Ординатура / Офтальмология / Английские материалы / Using and Understanding Medical Statistics_Matthews, Farewell_2007

Table 23.6. Details of hypothetical screening tests illustrating the dependence of on disease prevalence

approach would quickly move beyond the bounds of what is reasonable here. Therefore, if this subject of agreement is of particular interest, we are compelled to leave the reader to explore the topic elsewhere, or to consult a statistician if questions arise in a particular application.

In our discussion thus far, we have only considered the situation when observers have equal status. However, measures of agreement are also of interest when one or more methods of observation are being compared with a ‘gold standard’. The evaluation of diagnostic tests, which we discussed in chapter 22, is a special case of this particular problem. However, we will use this scenario in the next section to illustrate a particular feature of of which the reader should be aware.

23.7. The Dependence of on Prevalence

To illustrate that falls most naturally into the category of a reliability measure, and is not purely a measure of agreement, consider a hypothetical screening test, T, for a particular disease. This represents a slightly different

situation than having two raters or assessors of equal status, but is still one in which might well be used by some investigators.

As we discussed in chapter 22, relevant probabilities for this setting are the predictive value of the test for the disease states, i.e., the two post-test probabilities. We will assume that the post-test probability an individual is diseased, given that the screening test is positive, is 75%, and that the corresponding post-test probability an individual is disease-free, given that the screening test is negative, is also 75%. Table 23.6 summarizes the expected outcomes for a sample of 400 individuals who were tested using T when the disease prevalence in the population is equal to 50, 30 and 25.5%.

As the disease prevalence decreases by roughly one-half from 50 to 25.5%, table 23.6 shows that decreases from 0.5 to 0.02. Nevertheless, agreement between the test result and disease status which, in this situation, is probably most sensibly reflected by the post-test probabilities, is the same in all three scenarios. Likewise, the estimated odds ratio in each situation is equal to nine. Thus the change reflected in the marked decrease in appears to hinge on a reduced ability to discriminate between individuals as the disease prevalence decreases simply because the population becomes more homogeneous with respect to disease status. A statistic, such as , that depends on disease prevalence is a sensible choice for a measure of reliability but not for a measure of agreement.

We note that , and various alternatives to , are the continuing subject of considerable discussion. Many different views have been suggested, and some authors are quite passionate about the preferred choice. While we do have opinions on these matters, many of the pertinent issues involve concepts that are beyond the scope of this book. Nonetheless, we believe readers ought to be aware that depends on prevalence, and therefore exercise due caution if is portrayed elsewhere solely as a measure of agreement.

19Armitage P, Berry G, Matthews JNS: Statistical Methods in Medical Research, ed 4. Oxford, Blackwell Science, 2002.

20Duncan BBA, Zaimi F, Newman GB, Jenkins JG, Aveling W: Effect of premedication on the induction dose of thiopentone in children. Anaesthesia 1984;39:426–428.

21Von Bortkiewicz L: Das Gesetz der kleinen Zahlen. Leipzig, Teubner, 1898.

22Fallowfield L, Jenkins V, Farewell V, Saul J, Duffy A, Eves R: Efficacy of a Cancer Research UK communication skills training model for oncologists: a randomised controlled trial. Lancet 2002;359:650–656.

23Breslow NE, Day NE: Statistical Methods in Cancer Research, vol II: The Design and Analysis of Cohort Studies. Lyon, International Agency for Research in Cancer, 1987.

24Trinchieri G, Kobayashi M, Rosen M, Loudon R, Murphy M, Perussia B: Tumor necrosis factor and lymphotoxin induce differentiation of human myeloid cell lines in synergy with immune interferon. J Exp Med 1986;164:1206–1225.

25Cox DR: Regression models and life-tables (with discussion). J R Stat Soc B 1972;34:187–220.

26Prentice RL, Kalbfleisch JD, Peterson AV Jr, Flournoy N, Farewell VT, Breslow NE: The analysis of failure times in the presence of competing risks. Biometrics 1978;34:541–554.

27Calzavara LM, Coates RA, Raboud JM, Farewell VT, Read SE, Shepherd FA, Fanning MM, MacFadden D: Ongoing high-risk sexual behaviors in relation to recreational drug use in sexual encounters. Ann Epidemiol 1993;3:272–280.

28Liang KY, Zeger S: Longitudinal data analysis using generalized linear models. Biometrika 1986; 73:13–22.

