Skip to main content
SpringerLink
Log in

Issues in Data Analysis

  • Chapter
  • First Online:
Fundamentals of Clinical Trials

Abstract

The analysis of data obtained from a clinical trial represents the outcome of the planning and implementation already described. Primary and secondary questions addressed by the clinical trial can be tested and new hypotheses generated. Data analysis is sometimes viewed as simple and straightforward, requiring little time, effort, or expense. However, careful analysis usually requires a major investment in all three. It must be done with as much care and concern as any of the design or data-gathering aspects. Furthermore, inappropriate statistical analyses can introduce bias, result in misleading conclusions, and impair the credibility of the trial.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Pagano M, Gauvreau K. Principles of Biostatistics (2nd edition). Pacific Grove, CA: Duxbury Press, 2000.

    Google Scholar 

  2. Piantadosi S. Clinical Trials: A Methodologic Perspective (2nd edition). Wiley Series in Probability & Statistics. New Jersey: John Wiley and Sons, Inc., 2005.

    Book  Google Scholar 

  3. Armitage P. Statistical Methods in Medical Research. New York: John Wiley and Sons, 1977.

    Google Scholar 

  4. Hill AB. Principles of Medical Statistics (9th edition). New York: Oxford University Press, 1971.

    Google Scholar 

  5. Cook T, DeMets DL. Introduction to Statistical Methods for Clinical Trials. Boca Raton, FL: Chapman & Hall/CRC; Taylor & Francis Group, LLC, 2008.

    MATH  Google Scholar 

  6. Geller N. Advances in Clinical Biostatistics. New York: Marcel Dekker, 2004.

    MATH  Google Scholar 

  7. Woolson R. Statistical Methods for the Analysis of Biomedical Data. New York: John Wiley and Sons, 1987.

    Google Scholar 

  8. Fisher L, Van Belle G. Biostatistics – A Methodology for the Health Sciences. New York: John Wiley and Sons, 1993.

    Google Scholar 

  9. Peto R, Pike MC, Armitage P, et al. Design and analysis of randomized clinical trials requiring prolonged observation of each patient. I. Introduction and design. Br J Cancer 1976;34:585–612.

    Article  Google Scholar 

  10. Armitage P. The analysis of data from clinical trials. Statistician 1980;28:171–183.

    Article  Google Scholar 

  11. Newcombe RG. Explanatory and pragmatic estimates of the treatment effect when deviations from allocated treatment occur. Stat Med 1988;7:1179–1186.

    Article  Google Scholar 

  12. Fleiss JL. Analysis of data from multiclinic trials. Control Clin Trials 1986;7:267–275.

    Article  Google Scholar 

  13. Schwartz D, Lellouch J. Explanatory and pragmatic attitudes in therapeutic trials. J Chronic Dis 1967;20:637–648.

    Article  Google Scholar 

  14. Sackett DL, Gent M. Controversy in counting and attributing events in clinical trials. N Engl J Med 1979;301:1410–1412.

    Article  Google Scholar 

  15. ICH Expert Working Group. International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use. ICH Harmonised Tripartite Guideline. Statistical principles for clinical trials. Stat Med 1999;18:1903–1942.

    Article  Google Scholar 

  16. FDA Guidance. International Conference on Harmonization: Guidance on statistical principles for clinical trials. http://www.fda.gov/downloads/RegulatoryInformation/Guidances/UCM129505.pdf

  17. May GS, DeMets DL, Friedman LM, et al. The randomized clinical trial: bias in analysis. Circulation 1981;64:669–673.

    Article  Google Scholar 

  18. Ingle JN, Ahmann DL, Green SJ, et al. Randomized clinical trial of diethylstilbestrol versus tamoxifen in postmenopausal women with advanced breast cancer. N Engl J Med 1981;304:16–21.

    Article  Google Scholar 

  19. The Canadian Cooperative Study Group. A randomized trial of aspirin and sulfinpyrazone in threatened stroke. N Engl J Med 1978;299:53–59.

    Article  Google Scholar 

  20. Beta-blocker Heart Attack Trial Research Group. A randomized trial of propranolol in patients with acute myocardial infarction. I. Mortality results. JAMA 1982;247:1707–1714.

    Article  Google Scholar 

  21. The Coronary Drug Project Research Group. Clofibrate and niacin in coronary heart disease. JAMA 1975;231:360–381.

    Article  Google Scholar 

  22. Roberts R, Croft C, Gold HK, et al. Effect of propranolol on myocardial infarct size in a randomized blinded multicenter trial. N Engl J Med 1984;311:218–225.

    Article  Google Scholar 

  23. Collaborative Group on Antenatal Steroid Therapy. Effect of antenatal dexamethasone administration on the prevention of respiratory distress syndrome. Am J Obstet Gynecol 1981;141:276–287.

    Google Scholar 

  24. The Anturane Reinfarction Trial Research Group. Sulfinpyrazone in the prevention of sudden death after myocardial infarction. N Engl J Med 1980;302:250–256.

