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Outline of Randomization Lectures 1.Background and definitions 2.Generation of schedules 3.Implementation (to ensure allocation concealment, sometimes called blinded randomization) 4.Theory behind randomization

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Randomization Schedule A list showing the order in which subjects are to be assigned to the various treatment groups

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Implementation Schemes 1.Sealed envelopes -Opaque -Sequentially numbered 2.Telephone -Answering service -Coordinating center - IVRS 3.Personal computers -Local -Through communication with coordinating center 4.International coordinating centers in HIV treatment trials use web-based system 5.Through electronic medical record for point-of-care or clinically integrated randomized trials.

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Urokinase-Pulmonary Embolism Trial (UPET) Circulation, 1973 1.Telephone answering service in New York City; 24-hour coverage 2.Assignments obtained through hospital pharmacy 3.Sealed envelopes as back-up

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Multiple Risk Factor Intervention Trial (MRFIT) JAMA, 1982 1.Assignments obtained by calling coordinating center after: a.Three screening visits b.Informed consent c.Eligibility checklist 2.Sealed envelopes used as back-up

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Treatment of Mild Hypertension Study (TOHMS) 1.Assignment (bottle no.) obtained using personal computer to call coordinating center computer after: a.Three screening visits b.Informed consent c.Eligibility checklist 2.Call coordinating center for back-up 3.Unique bottle no. for each participant 4.Bottle no. not assigned in sequence Amer J Cardiol, 1987

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Community Programs for Clinical Research on AIDS (CPCRA) 1.Assignments obtained by calling Statistical Center: –Minimal data collection –Usually no data at Statistical Center prior to randomization –Eligibility checklist reviewed on telephone call 2.Pharmacist telephones to confirm assignment 3.Unique study ID number (SID) for each patient 4.SID numbers not assigned in sequence

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Components of CPCRA Randomization System 1.Randomization schedule, based on randomly permuted blocks 2.SID numbers, sheets, and notebooks 3.Randomization logbooks 4.Eligibility checking program 5.Pharmacy checking program 6.Backup procedures 7.Training (local and for clinical sites)

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Controlled Onset Verapamil Investigation of Cardiovascular Endpoints (CONVINCE) Interactive Voice Response System (IVRS) –Touch-tone keypad used for data entry of key eligibility data –System verifies eligibility and assigns medication code (bottle number) –Caller re-enters medication code as a double-check –System also used for medication refills

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IVIG Trial Randomization

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Procedure summarizes data entered & asks you to re-enter weight

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If randomization is successful, 3 documents are available to save and print

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Treatment Prescription Double-check dose against your calculation on the Baseline CRF, and complete bottom portion

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Timing of Randomization Usual Sequence of Events 1.Verify eligibility, informed consent, and completeness of baseline data. 2.Obtain assignment. 3.Record assignment on log and case report forms. 4.Initiate treatment as soon as possible after randomization.

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No. randomized193200 2 weeks No. given treatment6993 Excluded:124107 Disease history8474 Rx contraindication1110 Dead1718 Other125 Alprenolol vs. Placebo in Post-MI Alprenolol Placebo Ahlmark, Eur J Pharmac, Vol. 10, 1976

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Non-Hodgkins Lymphoma Trial Induction and Maintenance Treatment for Non-Hodgkins Lymphoma Cytoxan-PrednisoneBCNU-Prednisone BCVP Chlorambucil Response No Response BCVP Chlorambucil Response No Response See Pocock, Clinical Trials: A Practical Approach, Page 72.

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Adjuvant Chemotherapy for Breast Cancer 1 year of chemotherapy 2 years of chemotherapy (A) Stop Continue 1 more year (B) Rivkin N, et al. J Clin Oncology, 11:1710-1716;1993. OR 1 year of chemotherapy

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Recommendations Make assignments close to the onset of treatment from a central source after checking eligibility Implement the randomization with a method that ensures allocation concealment Never deviate from the schedule Verify assignments

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Examples of Problems with Allocations Concealment Hypertension Detection and Follow-up Program (HDFP) – a single site (envelopes that were opened in advance) Heparin for acute MI (N Engl J Med 1960) – (envelopes not opaque or consecutively numbered) Captopril for hypertension (Lancet 1999) (large baseline differences indicating envelopes opened in advance)

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Documentation and Reporting of Randomization Methods Document methods for generating schedules, but do not share details with the investigators Describe allocation ratio and stratification variables in the protocol Report how randomization was done in the trial report

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Example: Strategies for Management of AntiRetroviral Therapy (SMART) Study Protocol: Eligible patients will be randomized in a 1:1 ratio to either the DC or VS group. Randomization will be stratified by clinical site. Randomization schedules will be constructed to ensure that approximately equal numbers of patients are assigned each treatment within clinical site. Trial Report (N Engl J Med 2006; 355:2283-96): Randomization was stratified by clinical site with the use of permuted blocks of random sizes.

