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11 - Understanding P-values and confidence intervals

Published online by Cambridge University Press:  04 August 2010

Thomas B. Newman  and
Michael A. Kohn
Thomas B. Newman
Affiliation:
University of California, San Francisco
Michael A. Kohn
Affiliation:
University of California, San Francisco
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Summary

Introduction

In the previous two chapters, we discussed using the results of randomized trials and observational studies to estimate treatment effects. We were primarily interested in measures of effect size and in problems with design (in randomized trials) and confounding (in observational studies) that could bias effect estimates. We did not spend much time considering the precision of our effect estimates or whether the apparent treatment effects could be a result of chance. The statistics used to help us with these questions − P-values and confidence intervals – are the subject of this chapter.

No area in epidemiology and statistics is so widely misunderstood and mistaught. We cover a more sophisticated understanding of P-values and confidence intervals in this text because 1) it is right, 2) it is important, and 3) we think you can handle it. After all, you have survived three chapters (3, 4, and 8) on using the results of diagnostic tests and Bayes's Theorem to update a patient's probability of disease. So now you are poised to gain a Bayesian understanding of P-values and confidence intervals as well. We will give you a taste in this chapter; those wishing to explore these ideas in greater depth are encouraged to read an excellent series of articles on this topic by Steven Goodman. (Goodman 1999a; Goodman 1999b; Goodman 2001)

Type
Chapter
Information
Evidence-Based Diagnosis , pp. 220 - 238
Publisher: Cambridge University Press
Print publication year: 2009

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References

Browner, W. S., and Newman, T. B. (1987). “Are all significant P values created equal? The analogy between diagnostic tests and clinical research.” JAMA 257(18): 2459–63.CrossRefGoogle ScholarPubMed
Glantz, S. A. (2002). Primer of Biostatistics. New York, NY, McGraw-Hill, Medical Pub. Div.Google Scholar
Goodman, S. N. (1999a). “Toward evidence-based medical statistics. 1: The P value fallacy.” Ann Intern Med 130(12): 995–1004.CrossRefGoogle Scholar
Goodman, S. N. (1999b). “Toward evidence-based medical statistics. 2: The Bayes factor.” Ann Intern Med 130(12): 1005–13.CrossRefGoogle ScholarPubMed
Goodman, S. N. (2001). “Of P-values and Bayes: a modest proposal.” Epidemiology 12(3): 295–7.CrossRefGoogle ScholarPubMed
Guyatt, G., Rennie, D., et al. (2002). Users' Guides to the Medical Literature: Essentials of Evidence-Based Clinical Practice. Chicago, IL, AMA Press.Google Scholar
Hanley, J. A., and Lippman-Hand, A. (1983). “If nothing goes wrong, is everything all right? Interpreting zero numerators.” JAMA 249(13): 1743–5.CrossRefGoogle ScholarPubMed
Jaffe, D. M., Tanz, R. R., et al. (1987). “Antibiotic administration to treat possible occult bacteremia in febrile children.” N Engl J Med 317(19): 1175–80.CrossRefGoogle ScholarPubMed
Newman, T. B. (1995). “If almost nothing goes wrong, is almost everything all right? Interpreting small numerators.” JAMA 274(13): 1013.CrossRefGoogle ScholarPubMed
Newman, T. B., and Pantell, R. H. (1988). “Occult bacteremia in febrile children.” N Engl J Med 318(20): 1338–9.Google Scholar
Sackett, D. L., Haynes, R. B., et al. (1991). Clinical Epidemiology: A Basic Science for Clinical Medicine. Boston, MA, Little Brown.Google Scholar
Sackett, D. L., Haynes, R. B., et al. (2000). Evidence-Based Medicine: How to practice and teach EBM, 2nd Ed. Edinburgh: Churchill Livingstone: 233.
Weiss, R., Duckett, J., et al. (1992). “Results of a randomized clinical trial of medical versus surgical management of infants and children with grades III and IV primary vesicoureteral reflux (United States). The International Reflux Study in Children.” J Urol 148(5 Pt 2): 1667–73.CrossRefGoogle ScholarPubMed
Foxman, B., and Frerichs, R. R. (1985). “Epidemiology of urinary tract infection: I. Diaphragm use and sexual intercourse.” Am J Public Health 75(11): 1308–13.CrossRefGoogle ScholarPubMed
Keller, M. B., Ryan, N. D., et al. (2001). “Efficacy of paroxetine in the treatment of adolescent major depression: a randomized, controlled trial.” J Am Acad Child Adolesc Psychiatry 40(7): 762–72.CrossRefGoogle ScholarPubMed
Krag, D., and Ashikaga, T. (2003). “The design of trials comparing sentinel-node surgery and axillary resection.” N Engl J Med 349(6): 603–5.CrossRefGoogle ScholarPubMed
Veronesi, U., Paganelli, G., et al. (2003). “A randomized comparison of sentinel-node biopsy with routine axillary dissection in breast cancer.” N Engl J Med 349(6): 546–53.CrossRefGoogle ScholarPubMed
Browner, W. S., and Newman, T. B. (1987). “Are all significant P values created equal? The analogy between diagnostic tests and clinical research.” JAMA 257(18): 2459–63.CrossRefGoogle ScholarPubMed
Glantz, S. A. (2002). Primer of Biostatistics. New York, NY, McGraw-Hill, Medical Pub. Div.Google Scholar
Goodman, S. N. (1999a). “Toward evidence-based medical statistics. 1: The P value fallacy.” Ann Intern Med 130(12): 995–1004.CrossRefGoogle Scholar
Goodman, S. N. (1999b). “Toward evidence-based medical statistics. 2: The Bayes factor.” Ann Intern Med 130(12): 1005–13.CrossRefGoogle ScholarPubMed
Goodman, S. N. (2001). “Of P-values and Bayes: a modest proposal.” Epidemiology 12(3): 295–7.CrossRefGoogle ScholarPubMed
Guyatt, G., Rennie, D., et al. (2002). Users' Guides to the Medical Literature: Essentials of Evidence-Based Clinical Practice. Chicago, IL, AMA Press.Google Scholar
Hanley, J. A., and Lippman-Hand, A. (1983). “If nothing goes wrong, is everything all right? Interpreting zero numerators.” JAMA 249(13): 1743–5.CrossRefGoogle ScholarPubMed
Jaffe, D. M., Tanz, R. R., et al. (1987). “Antibiotic administration to treat possible occult bacteremia in febrile children.” N Engl J Med 317(19): 1175–80.CrossRefGoogle ScholarPubMed
Newman, T. B. (1995). “If almost nothing goes wrong, is almost everything all right? Interpreting small numerators.” JAMA 274(13): 1013.CrossRefGoogle ScholarPubMed
Newman, T. B., and Pantell, R. H. (1988). “Occult bacteremia in febrile children.” N Engl J Med 318(20): 1338–9.Google Scholar
Sackett, D. L., Haynes, R. B., et al. (1991). Clinical Epidemiology: A Basic Science for Clinical Medicine. Boston, MA, Little Brown.Google Scholar
Sackett, D. L., Haynes, R. B., et al. (2000). Evidence-Based Medicine: How to practice and teach EBM, 2nd Ed. Edinburgh: Churchill Livingstone: 233.
Weiss, R., Duckett, J., et al. (1992). “Results of a randomized clinical trial of medical versus surgical management of infants and children with grades III and IV primary vesicoureteral reflux (United States). The International Reflux Study in Children.” J Urol 148(5 Pt 2): 1667–73.CrossRefGoogle ScholarPubMed

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