    Article  Google Scholar 

  25. Temple R, Pledger GW. The FDA’s critique of the Anturane Reinfarction Trial. N Engl J Med 1980;303:1488–1492.

    Article  Google Scholar 

  26. Anturane Reinfarction Trial Policy Committee. The Anturane Reinfarction Trial: reevaluation of outcome. N Engl J Med 1982;306:1005–1008.

    Article  Google Scholar 

  27. Soran A, Nesbitt L, Mamounas EP, et al. Centralized medical monitoring in Phase III trials: the National Surgical Adjuvant Breast and Bowel Project (NSABP) experience. Clin Trials 2006;3:478–485

    Article  Google Scholar 

  28. MERIT-HF Study Group. Effect of metoprolol CR/XL in chronic heart failure: Metoprolol CR/XL randomised intervention trial in congestive heart failure (MERIT-HF). Lancet 1999;353:2001–2007.

    Article  Google Scholar 

  29. Packer M, Coats AJS, Fowler MB, et al. for the Carvedilol Prospective Randomized Cumulative Survival (COPERNICUS) Study Group. Effect of Carvedilol on survival in severe chronic heart failure. N Engl J Med 2001;344:1651–1658.

    Google Scholar 

  30. Kjekshus J, Apetrei E, Barrios V, et al. for the CORONA Group. Rosuvastatin in older patients with systolic heart failure. N Engl J Med 2007;357:2248–2261.

    Google Scholar 

  31. CIBIS II Investigators and Committees. The Cardiac Insufficiency Bisoprolol Study II (CIBIS II): a randomised trial. Lancet 1999;353:9–13.

    Article  Google Scholar 

  32. The GUSTO Investigators. An international randomized trial comparing four thrombolytic strategies for acute myocardial infarction. N Engl J Med 1993;329:673–682.

    Article  Google Scholar 

  33. The Coronary Drug Project Research Group. Influence of adherence to treatment and response of cholesterol on mortality in the Coronary Drug Project. N Engl J Med 1980;303:1038–1041.

    Article  Google Scholar 

  34. The Coronary Drug Project Research Group. Initial findings leading to modifications of its research protocol. JAMA 1970;214:1303–1313.

    Article  Google Scholar 

  35. Verter J, Friedman L. Adherence measures in the Aspirin Myocardial Infarction Study (AMIS) (abstract). Control Clin Trials 1984;5:306.

    Article  Google Scholar 

  36. Wilcox RG, Roland JM, Banks DC, et al. Randomised trial comparing propranolol with atenolol in immediate treatment of suspected myocardial infarction. Br Med J 1980;280:885–888.

    Article  Google Scholar 

  37. Detre K, Peduzzi P. The problem of attributing deaths of nonadherers: the VA coronary bypass experience. Control Clin Trials 1982;3:355–364.

    Article  Google Scholar 

  38. Lipid Research Clinics Program. The Lipid Research Clinics Coronary Primary Prevention Trial results. 1. Reduction in incidence of coronary heart disease. JAMA 1984;251:351–364.

    Article  Google Scholar 

  39. Diggle PJ. Testing for random dropouts in repeated measurement data. Biometrics 1989;45:1255–1258.

    Article  Google Scholar 

  40. Dolin R, Reichman RC, Madore HP, et al. A controlled trial of amantadine and rimantadine in the prophylaxis of influenza A infection. N Engl J Med 1982;307:580–584.

    Article  Google Scholar 

  41. Heyting A, Tolboom JTBM, Essers JGA. Statistical handling of drop-outs in longitudinal clinical trials. Stat Med 1992;11:2043–2061.

    Article  Google Scholar 

  42. Hoover DR, Munoz A, Carey V, and the Multicenter AIDS Cohort Study. Using events from dropouts in nonparametric survival function estimation with application to incubation of AIDS. J Am Stat Assoc 1993;88:37–43.

    Google Scholar 

  43. Lagakos SW, Lim LL-Y, Robins JM. Adjusting for early treatment termination in comparative clinical trials. Stat Med 1990;9:1417–1424.

    Article  Google Scholar 

  44. Morgan TM. Analysis of duration of response: a problem of oncology trials. Control Clin Trials 1988;9:11–18.

    Article  Google Scholar 

  45. Oakes D, Moss AJ, Fleiss JL, et al. and the Multicenter Diltiazem Post-Infarction Trial Research Group. Use of compliance measures in an analysis of the effect of diltiazem on mortality and reinfarction after myocardial infarction. J Am Stat Assoc 1993;88:44–49.

    Google Scholar 

  46. Pledger GW. Basic statistics: importance of compliance. J Clin Res Pharmacoepidemiol 1992;6:77–81.

    Google Scholar 

  47. Redmond C, Fisher B, Wieand HS. The methodologic dilemma in retrospectively correlating the amount of chemotherapy received in adjuvant therapy protocols with disease-free survival. Cancer Treat Rep 1983;67:519–526.

