## Abstract

The randomized controlled clinical trial is the standard by which all trials are judged since other designs have certain undesirable features. In the simplest case, randomization is a process by which each participant has the same chance of being assigned to either intervention or control. An example would be the toss of a coin, in which heads indicates intervention group and tails indicates control group. Even in the more complex randomization strategies, the element of chance underlies the allocation process. Of course, neither trial participant nor investigator should know what the assignment will be before the participant’s decision to enter the study. Otherwise, the benefits of randomization can be lost. The role that randomization plays in clinical trials has been discussed in Chap. 5 as well as by numerous authors [1–12]. While not all accept that randomization is essential [11, 12], most agree it is the best method for achieving comparability between study groups and is the basis for statistical inference [2, 3].

## Keywords

Adaptive Procedure Simple Randomization Stratify Randomization Equal Allocation Adaptive Randomization## References

- 1.Hill AB. The clinical trial.
*Br Med Bull*1951;7:278–282.Google Scholar - 2.Armitage P. The role of randomization in clinical trials.
*Stat Med*1982;1:345–352.CrossRefGoogle Scholar - 3.Byar DP, Simon RM, Friedewald WT, et al. Randomized clinical trials: Perspectives on some recent ideas.
*N Engl J Med*1976;295:74–80.CrossRefGoogle Scholar - 4.Zelen M. The randomization and stratification of patients to clinical trials.
*J Chronic Dis*1974;27:365–375.CrossRefMathSciNetGoogle Scholar - 5.Pocock SJ. Allocation of patients to treatment in clinical trials.
*Biometrics*1979;35:183–197.CrossRefGoogle Scholar - 6.Peto R. Clinical trial methodology.
*Biomedicine*1978;28(special issue):24–36.Google Scholar - 7.Peto R, Pike MC, Armitage P, et al. Design and analysis of randomised clinical trials requiring prolonged observation of each patient. 1. Introduction and design.
*Br J Cancer*1976;34: 585–612.CrossRefGoogle Scholar - 8.Brown BW. Statistical controversies in the design of clinical trials – some personal views.
*Control Clin Trials*1980;1:13–27.CrossRefGoogle Scholar - 9.Lachin JM. Statistical properties of randomization in clinical trials.
*Control Clin Trials*1988;9:289–311.CrossRefGoogle Scholar - 10.Lachin JM, Matts JP, Wei LJ. Randomization in clinical trials: Conclusions and recommendations.
*Control Clin Trials*1988;9:365–374.CrossRefGoogle Scholar - 11.Royall RM. Ethics and statistics in randomized clinical trials.
*Stat Sci*1991;6(1):52–88.CrossRefMATHMathSciNetGoogle Scholar - 12.Weinstein MC. Allocation of subjects in medical experiments.
*N Engl J Med*1974;291: 1278–1285.CrossRefGoogle Scholar - 13.Bather JA. On the allocation of treatments in sequential medical trials.
*Int Stat Rev*1985;53:1–13.CrossRefMATHMathSciNetGoogle Scholar - 14.Kalish LA, Begg CB. Treatment allocation methods in clinical trials: A review.
*Stat Med*1985;4:129–144.CrossRefGoogle Scholar - 15.Stigler SM. The use of random allocation for the control of selection bias.
*Biometrika*1969;56:553–560.CrossRefMATHMathSciNetGoogle Scholar - 16.Wei LJ. On the random allocation design for the control of selection bias in sequential experiments.
*Biometrika*1978;65:79–84.CrossRefMATHMathSciNetGoogle Scholar - 17.Altman D, Dore CJ. Randomization and baseline comparisons in clinical trials.
*Lancet*1990;335:149–155.CrossRefGoogle Scholar - 18.Williams DS, Davis CE. Reporting of assignment methods in clinical trials.
*Control Clin Trials*1994;15:294–298.CrossRefGoogle Scholar - 19.Moher D, Schulz KF, Altman DG, CONSORT Group (Consolidated Standards of Reporting Trials). The CONSORT statement: revised recommendations for improving the quality of reports of parallel-group randomized trials.
