenyan Crisis," Social Science & Medicine, Elsevier, vol. 74(9), pages 1324-1330.
    10. Roger M. Harbord & Julian P.T. Higgins, 2008. "Meta-regression in Stata," Stata Journal, StataCorp LP, vol. 8(4), pages 493-519, December.
    11. Roger Newson, 2008. "parmest and extensions," United Kingdom Stata Users' Group Meetings 2008 07, Stata Users Group.
    12. Roger B. Newson, 2013. "Bonferroni and Holm approximations for Sidak and Holland–Copenhaver q-values," Stata Journal, StataCorp LP, vol. 13(2), pages 379-381, June.
    13. Gisselquist, Rachel M. & Leiderer, Stefan & Niño-Zarazúa, Miguel, 2016. "Ethnic Heterogeneity and Public Goods Provision in Zambia: Evidence of a Subnational “Diversity Dividend”," World Development, Elsevier, vol. 78(C), pages 308-323.

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