    Google Scholar 

  48. Ridout MS. Testing for random dropouts in repeated measurement data. Biometrics 1991;47:1617–1621.

    Article  Google Scholar 

  49. Simon R, Makuch RW. A non-parametric graphical representation of the relationship between survival and the occurrence of an event: application to responder versus non-responder bias. Stat Med 1984;3:35–44.

    Article  Google Scholar 

  50. Sommer A, Zeger SL. On estimating efficacy from clinical trials. Stat Med 1991;10:45–52.

    Article  Google Scholar 

  51. Pizzo PA, Robichaud KJ, Edwards BK, et al. Oral antibiotic prophylaxis in patients with cancer: a double-blind randomized placebo-controlled trial. J Pediatr 1983;102:125–133.

    Article  Google Scholar 

  52. Dillman RO, Seagren SL, Propert KJ, et al. A randomized trial of induction chemotherapy plus high-dose radiation versus radiation alone in stage III non-small-cell lung cancer. N Engl J Med 1990;323:940–945.

    Article  Google Scholar 

  53. The Intermittent Positive Pressure Breathing Trial Group. Intermittent positive pressure breathing therapy of chronic obstructive pulmonary disease – A clinical trial. Ann Intern Med 1983;99:612–620.

    Article  Google Scholar 

  54. Espeland MA, Byington RP, Hire D, et al. Analysis strategies for serial multivariate ultrasonographic data that are incomplete. Stat Med 1992;11:1041–1056.

    Article  Google Scholar 

  55. Little RJA, Rubin DB. Statistical Analysis with Missing Data. Wiley: New York, 1987.

    MATH  Google Scholar 

  56. Fitzmaurice GM, Laird NM, Ware JH. Applied Longitudinal Analysis. New York: Wiley, 2004 (Chapter 13).

    MATH  Google Scholar 

  57. Conaway MR, Rejeski WJ, Miller ME. Statistical issues in measuring adherence: methods for incomplete longitudinal data. In Shumaker SA, Ockene JK, Riekert KA (eds.). The Handbook of Health Behavior Change. New York: Springer Publishing Co., 2009, pp. 375–391.

    Google Scholar 

  58. Rubin D. Inference and missing data. Biometrika 1976;63:581–592.

    Article  MATH  MathSciNet  Google Scholar 

  59. Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Series B Stat Methodol 1977;39:1–38.

    MATH  MathSciNet  Google Scholar 

  60. Efron B. Missing data, imputation, and the bootstrap. J Am Stat Assoc 1994;89:463–474.

    Article  MATH  MathSciNet  Google Scholar 

  61. Greenlees JS, Reece WS, Zieschang KD. Imputation of missing values when the probability of response depends on the variable being imputed. J Am Stat Assoc 1982;77:251–261.

    Article  Google Scholar 

  62. Laird NM. Missing data in longitudinal studies. Stat Med 1988;7:305–315.

    Article  Google Scholar 

  63. Little RJ. Modeling the drop out mechanism in repeated-measures studies. J Am Stat Assoc 1995;90:1112–1121.

    Article  MATH  MathSciNet  Google Scholar 

  64. Shao J, Zhong B. Last observation carry-forward and last observation analysis. Stat Med 2003;22:2429–2441.

    Article  Google Scholar 

  65. Molenberghs G, Kenward MG. Missing Data in Clinical Studies. New York: John Wiley and Sons, 2007.

    Book  Google Scholar 

  66. Steering Committee of the Physicians’ Health Study Research Group. Final report on the aspirin component of the ongoing Physicians’ Health Study. N Engl J Med 1989;321:129–135.

    Article  Google Scholar 

  67. Writing Group for the Women’s Health Initiative Investigators. Risks and benefits of estrogen plus progestin in health postmenopausal women: principal results from the Women’s Health Initiative randomized controlled trial. JAMA 2002;288:321–333.

    Article  Google Scholar 

  68. Wu MC, Carrell RJ. Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process. Biometrics 1988;44:175–188.

    Article  MATH  MathSciNet  Google Scholar 

  69. Wu MC, Bailey KR. Estimation and comparison of changes in the presence of informative right censoring: conditional linear model. Biometrics 1989;45:939–955.

    Article  MATH  MathSciNet  Google Scholar 

  70. Bristow MR, Saxon LA, Boehmer et al., for the Comparison of Medical Therapy, Pacing, and Defibrillation in Heart Failure (COMPANION) Investigators. Cardiac-resynchronization therapy with or without an implantable defibrillator in advanced chronic heart failure. N Engl J Med 2004;350:2140–2150.

    Google Scholar 

  71. Bresalier RS, Sandler RS, Quan H, et al., for the Adenomatous Polyp Prevention on Vioxx (APPROVe) Trial Investigators. Cardiovascular events associated with rofecoxib in a colorectal adenoma chemoprevention trial. N Engl J Med 2005;352:1092–1102.

