Outline of Randomization Lectures

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

2. Readings • Chapter 6 of Friedman, Furberg and DeMets • Supplemental notes for week 3 on the class web site • Other papers are cited in the notes

3. Key Points • A random process should be used to generate treatment allocations or assignments • Treatment allocations should be concealed until the time of randomization – “allocation concealment” is critical to prevent selection bias. Some refer to this as “blinded randomization”. (It should not be confused with blinding of treatments).

4. Randomization Assignment of experimental units to treatment by a random process such that neither investigator nor patient knows the treatment to be assigned at the time the patient is registered.

5. Timing of Randomized Trials - Considerations • 1st patient (Chalmers) • Strong degree of equipoise (collective and individual uncertainty) exists • Feasibility and timing See Freedman B N Engl J Med 1987.

6. 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)

7. Comparable GroupsESPRIT Study: Baseline Characteristics(N Engl J Med 2009; 361: 1548-59)

8. Steps in Patient (Study Participant) Registration (Randomization) 1. Patient requires treatment (participants screened for risk factor eligibility) 2. Patient (participant) eligible for inclusion in trial 3. Clinician willing to randomize patient (participant) 4. Patient (participant) is willing to be randomized (consent is obtained) 5. Patient (participant) formally entered in the trial • Treatment assignment obtained from randomization list (schedule) • Case-report and other records completed to document randomization 6. Treatment commences as soon as possible

9. Usual Sequence of Events in a Randomized Clinical Trial Not eligible Determine eligibility+ Obtain informed consent yes no Eligible randomize + In many trials consent must also be obtained for screening. B A follow-up

10. Key Elementsof Informed Consent • A fair explanation of the procedures to be followed, and their purposes, including identification of any procedures which are experimental • A description of any participant discomforts and risks reasonably to be expected • A description of any benefits to the subject or to others which may be expected • A disclosure of any appropriate alternative procedures that might be advantageous for the subject

11. Key Elementsof Informed Consent (cont.) • An offer to answer any inquiries concerning the procedures • Instructions to a subject concerning the freedom to withdraw his/her consent and to discontinue participation in the project or activity at any time without prejudice or explanation (this should be balanced by a statement that emphasizes participation until the end of the study to preserve integrity of research question) • Reasons study may be stopped • An explanation as to whether compensation and medical treatment are available if physical injury occurs and, if so, what it consists of or where further information may be obtained • A statement describing the extent, if any, to which confidentiality of records identifying the subject will be maintained • A commitment to share new findings that emerge. See also Chapter 2 of Friedman, Furberg and DeMets

12. Informed Consent (cont.) • Length of sample informed consents: • ESPRIT (8 pages) (experimental treatment: interleukin-2) • SMART (12 pages) (treatment strategy trial using approved drugs) • START (14 pages) (treatment strategy trial using approved drugs) • MRFIT (1 page) • Comprehension (when assessed) by participants is low on key items suggesting simpler, not longer, forms may be better. • Separate consent documents for stored specimens and substudies • Multiple reviews of consent: Institutional Review Board (IRB), Ethics Committee and sponsor

14. Bad Allocation Schemes 1. Ward 1 receives Drug A; ward 2, Drug B 2. M, T, W - Drug A TH, F - Drug B 3. Every other patient receives A 4. Drug A on odd days 5. Drug A to patients born Jan. - Jun.; Drug B, Jul. - Dec. AVOID SYSTEMATIC ALLOCATION

15. The Unit of Randomization is Not Always the Individual Study Participant • Right and left eye • Kidneys from deceased donors • Clusters of participants • Clinical sites (e.g., interventions aimed at adherence, informed consent, counseling to avoid high risk behaviors) • Households • Schools • Communities

16. Cluster Randomization J Acquir Immune Defic Syndr 2006; 43 (Suppl):S41-S47 38 clusters of clinical sites Randomized MedicationManager + Electronicreminder(N = 9) MedicationManager Alone(N = 10) Electronicreminder Alone(N = 10) Control(N = 9) • 200-250 patients/cluster • Embedded in treatment trial

17. Cluster Randomized Study of Short Versus Standard (Long) Consent Form 100+ clusters of clinical sites Randomized Short consent form(N = 800) Long consent form ( N=800) • 15-20 patients/cluster • Embedded in START study A similar design is being used to study of on-site monitoring: research on research!

