Adaptive randomization S. Balakrishnan Pondicherry Institute of Medical Sciences Clinical Trial Protocol Writing II- Sample Size Calculation & Randomization
Randomization
Randomization Definition: randomization is a process by which each participant has the same chance of being assigned to either intervention or control.
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.
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.
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.
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
Randomization Types Simple randomization Clinical Trial Protocol Writing II- Sample Size Calculation & Randomization
Simple randomization Random numbers: Treatment – A & B = 20 Patients 2 5 7 1 8 9 4 A B
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.
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
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.
Randomization Types Blocked randomization Clinical Trial Protocol Writing II- Sample Size Calculation & Randomization
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.
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.
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.
Randomization Types Stratified randomization geographic location previous exposure geographic location site Clinical Trial Protocol Writing II- Sample Size Calculation & Randomization
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.
Table 3. Stratification Factors and Levels (323=18 Strata)
Table 4 Stratified Randomization with Block Size of Four
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.
Disadvantages The prognostic factor used in stratified randomization may be unimportant and other factors may be identified later are of more importance
Mechanism
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)
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.
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.
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.”
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
Adaptive Designs
Adaptive Randomization Number adaptive Biased coin method Baseline adaptive (MINIMIZATION) Outcome adaptive
Biased Coin Method Advantages Investigators can not determine the next assignment by discovery the blocking factor. Disadvantages Complexity in use Statistical analysis cumbersome
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
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)
Minimization Factors
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
Table 3 Calculation of imbalance in patient characteristics Table 3 Calculation of imbalance in patient characteristics for allocating treatment to the thirtieth patient
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
Disadvantages It is a bit complicated process compare to the simple randomization
Practical Considerations
ADAPTIVE (DYNAMIC) RANDOMIZATION
BALANCING (COVARIATE) ADAPTIVE RANDOMIZATION
URN RANDOMIZATION
EFRON’S WEIGHTED COINE
RESPONSE (OUTCOME) ADAPTIVE RANDOMIZATION
PLAY THE WINNER
DROP THE LOSER
DOUBLY ADAPTIVE BIASED COINS
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