    Google Scholar 

  72. Lagakos S. Time-to-event analysis for long-term treatments – the APPROVe Trial. N Engl J Med 2006;355:113–117.

    Article  Google Scholar 

  73. Nissen S. Adverse cardiovascular effects of rofecoxib. N Engl J Med 2006;355:203–204.

    Article  Google Scholar 

  74. Baron JA, Sandler RS, Bresalier RS, et al. Cardiovascular events associated with rofecoxib: final analysis of the APPROVe trial. Lancet 2008;372:1756–1764.

    Article  Google Scholar 

  75. Kruskal WH. Some remarks on wild observations. Technometrics 1960;2:1–3.

    Article  MathSciNet  Google Scholar 

  76. Dixon WJ. Processing data for outliers. Biometrics 1953;9:74–89.

    Article  Google Scholar 

  77. Grubbs FE. Procedures for detecting outlying observations in samples. Technometrics 1969;11:1–21.

    Article  Google Scholar 

  78. Canner PL, Huang YB, Meinert CL. On the detection of outlier clinics in medical and surgical trials: I. Practical considerations. Control Clin Trials 1981;2:231–240.

    Article  Google Scholar 

  79. Canner PL, Huang YB, Meinert CL. On the detection of outlier clinics in medical and surgical trials: II. Theoretical considerations. Control Clin Trials 1981;2:241–252.

    Article  Google Scholar 

  80. The Scandinavian Simvastatin Survival Study Group. Randomised trial of cholesterol lowering in 4444 patients with coronary heart disease: the Scandinavian Simvastatin Survival Study (4S). Lancet 1994;344:1383–1389.

    Google Scholar 

  81. Shepherd J, Cobbe SM, Ford I, et al., for the West of Scotland Coronary Prevention Study Group. Prevention of coronary heart disease with pravastatin in men with hypercholesterolemia. N Engl J Med 1995;333:1301–1307.

    Google Scholar 

  82. Anand IS, Carson P, Galle E, et al. Cardiac resynchronization therapy reduces the risk of hospitalizations in patients with advanced heart failure: results from the Comparison of Medical Therapy, Pacing and Defibrillation in Heart Failure (COMPANION) trial. Circulation 2009;119:969–977.

    Article  Google Scholar 

  83. Cannon CP, Braunwald E, McCabe CH, et al. Intensive versus moderate lipid lowering with statins after acute coronary syndromes. N Engl J Med 2004;350:1495–1504.

    Article  Google Scholar 

  84. Ferreira-Gonzales I, Busse JW, Heels-Ansdell D, et al. Problems with use of composite end points in cardiovascular trials: systematic review of randomized controlled trials. BMJ 2007;334:756–757

    Article  Google Scholar 

  85. Tomlinson G, Detsky A. Composite end points in randomized trials; there is no free lunch. JAMA 2010;303:267–268.

    Article  Google Scholar 

  86. Weiss GB, Bunce H III, Hokanson JA. Comparing survival of responders and nonresponders after treatment: a potential source of confusion interpreting cancer clinical trials. Control Clin Trials 1983;4:43–52.

    Article  Google Scholar 

  87. Anderson JR, Cain KC, Gelber RD. Analysis of survival by tumor response. J Clin Oncol 1983;1:710–719.

    Google Scholar 

  88. Cox DR. Regression models and life-tables. J R Stat Soc Series B Stat Methodol 1972;34:187–220.

    MATH  Google Scholar 

  89. Efron B, Feldman D. Compliance as an explanatory variable in clinical trials. J Am Stat Assoc 1991;86:9–17.

    Article  Google Scholar 

  90. Egger MJ, Coleman ML, Ward JR, et al. Uses and abuses of analysis of covariance in clinical trials. Control Clin Trials 1985;6:12–24.

    Article  Google Scholar 

  91. Oye RK, Shapiro MF. Reporting results from chemotherapy trials. JAMA 1984;252:2722–2725.

    Article  Google Scholar 

  92. Rosenbaum PR. The consequences of adjustment for a concomitant variable that has been affected by the treatment. J R Stat Soc Ser A 1984;147:656–666.

    Article  Google Scholar 

  93. Albert JM, DeMets DL. On a model-based approach to estimating efficacy in clinical trials. Stat Med 1994;13:2323–2335.

    Article  Google Scholar 

  94. Beach ML, Meier P. Choosing covariates in the analysis of clinical trials. Control Clin Trials 1989;10:161S–175S.

    Article  Google Scholar 

  95. Byar DP. Assessing apparent treatment – covariate interactions in randomized clinical trials. Stat Med 1985;4:255–263.

    Article  Google Scholar 

  96. Canner PL. Covariate adjustment of treatment effects in clinical trials. Control Clin Trials 1991;12:359–366.

    Article  Google Scholar 

  97. Canner PL. Further aspects of data analysis. Control Clin Trials 1983;4:485–503.

    Article  Google Scholar 

  98. Crager MR. Analysis of covariance in parallel-group clinical trials with pretreatment baselines. Biometrics 1987;43:895–901.