18. Cluster Randomization Considerations • It is important that the unit of randomization be taken into account both in the design and analysis (e.g., matched pairs). • Like randomization of individual participants, allocation concealment (blinded randomization) is important. • Observations/measurements on different participants within clusters cannot be considered independent. • It is important to account for all members of the cluster in the analysis (clusters are randomized but measurements are usually on individuals). • The between-group (cluster) variability has to be accounted for in the analysis.

19. Example: Possible Biasin Treatment Assignment Distribution of Prognostic Variables According to Treatment Assignment Blinded randomization 57 14.0 Unblinded 45 26.7 randomization Non-random assignment 43 58.1 or historical controls At Least One Variable Maldistributed* (%) No. Studies * p<.05 Source: Chalmers et al., NEJM, 1983.

20. Treatment Resultsby Type of Assignment Blinded randomization 8.8 0.003 ± 0.008 Unblinded 24.4 0.052 ± 0.016 randomization Nonrandom assignment 58.1 0.105 ± 0.017 or historical controls Average Treatment Difference (Case-Fatality Rate) Percent p<0.05 Source: Chalmers et al., NEJM, 1983.

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

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

23. Categorization of Randomization Schemes 1. Fixed Allocation a. Simple randomization b. Permuted block (restricted) c. Permuted blocks of different sizes randomly mixed (restricted) 2. Adaptive Allocation Methods Treatments are assigned with probabilities which change during the course of the trial a. Baseline adaptive procedure b. Response adaptive

24. Simple Randomization The number and order of patients receiving treatments A and B is determined by chance. Example: Equal allocation • Toss a coin: A = head, B = tails • Random number table: A = odd, B = even (see next slide taken from Pocock, page 74) • Uniform random number generator (equally probable numbers between 0.0 and 1.0): A if < 0.5 B if > 0.5

26. TreatmentRandom Numbers Aspirin 1,2,3,4,5,6 No Aspirin 7,8,9 Don’t Use 0 Example: Non-uniform treatment allocation British Aspirin Study 2 treatments with allocation ratio 2:1 (Aspirin:no Aspirin) Source: Br Med J, 296:313-16, 1988.

27. Could result in loss of power and logistical problems Disadvantage of Simple Randomization • Chance imbalance in numbers assigned to each treatment • At end of study • At periodic looks

28. Probability of Specified Treatment Allocations Using Simple Randomization(10 Patients) 0 (10) 10 (0) 0.002 1 (9) 9 (1) 0.02 2 (8) 8 (2) 0.09 3 (7) 7 (3) 0.23 4 (6) 6 (4) 0.41 5 5 0.25 Binomial Probability Treatment A Treatment B

29. Binomial Probability

30. Difference in Numbers or More Extreme Total Number of Patients 10 2: 8 1: 9 20 6: 14 4: 16 50 18: 32 16: 34 100 40: 60 37: 63 200 86: 114 82: 118 500 228: 272 221: 279 1000 469: 531 459: 541 Prob. ≥ 0.01 Prob. ≥ 0.05

31. To find N to obtain allocation ratio which results in a Prob ≥ 0.05

32. For large sample sizes can use normal approximation

33. H0 : µA = µ B HA : µA ≠ µB ; µA - µB =  N = NA + NB and r = NA / N Loss of Power Due to Chance Imbalance Comparison of 2 Means 0.5 0.90 0.6 0.88 0.7 0.84 0.8 0.74 0.9 0.49   Z 1- = - Z 1 + 11/2 NA NB 1-/2   Z 1- = - Z 1 1/2 Nr (1-r) 1-/2 r Power

34. 1. Fixed Allocation Methods Treatments are assigned with a pre-specified probability A. Simple randomization B. Permuted blocks C. Permuted blocks randomly mixed { Restricted

35. Permuted Block Randomization 1) Divide patients into blocks of equal size according to time they enter the study 2) Choose a block size • Write down all possible permutations • Randomly choose one

