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Clinical Epidemiology and Biostatistics: A Primer for Orthopaedic Surgeons
Mininder S. Kocher, MD, MPH1; David Zurakowski, PhD1
1 Department of Orthopaedic Surgery, Children's Hospital, 300 Longwood Avenue, Boston, MA 02115. E-mail address for M.S. Kocher: mininder.kocher@childrens.harvard.edu
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The authors did not receive grants or outside funding in support of their research or preparation of this manuscript. They did not receive payments or other benefits or a commitment or agreement to provide such benefits from a commercial entity. No commercial entity paid or directed, or agreed to pay or direct, any benefits to any research fund, foundation, educational institution, or other charitable or nonprofit organization with which the authors are affiliated or associated.
Investigation performed at Harvard Medical School, Harvard School of Public Health, Boston, Massachusetts

The Journal of Bone and Joint Surgery, Incorporated
J Bone Joint Surg Am, 2004 Mar 01;86(3):607-620
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Epidemiology is the study of the distribution and determinants of disease frequency1. In the fifth century BC, Hippocrates suggested that the development of human disease might be related to the external and internal environment of an individual1. In the 1600s and 1800s in England, John Graunt and William Farr quantified vital statistics on the basis of birth and death records1. In the 1850s, John Snow associated cholera with water contamination in London by observing higher cholera rates in homes supplied by certain water sources1. Epidemiological methods gradually evolved with use of the case-control study to demonstrate an association between smoking and lung cancer, use of the prospective cohort study to determine risk factors for cardiovascular disease in the Framingham Heart Study, and use of the randomized clinical trial for the poliomyelitis vaccine1. The evidence-based medicine and patient-derived outcomes assessment movements burst onto the scene of clinical medicine in the 1980s and 1990s as a result of contemporaneous medical, societal, and economic influences. Pioneers such as Sackett and Feinstein emphasized levels of evidence and patient-centered outcomes assessment2-10. Work by Wennberg and colleagues revealed large small-area variations in clinical practice, with some patients being thirty times more likely to undergo an operative procedure than other patients with identical symptoms merely because of their geographic location11-16. Additional critical research suggested that up to 40% of some surgical procedures might be inappropriate and up to 85% of common medical treatments were not rigorously validated17-19. Meanwhile, the costs of health care were rapidly rising to over two billion dollars per day, increasing from 5.2% of the gross domestic product in 1960 to 16.2% in 199720. Health maintenance organizations and managed care emerged. In addition, increasing federal, state, and consumer oversight was brought to bear on the practice of clinical medicine.
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    These activities have been planned and implemented in accordance with the Essential Areas and policies of the Accreditation Council for Continuing Medical Education (ACCME) through the joint sponsorship of the American Academy of Orthopaedic Surgeons and The Journal of Bone and Joint Surgery, Inc. The American Academy of Orthopaedic Surgeons is accredited by the ACCME to provide continuing medical education for physicians.
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    Mininder S. Kocher, MD, MPH
    Posted on June 21, 2004
    Drs. Kocher and Zurakowski respond:
    Department of Orthopaedic Surgery, Children's Hospital Boston, Harvard Medical School

    To the Editor:

    We thank Drs. Lee and Lin very much for their letter. As they have pointed out, in our article on page 616 we describe when to use the Fisher exact test and when to use the Pearson chi-square test.[1] The information on choice of statistical tests in Table IV on page 613 is intended to be a general guideline for readers. We agree with Drs. Lee and Lin that readers should be cautioned when using the chi-square test.

    The chi-squared distribution is an approximation. It is increasingly valid for large expected frequencies. Therefore, the adequacy of using the chi-square distribution is made under the assumption that the expected values are not too small. This vague term has been interpreted as meaning that a satisfactory approximation can be achieved when expected cell frequencies are 5 or more. As a rough rule in 1954, Cochran suggested that the chi-square approximation is safe provided that relatively few expected cell frequencies are less than 5 (for example, 1 cell out of 5 or more) and that no expected frequency is less than 1.[2] However it is difficult to give general recommendations and Agresti has concluded that it seems hopeless to expect a single rule to cover all cases.[3] Nevertheless, in tables with smaller expected frequencies the result of a significance test should be viewed with caution. With modern scientific calculators and software programs, the Fisher exact test should be used for any table with an expected value less than 5.


    1. Kocher MS, Zurakowski D. Clinical epidemiology and biostatistics: a primer for orthopaedic surgeons. J Bone Joint Surg Am. 2004;86:607-20.

    2. Cochran WG. Some methods for strengthening the common chi-square tests. Biometrics. 1954; 10:417-51.

    3. Agresti A. Categorical Data Analysis. New York: John Wiley; 1990. p 244-7.

    –Mininder S. Kocher, MD, MPH and David Zurakowski, PhD

    Yu-Min Lin
    Posted on May 28, 2004
    Questions Regarding Use of the Fisher Exact Test and the Pearson Chi-square Test
    Taichung Veterans Hospital

    To the editor:

    We read, with interest, "Clinical epidemiology and biostatistics: A primer for Orthopaedic surgeons", by Kocher and Zurakowski(1). In table IV which is entitled,"Statistical tests for comparing independent groups and paired samples", the authors described that for nominal type of data, the Fisher exact test is used for comparing two independent groups and the Pearson Chi-square test is used to compare three or more independent groups. We believe that Table IV is misleading and confusing.

    As the authors stated in the text, the Pearson chi-square test is used for two or more independent groups and the Fisher exact test is used when expected frequencies are small (five or less)[1]. The readers should be cautioned that when using chi-square test, no cell in the contingency table should have an expected count less than 1, and no more than 20% of the cells should have an expected count of less than five[2]; otherwise a Fisher exact test will be more appropriate.

    Tu-Shen Lee

    Yu-Min Lin

    Department of Orthopaedics

    Taichung Veterans General Hospital

    Taichung 407


    e-mail: ymlin@vghtc.gov.tw


    1. Kocher MS, Zurakowski D. Clinical epidemiology and biostatistics: a primer for orthopaedic surgeons. J Bone Joint Surg Am 2004;86:607-20.

    2. Pagano M, Gauvreau K. Chapter 15. Contingency tables. In: Pagano M, Gauvreau K. Principles of Biostatistics, Second ed. Pacific Grove: Duxbury, Thomson Learning, 2000:342-73.

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