    Article  MATH  MathSciNet  Google Scholar 

  99. Morgan TM, Elashoff RM. Effect of covariate measurement error in randomized clinical trials. Stat Med 1987;6:31–41.

    Article  Google Scholar 

  100. Thall PF, Lachin JM. Assessment of stratum-covariate interactions in Cox’s proportional hazards regression model. Stat Med 1986;5:73–83.

    Article  Google Scholar 

  101. Shuster J, van Eys J. Interaction between prognostic factors and treatment. Control Clin Trials 1983;4:209–214.

    Google Scholar 

  102. Gail M, Simon R. Testing for qualitative interactions between treatment effects and patients subsets. Biometrics 1985;41:361–372.

    Article  MATH  Google Scholar 

  103. Aspirin Myocardial Infarction Study Research Group. A randomized, controlled trial of aspirin in persons recovered from myocardial infarction. JAMA 1980;243:661–669.

    Article  Google Scholar 

  104. Yates F. The analysis of multiple classifications with unequal numbers in the different classes. J Am Stat Assoc 1934;29:51–66.

    Article  MATH  Google Scholar 

  105. Report from the Committee of Principal Investigators. A co-operative trial in the primary prevention of ischaemic heart disease using clofibrate. Br Heart J 1978;40:1069–1118.

    Article  Google Scholar 

  106. Robins JM, Tsiatis AA. Correcting for non-compliance in randomized trials using rank preserving structural failure time models. Commun Stat Theory Methods 1991;20:2609–2631.

    Article  MATH  MathSciNet  Google Scholar 

  107. Peto R. Statistical aspects of cancer trials. In Halnan KE (ed.). Treatment of Cancer. London: Chapman and Hall, 1982.

    Google Scholar 

  108. Multicentre International Study. Improvement in prognosis of myocardial infarction by long-term beta-adrenoreceptor blockade using practolol. Br Med J 1975;3:735–740.

    Article  Google Scholar 

  109. Andersen MP, Bechsgaard P, Frederiksen J, et al. Effect of alprenolol on mortality among patients with definite or suspected acute myocardial infarction. Lancet 1979;ii:865–868.

    Article  Google Scholar 

  110. Furberg CD, Hawkins CM, Lichstein E. Effect of propranolol in postinfarction patients with mechanical or electrical complications. Circulation 1984;69:761–765.

    Article  Google Scholar 

  111. Simon R. Patient subsets and variation in therapeutic efficacy. Br J Clin Pharmacol 1982;14:473–482.

    Article  Google Scholar 

  112. Ingelfinger JA, Mosteller F, Thibodeau LA, Ware JH. Biostatistics in Clinical Medicine. New York: MacMillan, 1983, pp. 255–258.

    Google Scholar 

  113. Furberg CD, Byington RP. What do subgroup analyses reveal about differential response to beta-blocker therapy? The Beta-blocker Heart Attack Trial experience. Circulation 1983;67(suppl 1):I-98–I-101.

    Google Scholar 

  114. ISIS-2 (Second International Study of Infarct Survival) Study Collaborative Group. Randomized trial or streptokinase, oral aspirin, or both, or neither among 17,187 suspected cases of acute myocardial infarction ISIS-2. Lancet 1988;ii:349–360

    Google Scholar 

  115. Packer M, O’Conner CM, Ghali JK, et al. Effect of amlodipine on morbidity and mortality in severe chronic heart failure. Prospective Randomized Amlodipine Survival Evaluation Study Group. N Engl J Med 1996;335:1107–1114.

    Article  Google Scholar 

  116. Thackray S, Witte K, Clark AL, Cleland JG. Clinical trials update: OPTIME-CHF, PRAISE-2, ALLHAT. Eur J Heart Fail 2000;2:209–212.

    Article  Google Scholar 

  117. Helgason T, Jonasson MR. Evidence for a food additive as a cause of ketosis-prone diabetes. Lancet 1981;ii:716–720.

    Article  Google Scholar 

  118. Dijkstra BK. Origin of carcinoma of the bronchus. J Natl Cancer Inst 1963;31:511–519.

    Google Scholar 

  119. Davies JM. Cancer and date of birth. Br Med J 1963;ii:1535.

    Article  Google Scholar 

  120. Bass C, Strackee J, Jones I. Lung cancer and month of birth (Letter). Lancet 1964;i:47.

    Article  Google Scholar 

  121. Goudie RB. The birthday fallacy and statistics of Icelandic diabetes (Letter). Lancet 1981;ii:1173.

    Article  Google Scholar 

  122. Wedel H, DeMets D, Deedwania P, et al., on behalf of the MERIT-HF Study Group. Challenges of subgroup analyses in multinational clinical trials: experiences from the MERIT-HF trial. Am Heart J 2001;142:502–511.

    Google Scholar 

  123. Lee KL, McNeer JF, Starmer CF, et al. Clinical judgment and statistics. Lessons from a simulated randomized trial in coronary artery disease. Circulation 1980;61:508–515.