36. Advantages of Permuted Block Randomization 1. Forces balance at end of study and during patient accession 2. Reduces the likelihood of bias due to changing patient characteristics during course of study 3. Facilitates planning with regard to treatment administration (resource planning)

37. Disadvantages 1. If investigators become aware of block size, some assignments are known within certainty, e.g., block size 4: A A The next assignments have to be B 2. From a theoretical point of view, analysis more cumbersome (more on this later)

38. Example: Permuted Block Randomization: Block Size = 4 Write down the 6 possible different sequences of 2As and 2Bs and randomly choose one for the 1st 4 patients, next 4, etc. 1 2 3 4 5 6 A B A B A B A B B A B A B A A B B A B A B A A B

39. Unequal Allocation To determine block size, consider the sum of the integers which define the allocation ratio: Example: Mt. Sinai Hypertension Trial (MSHT); 3 treatment groups (K+, placebo, control) randomized 2:2:1 Use block size of 5 or multiples of 5 1. Generate all possible arrangements of numbers 1-5 2. Choose one at random 3. 1,2 = A; 3,4 = B; 5 = C 4. Repeat steps 2 and 3 as often as necessary

40. Randomly Mixed Permuted Blocks A solution to the problem of easily guessing future assignments (particularly important in non-blind trials. Example: The Multiple Risk Factor Intervention Trial (MRFIT) used randomly mixed block sizes of 2, 4 and 6.

41. Mixing Blocks of Sizes 2 and 4 Block Size 2 4 Permutations 1 AB AABB 2 BA BBAA 3 – ABAB 4 – BABA 5 – ABBA 6 – BAAB Two Step Procedure 1. Randomly choose block size 2. Randomly choose permutation within block size

42. Computer Program for Generating Random Permuted Blocks of Different Size 1. Set number of treatments. 2. Set number of stratum. 3. Set block sizes to be used considering allocation ratio. 4. Randomly choose a block size (K). 5. Generate K uniform random numbers.

43. Computer Program for Generating Random Permuted Blocks of Different Size (cont.) 6. Order the random numbers carrying along the original index (1-K). 7. Associate treatment codes with ordered index array. 8. Print the K random assignments. 9. Go to Step 4 and continue until desired number of allocations have been generated.

45. Other Variations • Mix block sizes with different probabilities. For example, • Flip a coin for 1st assignment and mix block sizes afterwards • Use a large block size initially (e.g., >8) and then smaller block sizes (e.g., mix 2, 4, and 6) Block sizeProb 2 1/4 4 1/4 6 1/2

46. Baseline Adaptive Randomization Procedure Def.: The probability of the next treatment assignment is altered on the basis of the previous assignments in order to achieve better balance (biased coin). • Considerations: • 1. Implementation (central) • Multiple treatments • Definition of lack of balance

47. Let D = No. of patients assigned to A - No. assigned to B D = 0 Simple randomization (P = 1/2) D > 0 Assign to B with prob. (P) > 1/2 D < 0 Assign to B with prob. (1 - P) < 1/2 What should P be set equal to? Note P = 1 corresponds to permuted blocks of size 2.

48. Example Baseline Adaptive Randomization • 20 patients are to be randomized, 1:1 allocation. After 10 patients, we have: • 5A and 5B (D=0): use schedule with 1:1 allocation (e.g., created with simple randomization) • A is assigned • 6A and 5B (D=1): use schedule with Prob (B) = 2/3 (could also be created with simple randomization) • B is assigned • 6A and 6B (D=0): continue as above This could be implemented by preparing 3 schedules in advance: 1) 1:1 allocation; 2) 2:1 allocation favoring B; and 3) 1:2 allocation Favoring A. All could be prepared with simple randomization.

49. Suppose there are k treatments: 1) Rank treatments according to number of patients (fewest to largest); 2) Assign next patient with probability

50. Response AdaptiveRandomization The probability of the next treatment assignment is altered on the basis of the responses of previous patients enrolled. Motivation: More patients receive the “best” treatment Rosenberger, Cont Clinical Trials, 1999;20:328-342.