29Zeger SL, Liang KY: Longitudinal data analysis for discrete and continuous outcomes. Biometrics 1986;42:121–130.

30Gladman DD, Farewell VT, Nadeau C: Clinical indicators of progression in psoriatic arthritis (PSA): a multivariate relative risk model. J Rheumatol 1995;22:675–679.

31Kalbfleisch JD, Lawless JF: The analysis of panel data under a Markov assumption. J Am Stat Assoc 1985;80:863–871.

32Mantle MJ, Greenwood RM, Currey HLF: Backache in pregnancy. Rheumatol Rehabil 1977;16: 95–101.

33Benjamini Y, Hochberg Y: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc B 1995;57:289–300.

34Freedman LS: Tables of the number of patients required in clinical trials using the logrank test. Stat Med 1982;1:121–129.

35Pocock SJ: Clinical Trials, a Practical Approach. Chichester, Wiley, 1983.

36Peto R, Pike MC, Armitage P, Breslow NE, Cox DR, Howard SV, Mantel N, McPherson K, Peto J, Smith PG: Design and analysis of randomized clinical trials requiring prolonged observation of each patient. I. Introduction and design. Br J Cancer 1976;34:585–612.

37Breslow N: Perspectives on the statistician’s role in cooperative clinical research. Cancer 1978; 41:326–332.

38Byar DP, Simon RM, Friedewald WT, Schlesselman JJ, DeMets DL, Ellenberg JH, Gail MH, Ware JH: Randomized clinical trials. N Engl J Med 1976;295:74–80.

39Chalmers TC: Randomized clinical trials in surgery; in Varco RL, Delaney JP (eds): Controversy in Surgery. Philadelphia, Saunders, 1976, pp 3–11.

40Chalmers TC, Block JB, Lee S: Controlled studies in clinical cancer research. N Engl J Med 1972; 287:75–78.

41Cox DR: Summary views: a statistician’s perspective. Cancer Treat Rep 1980;64:533–535.

42Farewell VT, D’Angio GJ: A simulated study of historical controls using real data. Biometrics 1981;37:169–176.

43Freireich EJ: The randomized clinical trial as an obstacle to clinical research; in Delaney JP, Varco RL (eds): Controversies in Surgery. II. Philadelphia, Saunders, 1983, pp 5–12.

44Gehan EA, Freireich EJ: Non-randomized controls in cancer clinical trials. N Engl J Med 1974; 290:198–203.

45Sacks H, Chalmers TC, Smith H: Randomized versus historical controls for clinical trials. Am J Med 1982;72:233–240.

46Pocock SJ, Elbourne DR: Randomized trials or observational tribulations. N Engl J Med 2000; 342:1907–1909.

47Deeks JJ, Dinnes J, D’Amico R, Sowden AJ, Sakarovitch C, Song F, Petticrew M, Altman DG: Evaluating non-randomised intervention studies. Health Technol Assess 2003;7(27):iii–x, 1– 173.

48Yule GU: The Function of Scientific Method in Scientific Investigation. Industrial Fatigue Research Board Report 28. London, HMSO, 1924.

49Irwin JO: The place of mathematics in medical and biological statistics. J R Stat Soc A 1963;126: 1–45.

50McPherson K: Statistics: the problem of examining accumulating data more than once. N Engl J Med 1974;290:501–502.

51Whitehead J: The Design and Analysis of Sequential Clinical Trials, ed 2. New York, Horwood, 1991.

52Fleming TR, Harrrington DP, O’Brien PC: Designs for group sequential tests. Control Clin Trials 1984;5:348–361.

53Prentice RL: Surrogate endpoints in clinical trials: definition and operational criteria. Stat Med 1989;8:431–440.

54Fleming TR: Evaluating therapeutic interventions: some issues and experiences. Stat Sci 1992;7: 428–456.

55Burzykowski T, Molenberghs G, Buyse M (eds): The Evaluation of Surrogate Endpoints. New York, Springer, 2005.

56Fleming TR: Evaluation of active control trials in AIDS. J Acquir Immune Defic Syndr 1990;3: S82–S87.

57Cox DR: A remark on multiple comparison methods. Technometrics 1965;7:223–224.

58Pocock SJ, Geller NL, Tsiatis AA: The analusis of multiple endpoints in clinical trials. Biometrics 1987;43:487–498.

59Torrance GW: Utility approach to measuring health-related quality of life. J Chronic Dis 1987; 40:593–600.