    Article  Google Scholar 

  124. Miller RG Jr. Simultaneous Statistical Inference. New York: McGraw-Hill, 1966.

    MATH  Google Scholar 

  125. Holm S. A simple sequentially rejective multiple test procedure. Scand Stat Theory Appl 1979;6:65–70.

    MATH  MathSciNet  Google Scholar 

  126. Hochberg Y. A sharper Bonferroni procedure for multiple tests of significance. Biometrika 1988;75:800–802.

    Article  MATH  MathSciNet  Google Scholar 

  127. Piaggio G, Elbourne DR, Altman DG, for the CONSORT Group. Reporting of noninferiority and equivalence randomized trials. An extension of the CONSORT statement. JAMA 2006;295:1152–1160.

    Google Scholar 

  128. Koch A, Rohmel J. The impact of sloppy conduct of noninferiority studies. Drug Info J 2002;36:3–6.

    Article  Google Scholar 

  129. Pocock SJ, Ware JH. Translating statistical findings into plain English. Lancet 2009;373:1926–1928.

    Article  Google Scholar 

  130. Kaul S, Diamond GA. Good enough: a primer on the analysis and interpretation of noninferiority trials. Ann Intern Med 2006;145:62–69.

    Article  Google Scholar 

  131. Diamond GA, Kaul S. An Orwellian discourse on the meaning and measurement of noninferiority. Am J Cardiol 2006;99:284–287.

    Article  Google Scholar 

  132. Kaul S, Diamond GA. Making sense of noninferiority: a clinical and statistical perspective on its application to cardiovascular clinical trials. Prog Cardiovasc Dis 2007;49:284–299.

    Article  Google Scholar 

  133. Califf RM. A perspective on the regulation of the evaluation of new antithrombotic drugs. Am J Cardiol 1998;82(Suppl):25P–35P.

    Article  Google Scholar 

  134. SPORTIF Executive Steering Committee for the SPORTIFV Investigators. Ximelagatran vs warfarin for stroke prevention in patients with nonvalvular atrial fibrillation. A randomized trial. JAMA 2005;293:690–698.

    Article  Google Scholar 

  135. Kaul S, Diamond GA, Weintraub WS. Trials and tribulations of non-inferiority: the ximelegatran experience. J Am Coll Cardiol 2005;46:1986–1995.

    Article  Google Scholar 

  136. Temple R, Ellenberg SS. Placebo-controlled trials and active-control in the evaluation of new treatments. Part 1: ethical and scientific issues. Ann Intern Med 2000;133:455–463.

    Article  Google Scholar 

  137. Ellenberg SS, Temple R. Placebo-controlled trials and active-control trials in the evaluation of new treatments. Part 2: practical issues and specific cases. Ann Intern Med 2000;133:464–470.

    Article  Google Scholar 

  138. Siegel JP. Equivalence and noninferiority trials. Am Heart J 2000;139(Suppl):166–170.

    Article  Google Scholar 

  139. Hung JHM, Wang SJ, Tsong Y, et al. Some fundamental issues with non-inferiority testing in active controlled trials. Stat Med 2003;22:213–225.

    Article  Google Scholar 

  140. Hung HM, Wang SJ, O’Neill R. A regulatory perspective on choice of margin and statistical inference issue in non-inferiority trials. Biom J 2005;47:28–36.

    Article  MathSciNet  Google Scholar 

  141. D’Agostino RB Sr, Massaro JM, Sullivan LM. Non-inferiority trials: design concepts and issues-the encounters of academic consultants in statistics. Stat Med 2003;22:169–186.

    Article  Google Scholar 

  142. Blackwelder WC. “Proving the null hypothesis” in clinical trials. Control Clin Trials 1982;3:345–353.

    Article  Google Scholar 

  143. Hasselblad V, Kong DF. Statistical methods for comparison to placebo in active-control trials. Drug Info J 2001;35:435–449.

    Google Scholar 

  144. Fleming TR. Current issues in non-inferiority trials. Stat Med 2008;27:317–332.

    Article  MathSciNet  Google Scholar 

  145. Peto R. Why do we need systematic overviews of randomized trials? (Modified transcript of an oral presentation). Stat Med 1987;6:233–240.

    Article  Google Scholar 

  146. Yusuf S. Obtaining medically meaningful answers from an overview of randomized clinical trials. Stat Med 1987;6:281–286.

    Article  Google Scholar 

  147. Hennekens CH, Buring JE, Hebert PR. Implications of overviews of randomized trials. Stat Med 1987;6:397–402.

    Article  Google Scholar 

  148. Simon R. The role of overviews in cancer therapeutics. Stat Med 1987;6:389–393.

    Article  Google Scholar 

  149. Goodman SN. Meta-analysis and evidence. Control Clin Trials 1989;10:188–204.

    Article  Google Scholar 

  150. Meinert CL. Meta-analysis: science or religion? Control Clin Trials 1989;10(Suppl):257S–263S.

    Article  Google Scholar 

  151. Altman L. New method of analyzing health data stirs debate. New York Times, August 21, 1990.

    Google Scholar 

  152. Sacks HS, Berrier J, Reitman D, et al. Meta-analyses of randomized controlled trials. N Engl J Med 1987;316:450–455.

