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Calculating the “number needed to be exposed” with adjustment for confounding variables in epidemiological studies

  • Ralf Bender
    Correspondence
    Corresponding author. Department of Epidemiology and Medical Statistics, School of Public Health, University of Bielefeld, P.O. Box 100131, D-33501 Bielefeld, Germany. Tel.: +49 521 106-3803; fax: +49 521 106-6465. E-mail address:(R. Bender)
    Affiliations
    Department of Epidemiology and Medical Statistics, School of Public Health, University of Bielefeld, Bielefeld, Germany
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  • Maria Blettner
    Affiliations
    Department of Epidemiology and Medical Statistics, School of Public Health, University of Bielefeld, Bielefeld, Germany
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      Abstract

      The number needed to treat (NNT) is a popular summary statistic to describe the absolute effect of a new treatment compared with a standard treatment or control concerning the risk of an adverse event. The NNT concept can be applied whenever the risk of an adverse event is compared between two groups; for the comparison of exposed with unexposed subjects in epidemiological studies, we propose the term “number needed to be exposed” (NNE). Whereas in randomized clinical trials NNT can be calculated on the basis of a simple 2×2 table, in epidemiological studies methods to adjust for confounders are required in most applications. We derive a method based upon multiple logistic regression analysis to perform point and interval estimation of NNE with adjustment for confounding variables. The adjusted NNE can be calculated from the adjusted odds ratio (OR) and the unexposed event rate (UER) estimated by means of an appropriate multiple logistic regression model. As UER is dependent on the confounders, the adjusted NNEs also vary with the values of the confounding variables. Two methods are proposed to take the dependence of NNE on the values of the confounders into account. The adjusted number needed to be exposed can be a useful complement to the commonly presented results in epidemiological studies, such as ORs and attributable risks.

      Keywords

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      References

        • Cook R.J.
        • Sackett D.L.
        The number needed to treat.
        BMJ. 1995; 310: 452-454
        • Laupacis A.
        • Sackett D.L.
        • Roberts R.S.
        An assessment of clinically useful measures of the consequences of treatment.
        N Engl J Med. 1988; 318: 1728-1733
        • McQuay H.J.
        • Moore A.
        Using numerical results from systematic reviews in clinical practice.
        Ann Intern Med. 1997; 126: 712-720
        • Rembold C.M.
        Number needed to screen.
        BMJ. 1998; 317: 307-312
        • Bjerre L.M.
        • LeLorier L.
        Expressing the magnitude of adverse effects in case-control studies.
        BMJ. 2000; 320: 503-506
        • Wu L.A.
        • Kottke T.E.
        Number needed to treat.
        J Clin Epidemiol. 2001; 54: 111-116
        • Smeeth L.
        • Haines A.
        • Ebrahim S.
        Numbers needed to treat derived from meta-analyses – sometimes informative, usually misleading.
        BMJ. 1999; 318: 1548-1551
        • Feinstein A.R.
        Indexes of contrast and quantitative significance for comparisons of two groups.
        Stat Med. 1999; 18: 2557-2581
        • Altman D.G.
        Confidence intervals for the number needed to treat.
        BMJ. 1998; 317: 1309-1312
        • Rothman K.J.
        • Greenland S.
        Modern epidemiology. Lippincott-Raven Publishers;, Philadelphia1998 (p. 47–54.)
        • Altman D.G.
        • Bland J.M.
        Treatment allocation in controlled trials.
        BMJ. 1999; 318: 1209
        • Hosmer D.W.
        • Lemeshow S.
        Applied logistic regression. Wiley;, New York1989
      1. Bender R. Expressing the number needed to treat as a function of the odds ratio and the unexposed event rate (rapid response). eBMJ (http://www.bmj.com/cgi/eletters/320/7233/503#EL7).

        • Lesaffre E.
        • Pledger G.
        A note on the number needed to treat.
        Control Clin Trials. 1999; 20: 439-447
        • Bender R.
        Calculating confidence intervals for the number needed to treat.
        Control Clin Trials. 2001; 22: 102-110
        • Bishop Y.M.M.
        • Fienberg S.E.
        • Holland P.W.
        Discrete multivariate analysis. MIT Press;, Cambridge, MA1975
        • SAS
        SAS/IML® Software. First Edition. SAS Institute;, Cary, NC1990
        • Mühlhauser I.
        • Bender R.
        • Bott U.
        • Jörgens V.
        • Grüsser M.
        • Wagener W.
        • et al.
        Cigarette smoking and progression of retinopathy and nephropathy in type 1 diabetes.
        Diabetic Med. 1996; 13: 536-543
        • Bender R.
        • Grouven U.
        Using binary logistic regression models for ordinal data with non-proportional odds.
        J Clin Epidemiol. 1998; 51: 809-816
        • Sackett D.L.
        On some clinically useful measures of the effects of treatment.
        Evidence-Based Med. 1996; 1: 37-38
        • Chatellier G.
        • Zapletal E.
        • Lemaitre D.
        • Ménard J.
        • Degoulet P.
        The number needed to treat.
        BMJ. 1996; 312: 426-429
        • North D.
        Number needed to treat.
        BMJ. 1995; 310: 1269
        • Newcombe R.G.
        Confidence intervals for the number needed to treat.
        BMJ. 1999; 318: 1765
        • Hutton J.L.
        Number needed to treat.
        J R Stat Soc A. 2000; 163: 403-415
        • Walter S.D.
        Choice of effect measure for epidemiological data.
        J Clin Epidemiol. 2000; 53: 931-939
        • Altman D.G.
        Statistics in medical journals.
        Stat Med. 1991; 10: 1897-1913
        • Levy P.S.
        • Stolte K.
        Statistical methods in public health and epidemiology.
        Stat Meth Med Res. 2000; 9: 41-55
        • Altman D.G.
        • Deeks J.J.
        Comments on the paper by Hutton.
        J R Stat Soc A. 2000; 163: 415-416
        • McGettigan P.
        • Sly K.
        • O'Connell D.
        • Hill S.
        • Henry D.
        The effects of information framing on the practices of physicians.
        J Gen Intern Med. 1999; 14: 633-642
        • Altman D.G.
        • Andersen P.K.
        Calculating the number needed to treat where the outcome is time to an event.
        BMJ. 1999; 319: 1492-1495
        • Bender R.
        • Grouven U.
        Logistic regression models used in medical research are poorly presented.
        BMJ. 1996; 313: 628
        • Heller R.F.
        • Dobson A.
        Disease impact number and population impact number.
        BMJ. 2000; 321: 950-952
        • Davies H.T.O.
        • Crombie I.K.
        • Tavakoli M.
        When can odds ratios mislead?.
        BMJ. 1998; 316: 989-991
        • Zhang J.
        • Yu K.F.
        What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes.
        JAMA. 1998; 280: 1690-1691