*Ann Intern Med*2001;134:657-662.CrossRefGoogle Scholar - 20.Mills EJ, Wu P, Gagnier J, Devereaux PJ. The quality of randomized trial reporting in leading medical journals since the revised CONSORT statement.
*Contemp Clin Trials*2005;26: 480–487.CrossRefGoogle Scholar - 21.Brittain E, Schlesselman JJ. Optimal allocation for the comparison of proportions.
*Biometrics*1982;38:1003–1009.CrossRefGoogle Scholar - 22.Lachin JM. Properties of simple randomization in clinical trials.
*Control Clin Trials*1988;9:312–326.CrossRefGoogle Scholar - 23.Louis TA. Optimal allocation in sequential tests comparing the means of two Gaussian populations.
*Biometrika*1975;62:359–369.CrossRefMATHMathSciNetGoogle Scholar - 24.Louis TA. Sequential allocation in clinical trials comparing two exponential survival curves.
*Biometrics*1977;33:627–634.CrossRefMathSciNetGoogle Scholar - 25.Kalish LA, Harrington DP. Efficiency of balanced treatment allocation for survival analysis.
*Biometrics*1988;44:815–821.CrossRefMATHGoogle Scholar - 26.Matts JP, Lachin JM. Properties of permutated-block randomization in clinical trials.
*Control Clin Trials*1988;9:327–344.CrossRefGoogle Scholar - 27.Kalish LA, Begg CB. The impact of treatment allocation procedures on nominal significance levels and bias.
*Control Clin Trials*1987;8:121–135.CrossRefGoogle Scholar - 28.Smythe RT, Wei LJ. Significance tests with restricted randomization design.
*Biometrika*1983;70:496–500.CrossRefMATHMathSciNetGoogle Scholar - 29.Steele JM. Efron’s conjecture on vulnerability to bias in a method for balancing sequential trials.
*Biometrika*1980;67:503–504.CrossRefMATHMathSciNetGoogle Scholar - 30.Titterington DM. On constrained balance randomization for clinical trials.
*Biometrics*1983;39:1083–1086.CrossRefGoogle Scholar - 31.Matts JP, McHugh RB. Analysis of accrual randomized clinical trials with balanced groups in strata.
*J Chronic Dis*1978;31:725–740.CrossRefGoogle Scholar - 32.Zelen M. Aspects of the planning and analysis of clinical trials in cancer. In Srivastava JN (ed.).
*A Survey of Statistical Design and Linear Models.*Amsterdam: North-Holland, 1975.Google Scholar - 33.Coronary Drug Project Research Group. Factors influencing long term prognosis after recovery from myocardial infarction – Three year findings of the Coronary Drug Project.
*J Chronic Dis*1974;27:267–285.CrossRefGoogle Scholar - 34.Pocock SJ, Simon R. Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial.
*Biometrics*1975;31:103–115.CrossRefGoogle Scholar - 35.Green SB, Byar DP. The effect of stratified randomization on size and power of statistical tests in clinical trials.
*J Chronic Dis*1978;31:445–454.CrossRefGoogle Scholar - 36.Ducimetiere P. Stratification. In Boissel JP, Klimt CR (eds.).
*Multi-center Controlled Trials: Principals and Problems.*Paris: INSERM, 1979.Google Scholar - 37.Simon R. Restricted randomization designs in clinical trials.
*Biometrics*1979;35:503–512.CrossRefGoogle Scholar - 38.Meier P. Stratification in the design of a clinical trial.
*Control Clin Trials*1981;1:355–361.CrossRefGoogle Scholar - 39.Grizzle JE. A note on stratifying versus complete random assignment in clinical trials.
*Control Clin Trials*1982;3:365–368.CrossRefMathSciNetGoogle Scholar - 40.McHugh R, Matts J. Post-stratification in the randomized clinical trial.