    Article  Google Scholar 

  153. DeMets DL. Methods for combining randomized clinical trials: strengths and limitations. Stat Med 1987;6:341–348.

    Article  Google Scholar 

  154. Cochran WG. Some methods for strengthening the common chi-square tests. Biometrics 1954;10:417–451.

    Article  MATH  MathSciNet  Google Scholar 

  155. Mantel N, Haenszel W. Statistical aspects of the analysis of data from retrospective studies of disease. J Natl Cancer Inst 1959;22:719–748.

    Google Scholar 

  156. Thompson SG. Meta-analysis of clinical trials. In Encyclopedia of Biostatistics. New York: Wiley, 1998, pp. 2570–2579.

    Google Scholar 

  157. Pocock SJ, Hughes MD. Estimation issues in clinical trials and overviews. Stat Med 1990;9:657–671.

    Article  Google Scholar 

  158. Galbraith RF. A note on graphical presentation of estimated odds ratios from several clinical trials. Stat Med 1988;7:889–894.

    Article  Google Scholar 

  159. Berlin JA, Laird NM, Sacks HS, Chalmers TC. A comparison of statistical methods for combining event rates from clinical trials. Stat Med 1989;8:141–151.

    Article  Google Scholar 

  160. DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials 1986;7:177–188.

    Article  Google Scholar 

  161. Whitehead A, Whitehead J. A general parametric approach to the meta-analysis of randomized clinical trials. Stat Med 1991;10:1665–1677.

    Article  Google Scholar 

  162. Brand R, Kragt H. Importance of trends in the interpretation of an overall odds ratio in the meta-analysis of clinical trials. Stat Med 1992;11:2077–2082.

    Article  Google Scholar 

  163. Carroll RJ, Stefanski LA. Measurement error, instrumental variables and corrections for attenuation with applications to meta-analyses. Stat Med 1994;13:1265–1282.

    Article  Google Scholar 

  164. Higgins JPT, Green S (eds.). Cochrane Handbook for Systematic Reviews of Interventions. Chichester, UK: John Wiley & Sons, 2008.

    Google Scholar 

  165. Moher D, Liberati A, Tetzlaff J, Altman DG, The PRISMA Group. Preferred reporting items for systematic reviews and meta-analyses: the PRISMA Statement. PLoS Med 2009;6:e1000097.

    Article  Google Scholar 

  166. Liberati A, Altman DG, Tetzlaff J, et al. The PRISMA statement for reporting systematic reviews and meta analyses of studies that evaluate health care interventions: explanation and elaboration. PLoS Med 2009;6:e1000100.

    Article  Google Scholar 

  167. Chalmers TC, Matta RJ, Smith H, Kunzler AM. Evidence favoring the use of anticoagulants in the hospital phase of acute myocardial infarction. N Engl J Med 1977;297:1091–1096

    Article  Google Scholar 

  168. May GS, Furberg CD, Eberlein KA, Geraci BJ. Secondary prevention after myocardial infarction: a review of short-term acute phase trials. Prog Cardiovasc Dis 1983;25:335–359.

    Article  Google Scholar 

  169. Baum ML, Anish DS, Chalmers TC, et al. A survey of clinical trials of antibiotic prophylaxis in colon surgery: evidence against further use of no-treatment controls. N Engl J Med 1981;305:795–799.

    Article  Google Scholar 

  170. Canner PL. Aspirin in coronary heart disease: comparison of six trials. Ir J Med Sci 1983;19:413–423

    Google Scholar 

  171. Wang PH, Lau J, Chalmers TC. Meta-analysis of effects of intensive blood-glucose control on late complications of type I diabetes. Lancet 1993;341:1306–1309.

    Article  Google Scholar 

  172. Himel HN, Liberati A, Gelber RD, Chalmers TC. Adjuvant chemotherapy for breast cancer – A pooled estimate based on published randomized control trials. JAMA 1986;256:1148–1159.

    Article  Google Scholar 

  173. Yusuf S, Peto R, Lewis J, et al. Beta blockade during and after myocardial infarction: an overview of the randomized trials. Prog Cardiovasc Dis 1985;27:335–371.

    Article  Google Scholar 

  174. Yusuf S, Collins R, Peto R, et al. Intravenous and intracoronary fibronolytic therapy in acute myocardial infarction: overview of results on mortality, reinfarction and side-effects from 33 randomized controlled trials. Eur Heart J 1985;6:556–585.

    Google Scholar 

  175. Hennekens CH, Buring JE, Sandercock P, et al. Aspirin and other antiplatelet agents in the secondary and primary prevention of cardiovascular disease. Circulation 1989;80:749–756.

