1. Adaptive randomization
S. Balakrishnan
Pondicherry Institute of Medical Sciences
Clinical Trial Protocol Writing II- Sample Size Calculation & Randomization

2. Randomization

3. Randomization Definition:
randomization is a process by which each participant has the same chance of being assigned to either intervention or control.

4. Fundamental Point
Randomization trends to produce study groups comparable with respect to known and unknown risk factors, removes investigator bias in the allocation of participants, and guarantees that statistical tests will have valid significance levels.

5. Randomization: Types:
Complete (Simple): equal allocation
Restricted: When equal number of patients required in each treatment group
Covariate adaptive: Similar number of patients in each treatment group
– Patients groups similar with respect to prognostic factors.
Response adaptive randomization: treatment assignments depend upon previous patients response to treatment.

6. Two Types of Bias in Randomization
Selection bias
occurs if the allocation process is predictable. If any bias exists as to what treatment particular types of participants should receive, then a selection bias might occur.
Accidental bias
can arise if the randomization procedure does not achieve balance on risk factors or prognostic covariates especially in small studies.

7. Fixed Allocation Randomization
Fixed allocation randomization procedures assign the intervention to participants with a pre-specified probability, usually equal, and that allocation probability is not altered as the study processes
Simple randomization
Blocked randomization
Stratified randomization

8. Randomization Types Simple randomization
Clinical Trial Protocol Writing II- Sample Size Calculation & Randomization

9. Simple randomization Random numbers: Treatment – A & B = 20 Patients2 5 7 1 8 9 4 A B

10. Simple Randomization
Option 1: to toss an unbiased coin for a randomized trial with two treatment (call them A and B)
Option 2: to use a random digit table. A randomization list may be generated by using the digits, one per treatment assignment, starting with the top row and working downwards:
Option 3: to use a random number-producing algorithm, available on most digital computer systems.

11. Advantages
Each treatment assignment is completely unpredictable, and probability theory guarantees that in the long run the numbers of patients on each treatment will not be radically different and easy to implement

12. Disadvantages Unequal groups
one treatment is assigned more often than another
Time imbalance or chronological bias
One treatment is given with greater frequency at the beginning of a trial and another with greater frequency at the end of the trial.
Simple randomization is not often used, even for large studies.

13. Randomization Types Blocked randomization
Clinical Trial Protocol Writing II- Sample Size Calculation & Randomization

14. Blocked Randomization (permuted block randomization)
Blocked randomization is to ensure exactly equal treatment numbers at certain equally spaced point in the sequence of patients assignments
A table of random permutations is used containing, in random order, all possible combinations (permutations) of a small series of figures.
Block size: 6,8,10,16,20.

15. Advantages
The balance between the number of participants in each group is guaranteed during the course of randomization. The number in each group will never differ by more than b/2 when b is the length of the block.

16. Disadvantages Analysis may be more complicated (in theory)
Correct analysis could have bigger power
Changing block size can avoid the randomization to be predictable
Mid-block inequality might occur if the interim analysis is intended.

17. Randomization Types Stratified randomization geographic location
previous exposure
geographic location
site
Clinical Trial Protocol Writing II- Sample Size Calculation & Randomization

18. Stratified Randomization
Stratified randomization process involves measuring the level of the selected factors for participants, determining to which stratum each belongs, and performing the randomization within the stratum. Within each stratum, the randomization process itself could be simple randomization, but in practice most clinical trials use some blocked randomization strategy.

19. Table 3. Stratification Factors and Levels (323=18 Strata)

20. Table 4 Stratified Randomization with Block Size of Four

21. Advantages
To make two study groups appear comparable with regard to specified factors, the power of the study can be increased by taking the stratification into account in the analysis.

22. Disadvantages
The prognostic factor used in stratified randomization may be unimportant and other factors may be identified later are of more importance

23. Mechanism

24. An Example of Stratified Randomization
Patients will be stratified according to the following criteria:
1) Treatment center (Hospital A vs Hospital B vs Hospital C)
2) N-stage(N2 vs N3)
3) T-stage (T1-2 vs T3-4)

25. What should be in the protocol?
A dynamic allocation scheme will be used to randomize patients in equal proportions within each of 12 strata. The scheme first creates time-ordered blocks of size divisible by three and then uses simple randomization to divide the patients in each block into three treatment arms, in equal proportion. The block sizes will be chosen randomly so that each block contains either 6 or 9 patients.

26. Cont…
This procedure helps to ensure both randomness and investigator blinding (the block sizes are known only to the statistician), as recommended by Freedman et al. Randomization will be generated by the consulting statistician in sealed envelopes, labeled by stratum, which will be unsealed after patient registration.

27. Adaptive designs
“An adaptive design is a CT design that uses accumulating data to decide how to modify aspects of the study after its initiation without undermining the trial’s validity and integrity.”

28. Adaptive designs:
Balancing based upon probabilistic baseline covariate adaptive randomization
Combining phases I & II.
Dropping a treatment arm
Modifying the sample size
Stopping early—success / failure

29. Adaptive Designs

33. Adaptive Randomization
Number adaptive
Biased coin method
Baseline adaptive (MINIMIZATION)
Outcome adaptive

34. Biased Coin Method Advantages
Investigators can not determine the next assignment by discovery the blocking factor.
Disadvantages
Complexity in use
Statistical analysis cumbersome

35. Minimization
Minimization is an well -accepted statistical method to limit imbalance in relative small randomized clinical trials in conditions with known important prognostic baseline characteristics.
It called minimization because imbalance in the distribution of prognostic factors are minimized

36. Table 1 Some baseline characteristics of patients in a controlled
Table 1 Some baseline characteristics of patients in a controlled trial of mustine versus talc in the control of pleural effusions in patients with breast cancer (Frientiman et al, 1983)

37. Minimization Factors

38. Table 2 Characteristics of the first 29 patients in a clinical
Table 2 Characteristics of the first 29 patients in a clinical trial using minimization to allocate treatment

39. Table 3 Calculation of imbalance in patient characteristics
Table Calculation of imbalance in patient characteristics for allocating treatment to the thirtieth patient

40. Advantages
It can reduce the imbalance into the minimum level especially in small trial
Computer Program available (called Mini) and also not difficult to perform ‘by hand’
Minimization and stratification on the same prognostic factors produce similar levels of power, but minimization may add slightly more power if stratification does not include all of the covariance

41. Disadvantages
It is a bit complicated process compare to the simple randomization

42. Practical Considerations

43. ADAPTIVE (DYNAMIC) RANDOMIZATION

44. BALANCING (COVARIATE) ADAPTIVE RANDOMIZATION

45. URN RANDOMIZATION

46. EFRON’S WEIGHTED COINE

47. RESPONSE (OUTCOME) ADAPTIVE RANDOMIZATION

48. PLAY THE WINNER

49. DROP THE LOSER

50. DOUBLY ADAPTIVE BIASED COINS

51. Example of How Minimization Works Using Hypothetical trial Data
Prognostic Factor
Intervention
Control
Sex
Male 4 3
Female 1 2
Age group
< 40
40 – 60
> 60
Previous surgery
Yes No