60Cox DR, Fitzpatrick R, Fletcher AE, Gore SM, Spiegelhalter DJ, Jones DR: Quality of life assessment: can we keep it simple? J R Stat Soc A 1992;155:353–393.

61Cook RJ, Farewell VT: Guidelines for monitoring efficacy and toxicity responses in clinical trials. Biometrics 1994;50:1146–1152.

62DeMets DL: Stopping guidelines vs. stopping rules: a practitioner’s point of view. Commun Stat Theory Methods 1984;13:2395–2417.

63Cook RJ: Coupled error spending functions for parallel bivariate sequential tests. Biometrics 1996;52:442–450.

64Peto R, Collins R, Gray R: Large-scale randomized evidence: large, simple trials and overviews of trials; in Warren KS, Mosteller F (eds): Doing More Good Than Harm: The Evaluation of Health Care Interventions. Ann NY Acad Sci 1993;703:314–340.

65Lilienfeld AM, Lilienfeld DE: Foundations of Epidemiology, ed 3. New York, Oxford University Press, 1994.

66Prentice RL, Shimizu Y, Lin CH, Peterson AV, Kato H, Mason MW, Szatrowski TP: Serial blood pressure measurements and cardiovascular disease in a Japanese cohort. Am J Epidemiol 1982; 116:1–28.

67Weiss NS, Szekeley DR, English DR, Schweid AJ: Endometrial cancer in relation to patterns of menopausal estrogen use. JAMA 1979;242:261–264.

68Breslow NE, Day NE: Statistical Methods in Cancer Research, vol 1: The Analysis of Case-Con- trol Studies. Lyon, International Agency for Research in Cancer, 1980.

69Hauck WW: The large sample variance of the Mantel-Haenszel estimator of a common odds ratio. Biometrics 1979;35:817–819.

70Robins J, Breslow N, Greenland S: Estimators of the Mantel-Haenszel variance consistent in both sparse data and large-strata limiting models. Biometrics 1986;42:311–323.

71Doll R, Hill AB: Mortality of British doctors in relation to smoking: observations on coronary thrombosis. Natl Cancer Inst Monogr 1996;19:205–268.

72McNeil D: Epidemiological Research Methods. New York, Wiley, 1996.

73Weiss NS: Clinical Epidemiology: The Study of the Outcome of Illness, ed 2. New York, Oxford University Press, 1996.

74Catalona WJ, Hudson MA, Scardino PT, Richie JP, Ahmann FR, Flanigan RC, deKernion JB, Ratliff TL, Kavoussi LR, Dalkin BL, et al: Selection of optimal prostate-specific antigen cutoffs for early detection of prostate cancer: receiver operating characteristic curves. J Urol 1994;152: 2037–2042.

75Ransohoff DF, Feinstein AR: Problems of spectrum and bias in evaluating the efficacy of diagnostic tests. N Engl J Med 1978;299:926–930.

76Reid MC, Lachs MS, Feinstein AR: Use of methodological standards in diagnostic test research: getting better but still not good. JAMA 1995;274:645–651.

77Lusted LB: Introduction to Medical Decision Making. Springfield, Thomas, 1968.

78Sackett DL, Haynes RB, Guyatt GH, Tugwell P: Clinical Epidemiology: A Basic Science for Clinical Medicine, ed 2. London, Little, Brown, 1991.

79Fagan TJ: Nomogram for Bayes’ theorem. N Engl J Med 1975;293:257–261.

80Guyatt GH, Oxman AD, Ali M, Willan A, Mcllroy W, Patterson C: Laboratory diagnosis of irondeficiency anaemia: an overview. J Gen Intern Med 1992;7:145–153.

81Peabody GW: The physician and the laboratory. Boston Med Surg J 1922;187:324–327.

82De Vet H: Observer reliability and agreement; in Armitage P, Colton T (eds): Encyclopedia of Biostatistics, ed 2. Chichester, Wiley, 2005, pp 3801–3805.

83Isenberg DA, Allen E, Farewell VT, Ehrenstein MR, Hanna MG, Lundberg IE, Oddis D, Pilkinton C, Plotz P, Scott D, Vencovsky J, Cooper R, Rider L, Miller F: International consensus outcome measures for patients with idiopathic inflammatory myopathies. Development and initial validation of myositis activity and damage indices in patients with adult onset disease. Rheumatology 2004;43:49–54.