    Article  Google Scholar 

  176. Goldman L, Feinstein AR. Anticoagulants and myocardial infarction. The problems of pooling, drowning, and floating. Ann Intern Med 1979;90:92–94.

    Article  Google Scholar 

  177. Furberg CD, Morgan TM. Lessons from overviews of cardiovascular trials. Stat Med 1987;6:295–303.

    Article  Google Scholar 

  178. Collins R, Gray R, Godwin J, Peto R. Avoidance of large biases and large random errors in the assessment of moderate treatment effects: the need for systematic overviews. Stat Med 1987;6:245–250.

    Article  Google Scholar 

  179. Wittes RE. Problems in the medical interpretation of overviews. Stat Med 1987;6:269–276.

    Article  Google Scholar 

  180. Chalmers TC, Levin H, Sacks HS, et al. Meta-analysis of clinical trials as a scientific discipline. I: Control of bias and comparison with large co-operative trials. Stat Med 1987;6:315–325.

    Article  Google Scholar 

  181. Bailey KR. Inter-study differences: how should they influence the interpretation and analysis of results? Stat Med 1987;6:351–358.

    Article  Google Scholar 

  182. Furberg CD. Lipid-lowering trials: results and limitations. Am Heart J 1994;128:1304–1308.

    Article  Google Scholar 

  183. Berlin JA, Begg CB, Louis TA. An assessment of publication bias using a sample of published clinical trials. J Am Stat Assoc 1989;84:381–392.

    Article  Google Scholar 

  184. Simes RJ. Confronting publication bias: a cohort design for meta-analysis. Stat Med 1987;6:11–29.

    Article  Google Scholar 

  185. Chalmers TC, Frank CS, Reitman D. Minimizing the three stages of publication bias. JAMA 1990;263:1392–1395..

    Article  Google Scholar 

  186. Thompson SG. Why sources of heterogeneity in meta-analysis should be investigated. Br Med J 1994;309:1351–1355.

    Article  Google Scholar 

  187. Johnson RT, Dickersin K. Publication bias against negative results from clinical trials: three of the seven deadly sins. Nat Clin Pract Neurol 2007;3:590–591.

    Article  Google Scholar 

  188. Chalmers TC. Randomization of the first patient. Med Clin North Am 1975;59:1035–1038.

    Google Scholar 

  189. Cui L, Hung HM, Wang SJ. Modification of sample size in group sequential clinical trials. Biometrics 1999;55:853–857.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bethesda, MD, USA

    Lawrence M. Friedman

  2. School of Medicine, Wake Forest University, Winston-Salem, NC, USA

    Curt D. Furberg

  3. Department of Biostatistics & Medical Informatics, University of Wisconsin, Madison, WI, USA

    David L. DeMets

Authors
  1. Lawrence M. Friedman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Curt D. Furberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David L. DeMets
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lawrence M. Friedman .

Appendix

Appendix

Mantel–Haenszel Statistic

Suppose an investigator is comparing response rates and divides the data into a number of strata using baseline characteristics. For each stratum i, a 2 × 2 table is constructed.

2 × 2 Table for ith Stratum

 

Response

 
 

Yes

No

 

Intervention

a i

b i

a i + b i

Control

c i

d i

c i + d i

Total

a i + c i

b i + d i

n i

The entries a i , b i , c i , and d i represent the counts in the four cells and n i is the number of participants in the ith stratum. The marginals represent totals in the various categories. The value (a i + c i )/n i represents the overall response rate for the ith stratum. Within the ith stratum, the rates a i /(a i + b i ) with c i /(c i +d i ) are compared. The standard chi-square test for 2 × 2 tables could be used to compare group differences in this stratum. However, the investigator is interested in “averaging” the comparison over all the strata. The method for combining several 2 × 2 tables over all tables or strata was described by Cochran [157] and Mantel and Haenszel [158]. The summary statistic, denoted MH, is given by:

$$ \text{MH}=\frac{{\left\{{\displaystyle \sum _{i=1}^{K}\left[{a}_{i}-(a+{c}_{i})({a}_{i}+{b}_{i})/{n}_{i}\right]}\right\}}^{2}}{{\displaystyle \sum _{i=1}^{K}({a}_{i}+{c}_{i})({b}_{i}+{d}_{i})({a}_{i}+{b}_{i})({c}_{i}+{d}_{i})/{n}_{i}^{2}({n}_{i}-1)}}$$

The MH statistic has a chi-square distribution with one degree of freedom. The square root of MH has a normal distribution. Tables for this distribution are available in standard statistical textbooks. Any value for MH greater than 3.84 is significant at the 0.05 level, and any value greater than 6.63 is significant at the 0.01 level. This method is particularly appropriate for covariates that are discrete or continuous covariates that have been classified into intervals.

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer New York

About this chapter

Cite this chapter

Friedman, L.M., Furberg, C.D., DeMets, D.L. (2010). Issues in Data Analysis. In: Fundamentals of Clinical Trials. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1586-3_17

Download citation

Publish with us

Policies and ethics

Search

Navigation