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Reporting Example That Includes Method of Implementation: HIV Trial in South Africa (Phidisa II) Trial Report (JID 2010; 202:1529-1537): Randomization was stratified by site, using randomly mixed permuted blocks of different sizes. Assignments were obtained by calling a central toll-free number

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Outline of Randomization Lectures 1.Background and definitions 2.Generation of schedules 3.Implementation (to ensure allocation concealment, sometimes called blinded randomization) 4.Theory behind randomization

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Advantages of Randomization Bradford Hill: 1.Eliminates bias from treatment assignment 2.Balances known and unknown differences between groups on average 3.More credible study RA Fisher: 1.Assures validity of statistical tests (type 1 error)

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Fisher and the Validity of Statistical Tests (1) Randomization guarantees that statistical tests will have the valid significance levels. Even though groups may not be exactly balanced with respect to covariates, randomization permits a probability distribution to be determined for comparing treatments for outcomes of interest

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Fisher and the Validity of Statistical Tests (2) Randomization provides a basis for an assumption free statistical test of the equality of treatments – need to analyze your data taking into account the way the randomization schedule was prepared. Such tests are referred to as randomization tests or permutation tests

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Test of Significance at the End of a Trial Statistically Significant? YesNo Reject null hypothesis (H O ) Do not reject H O Sampling variation is an unlikely explanation for the discrepancy Sampling variation is a likely explanation for the discrepancy

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Relationship of Study Sample to Study Population and Population at Large Population at Large Population without Condition Population with Condition With Condition but Ineligible Study Population Eligible but not Enrolled Study Sample Source: Chapter 4, Friedman, Furberg and DeMets. Definition of Condition Entry Criteria Enrollment

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Population Model as a Basis for Statistical Testing Population A y ~ G(y | A ) Random Sample n A patients y Aj ~ G(y | A ) Population B y ~ G(y | B ) Random Sample n B patients y Bj ~ G(y | B )

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Example G is normal, i ~ N( i, 2 ) Students t-test is most powerful test for testing H o : A = B

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Invoked Population Model – Randomization Model Nonrandom Selection of Clinics in a Nonrandom Selection of Communities Undefined Sampling Procedure for Patients (a variety of sources are used) N = N A + N B patients Randomization N A patientsN B patients Source: Lachin J. Cont Clin Trials, 1988.

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Randomization Model Assumptions Under H O responses are assumed to be fixed (non- random) values – each patients response is what it would have been regardless of treatment A or B The observed difference between A and B only depends on the way treatments were assigned (independent of other patient characteristics) To assess whether observed difference is unusual, consider all possible ways patients could have been assigned A or B (permutation test) Under simple randomization, permutation test is asymptotically equal to homogenous population model.

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Randomization or Permutation Test 1.Calculate test statistic for sample data, e.g., A - B difference, t-statistic 2.Determine the number of possible randomization sequences 3.Enumerate all of these permutations; calculate the test statistic for each and their cumulative distribution 4.Determine where the test-statistic for sample lies on distribution of all possible values

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Example 3: Eight experimental units are randomly allocated to receive treatment A or B Treatment Group A B 189 1316 31717 n44 mean12.7514.75 (sd) 2 46.9214.92 pooled (sd) 2 30.92

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30.92 12.75 - 14.75 = -0.51, p = 0.628t(6) = 1414 1414 + t-statistic with 6 degrees of freedom

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The number of permutations using simple random allocation (1:1) of N A and N B assignments is given by: N A + N B N A ( ) N A = N B = 4 and number of permutations =70 = (N A + N B )!/ N A ! N B !

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Cumulative Distribution of t-statistic Obtained from Randomization and Students Distribution -2.481/70.014.024 -2.154/70.057.038 -1.885/70.071.055 -1.458/70.114.097 -1.2612/70.171.127 -1.0915/70.214.159 -.7818/70.257.233 -.6422/70.314.273 -.51*25/70.357*.314* -.2528/70.400.405 -.12532/70.457.452 0.038/70.543.500.12542/70.600.548.2545/70.643.595.5148/70.686.686.6452/70.743.727.7855/70.786.767 1.0958/70.828.841 1.2662/70.886.873 1.4565/70.928.901 1.8866/70.943.945 2.1569/70.986.962 2.4870/701.000.976 Cumulative Distribution RandomizationStudents t(6) t * * sample value, 2-sided p-value 50/70 = 0.71 versus 0.63

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Impact on P-value of Ignoring Blocking in the Analysis 1AA 2BD 3AD 4BD 5BD 6BD 7AD 8AA 9BD 10BD 11AA 12AA 13BD 14AA 15AA 16BD 17AA 18BA 19BA 20AA Simple Randomization of 20 Patients Treatment Outcome (Alive/Dead) Accession No. Fishers exact test p-value = 0.0115 (1-tailed) 8 2 2 8 A B Alive Dead

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8 2 2 8 A B Alive Dead P-value = Probability 2 or fewer of the 10 deaths were randomly allocated to A 9 1 1 9 A B AliveDead 10 0 0 A B Alive Dead or

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Fishers Exact Test P value= 10 2 10 8 20 10 10 1 10 9 20 10 10 0 10 20 10.01096.00054125.00000541 0.0115

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Restricted Randomization (block size = 4) 1AA 2BD 3AD 4BD 5BD 6BD 7AD 8AA 9BD 10BD 11AA 12AA 13BD 14AA 15AA 16BD 17AA 18BA 19BA 20AA Treatment Outcome (Alive/Dead) Accession No.

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1 1 0 2 A B Alive Dead Probability Block 1 1 1 0 2 A B Alive Dead Block 2 2 0 0 2 A B Alive Dead Block 3 2 0 0 2 A B Alive Dead Block 4 2 0 2 0 A B Alive Dead Block 5 1212 1212 1616 1616 1 p-value == 0.0069 1212 1212 1616 1616 1

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General Setup Based on hypergeometric distribution. A B r R - r Alive R n - r (N - R) – (n - r) Dead N - R n N - n N n N rn RN r R A)on alive Prob (r

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Randomization Theory Summary Guarantees control of type I error in hypothesis tests Permutation or randomization tests are motivated by the random assignment of patients The more restrictions imposed on the randomization, the harder it is to determine the permutation distribution. Permutation tests are not routinely used in the analysis of trials (conservative). Can be useful to consider blocking if population is heterogeneous over time.

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