*Biometrics*1983;39:217–225.CrossRefMATHMathSciNetGoogle Scholar - 41.Fleiss JL. Multicentre clinical trials: Bradford Hill’s contributions and some subsequent developments.
*Stat Med*1982;1:353–359.CrossRefGoogle Scholar - 42.Feinstein AR, Landis JR. The role of prognostic stratification in preventing the bias permitted by random allocation of treatment.
*J Chronic Dis*1976;29:277–284.CrossRefGoogle Scholar - 43.Mantel N. Pre-stratification or post-stratification (Letter).
*Biometrics*1984;40:256–258.Google Scholar - 44.Palta M. Investigating maximum power losses in survival studies with nonstratified randomization.
*Biometrics*1985;41:497–504.CrossRefMATHMathSciNetGoogle Scholar - 45.Palta M, Amini SB. Magnitude and likelihood of loss resulting from non-stratified randomization.
*Stat Med*1982;1:267–275.CrossRefGoogle Scholar - 46.Aspirin Myocardial Infarction Study Research Group. A randomized controlled trial of aspirin in persons recovered from myocardial infarction.
*JAMA*1980;243:661–669.CrossRefGoogle Scholar - 47.Efron B. Forcing a sequential experiment to be balanced.
*Biometrika*1971;58:403–417.CrossRefMATHMathSciNetGoogle Scholar - 48.Freedman LS, White SJ. On the use of Pocock and Simon’s method for balancing treatment numbers over prognostic factors in the controlled clinical trial.
*Biometrics*1976;32:691–694.CrossRefMATHGoogle Scholar - 49.Begg CD, Iglewicz B. A treatment allocation procedure for sequential clinical trials.
*Biometrics*1980;36:81–90.CrossRefMATHGoogle Scholar - 50.Atkinson AC. Optimum biased coin designs for sequential clinical trials with prognostic factors.
*Biometrika*1982;69:61–67.CrossRefMATHMathSciNetGoogle Scholar - 51.Taves DR. Minimization: A new method of assigning patients to treatment and control groups.
*Clin Pharmacol Ther*1974;15:443–453.Google Scholar - 52.White SJ, Freedman LS. Allocation of patients to treatment groups in a controlled clinical study.
*Br J Cancer*1978;37:849–857.CrossRefGoogle Scholar - 53.Forsythe AB, Stitt FW. Randomization or minimization in the treatment assignment of patient trials: validity and power of tests. Technical Report No. 28, Health Science Computer Facility, University of California, Los Angeles, 1977.Google Scholar
- 54.Begg CB. On inferences from Wei’s biased coin design for clinical trials.
*Biometrika*1990;77:467–484.CrossRefMATHMathSciNetGoogle Scholar - 55.Efron B. Randomizing and balancing a complicated sequential experiment. In Miller RG Jr. Efron B, Brown BW Jr, Moses LE (eds.).
*Biometrics Casebook*. New York: Wiley, 1980, pp. 19–30.Google Scholar - 56.Halpern J, Brown BW Jr. Sequential treatment allocation procedures in clinical trials – with particular attention to the analysis of results for the biased coin design.
*Stat Med*1986;5: 211–229.CrossRefGoogle Scholar - 57.Hannigan JR Jr, Brown BW Jr. Adaptive randomization based coin-design: Experience in a cooperative group clinical trial. Technical Report 74, Division of Biostatistics, Stanford University, Stanford, California, 1982.Google Scholar
- 58.Klotz JH. Maximum entropy constrained balance randomization for clinical trials.
*Biometrics*1978;34:283–287.CrossRefGoogle Scholar - 59.Raghavaro D. Use of distance function in sequential treatment assignment for prognostic factors in the controlled clinical trial.
*Calcutta Stat Assoc Bull*1980;29:99–102.Google Scholar - 60.Smith RL. Sequential treatment allocation using biased coin designs.
*J R Stat Soc Series B Stat Methodol*1984;46:519–543.MATHGoogle Scholar - 61.Soares JF, Wu CFJ. Some restricted randomization rules in sequential designs.
*Commun Stat Theory Methods A*1983;12:2017–2034.CrossRefMATHMathSciNetGoogle Scholar - 62.Wei LJ. The adaptive biased coin design for sequential experiments.
*Ann Stat*1978;6: 92–100.CrossRefMATHGoogle Scholar - 63.Wei LJ. A class of designs for sequential clinical trials.
*J Am Stat Assoc*1977;72:382–386.CrossRefGoogle Scholar - 64.Wei LJ. A class of treatment assignment rules for sequential experiments.
*Commun Stat Theory Methods A*1978;7:285–295.CrossRefGoogle Scholar - 65.Wei LJ, Lachin JM. Properties of the urn randomization in clinical trials.
*Control Clin Trials*1988;9:345–364.CrossRefGoogle Scholar - 66.Wei LJ, Smythe RT, Lin DY, Park TS. Statistical inferences with data-dependent treatment allocation rules.
*J Am Stat Assoc*1990;85:156–162.CrossRefMathSciNetGoogle Scholar - 67.Wei LJ, Smythe RT, Smith RL. K-treatment comparisons with restricted randomization rules in clinical trials.
*Ann Stat*1986;14:265–274.CrossRefMATHMathSciNetGoogle Scholar - 68.Wei LJ. An application of an urn model to the design of sequential controlled clinical trials.
*J Am Stat Assoc*1978;73:559–563.CrossRefMATHGoogle Scholar - 69.The DCCT Research Group. Diabetes Control and Complications Trial (DCCT): Design and methodologic considerations for the feasibility phase.
*Diabetes*1986;35:530–545.CrossRefGoogle Scholar - 70.Begg CB, Kalish LA. Treatment allocation for nonlinear models in clinical trials: The logistic model.
*Biometrics*1984;40:409–420.CrossRefGoogle Scholar - 71.Begg CB, Kalish LA. Treatment allocation in sequential clinical trials: Nonlinear models.
*Proc Stat Comput Sect, Am Stat Assoc*1982:57–60.Google Scholar - 72.Gail MH, Wieand S, Piantadosi S. Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates.
*Biometrika*1984;71:431–444.CrossRefMATHMathSciNetGoogle Scholar - 73.Birkett JJ. Adaptive allocation in randomized controlled trials.
*Control Clin Trials*1985;6:146–155.CrossRefGoogle Scholar - 74.Russell M, Fleg JL, Galloway J, et al. Examination of lower targets for low-intensity lipoprotein cholesterol and blood pressure in diabetes—the Stop Atherosclerosis in Native Diabetics Study (SANDS).
*Am Heart J*2006:152;867–875.CrossRefGoogle Scholar - 75.Howard BV, Roman MJ, Devereux RB, et al. Effect of lower targets for blood pressure and LDL cholesterol on atherosclerosis in diabetes: The SANDS randomized trial.
*JAMA*2008:299;1678–1689.CrossRefGoogle Scholar - 76.Zelen M. Play-the-winner rule and the controlled clinical trial.
*J Am Stat Assoc*1969;64: 131–146.CrossRefMathSciNetGoogle Scholar - 77.Robbins H. Some aspects of the sequential design of experiments.
*Bull Am Math Soc*1952;58:527–535.CrossRefMATHMathSciNetGoogle Scholar - 78.Bailar JC. Patient assignment algorithms: An overview. In
*Proceedings of the 9th International Biometric Conference*, Raleigh, NC: The Biometric Society, 1976; Vol I, pp. 189–206.Google Scholar - 79.Simon R. Adaptive treatment assignment methods and clinical trials.
*Biometrics*1977;33: 743–749.CrossRefGoogle Scholar - 80.Armitage P. The search for optimality in clinical trials.
*Int Stat Rev*1985;53:15–24.CrossRefMATHMathSciNetGoogle Scholar - 81.Nordbrock E. An improved play-the-winner sampling procedure for selecting the better of two binomial populations.
*J Am Stat Assoc*1976;71:137–139.CrossRefMATHMathSciNetGoogle Scholar - 82.Wei LJ. Exact two-sample permutation tests based on the randomized play-the-winner rule.
*Biometrika*1988;75:603–606.CrossRefMATHMathSciNetGoogle Scholar - 83.Bartlett RH, Roloff DW, Cornell RG, et al. Extracorporeal circulation in neonatal respiratory failure: A prospective randomized study.
*Pediatrics*1985;76:479–487.Google Scholar - 84.O’Rourke PP, Crone RK, Vacanti JP, et al. Extracorporeal membrane oxygenation and conventional medical therapy in neonates with persistent pulmonary hypertension of the newborn: A prospective randomized study.
*Pediatrics*1989;84:957–963.Google Scholar - 85.Simon R, Weiss GH, Hoel DG. Sequential analysis of binomial clinical trials.
*Biometrika*1975;62:195–200.CrossRefMATHMathSciNetGoogle Scholar - 86.Simon R, Hoel DG, Weiss GH. The use of covariate information in the sequential analysis of dichotomous response experiments.
*Commun Stat Theory Methods*1977;8:777–788.CrossRefGoogle Scholar - 87.Paneth N, Wallenstein S. Extracorporeal membrane oxygenation and the play the winner rule.
*Pediatrics*1985;76:622–623.Google Scholar - 88.Ware JH. Investigating therapies of potentially great benefit: ECMO.
*Stat Sci*1989;4:298–340.CrossRefMATHMathSciNetGoogle Scholar - 89.Ware JH, Epstein MF. Extracorporeal circulation in neonatal respiratory failure: A prospective randomized study.
*Pediatrics*1985;76:849–851.Google Scholar - 90.Pocock SJ, Lagakos SW. Practical experience of randomization in cancer trials: An international survey.
*Br J Cancer*1982;46:368–375.CrossRefGoogle Scholar - 91.Chalmers TC, Celano P, Sacks HS, et al. Bias in treatment assignment in controlled clinical trials.
*N Engl J Med*1983;309:1358–1361.CrossRefGoogle Scholar - 92.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.CrossRefGoogle Scholar - 93.Hypertension Detection and Follow-up Program Cooperative Group. Five-year findings of the Hypertension Detection and Follow-up Program. Reduction in mortality of persons with high blood pressure, including mild hypertension.
*JAMA*1979;242:2562–2571.CrossRefGoogle Scholar - 94.Multiple Risk Factor Intervention Trial Research Group. Multiple Risk Factor Interventional Trial. Risk factor changes and mortality results.
*JAMA*1982;248:1465–1477.CrossRefGoogle Scholar - 95.CASS Principal Investigators and Their Associates. Coronary Artery Surgery Study (CASS): A randomized trial of coronary artery bypass surgery, survival data.
*Circulation*1983;68:939–950.CrossRefGoogle Scholar - 96.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 - 97.Krischer J, Hurley C, Pillamarri M, et al. An automated patient registration and treatment randomization system for multicenter clinical trials.
*Control Clin Trials*1991;12:367–377.CrossRefGoogle Scholar - 98.Kjekshus J, Apetrei E, Barrios V, et al. Rosuvastatin in older patients with systolic heart failure.
*N Engl J Med*2007;357:2248–2261.CrossRefGoogle Scholar - 99.SPORTIF Executive Steering Committee for the SPORTIF-V Investigators. Ximelagatran vs Warfarin for stroke prevention in patients with nonvalvular atrial fibrillation. A randomized trial.
*JAMA*2005;293:690–698.CrossRefGoogle Scholar - 100.Ahlmark G, Saetre H. Long-term treatment with β-blockers after myocardial infarction.
*Eur J Clin Pharmacol*1976;10:77–83.CrossRefGoogle Scholar