1. The 4th ICTMC & 38th Annual Meeting of SCT
Numerical Evaluation for Optimal Selection of Randomization Methods in Clinical Trials
Mi Z. , Horney RA, Stock EM and Biswas K.  
VA Cooperative Studies Program Coordinating Center,
Perry Point/Baltimore, MD 21902

2. Clinical Trial Schema To study a treatment efficacy on certain disease
Every individual with the disease (N)
Intended Target Population
Patients from participating centers during certain time
Those who are interested in participating in the trial
Unspecified Sampling Procedure
Filtering
Those who meet inclusion/exclusion criteria
Unspecified Target Population
Those who consent to participate the trial
Targeted trial subjects
( Sample size = n)
Not A Random Sample
Randomization
Only Random Mechanism
Treatment
( nT )
Placebo
( nP )
Foundation of Causal Inferences
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The 4th ICTMC & 38th Annual Meeting of SCT

3. Baseline Characteristics
Why Randomization
Introduces random mechanism to treatment allocation
Avoids selection bias to treatment allocation
Balances known/unknown baseline/confounding factors between treatment arms
Allows to assess treatment attributable efficacy
Baseline Characteristics
Category
Intervention
p- value
Treatment
Placebo
Total
Prognostic factor 1
Yes
nT(F1)
nP(F1)
nF1 c1 No
nT(No F1)
nP(No F1)
nNo F1
Prognostic factor 2
nT(F2)
nP(F2)
nF2 c2
nT(No F2)
nP(No F2)
nNo F2
Participating Sites 1
nT(S1)
nP(S1)
nS1 c3 2
nT(S2)
nP(S2)
nS2 3
nT(S3)
nP(S3)
nS3 4
nT(S4)
nP(S4)
nS4 …
...
Other factors
nT(OT)
nP(OT)
nOT c4
nT(No OT)
nP(No OT)
nNo OT
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The 4th ICTMC & 38th Annual Meeting of SCT

4. The 4th ICTMC & 38th Annual Meeting of SCT
Commonly Randomization Methods
Simple Randomization
Restricted Randomizations
* Static Randomizations
- Permuted Block Randomization (Fixed/Random Blocks)
- Stratified Block Randomization
* Dynamic Randomizations (Adaptive)
- Covariate-adaptive Allocation (Minimization)
- Response-adaptive Allocation
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The 4th ICTMC & 38th Annual Meeting of SCT

5. The 4th ICTMC & 38th Annual Meeting of SCT
Rationale
When design a clinical trial, one task is to select an appropriate randomization method based on
Sample size
Treatment allocation ratio
Prognostic factors need to be controlled
Number of participating sites
Conditions
Random (no specific pattern with known probability)
Balanced
Unpredictable
Easy to Implement
Considerations
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The 4th ICTMC & 38th Annual Meeting of SCT

6. The 4th ICTMC & 38th Annual Meeting of SCT
Goal
To evaluate randomization performance by simulations
Simple Randomization
Random Permuted Block Randomization
Stratified Randomized Block Randomization
Covariate-adaptive Allocation (Minimization)
- Deterministic
- 15% rule
- 1/3 rule
- Probability based on Imbalance score
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The 4th ICTMC & 38th Annual Meeting of SCT

7. The 4th ICTMC & 38th Annual Meeting of SCT
Simulation Methods
Parameters
Treatment Arms
Two arms – Allocation 1:1
Participating Sites
5 ( 5 ~ 20, by 5)
Prognostic Factors
Two level-two factors: Factor 1 (0.5/0.5); Factor 2 (0.3/0.7)
Sample Size
100~2000 (by 100)
Simulation Replicates
10, 000 Times
Algorithms
Simple Randomization
Randomly assign all subjects in each treatment arms based on a probability 0.5
Permuted Blocks
Generate random permuted blocks (2 and 4, 4 and 6) for each treatment arm assignment
Stratified Blocks
Stratify prognostic factors and sites, then within each stratum generate random permuted blocks for treatment assignment
Adaptive (Minimization)
Balance treatment arms simultaneously over prognostic factors and sites (marginal balances based on varied conditional probability over time )
Metrics
Imbalance
Marginal difference between treatment arms of each controlling factors divided by sample size
Average of P-values
Based on Person 2 test
Significance of Imbalance
Based on p-value < 0.05
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The 4th ICTMC & 38th Annual Meeting of SCT

8. The 4th ICTMC & 38th Annual Meeting of SCT
Imbalance of Four Randomization Methods
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The 4th ICTMC & 38th Annual Meeting of SCT

9. The 4th ICTMC & 38th Annual Meeting of SCT
Imbalance of Minimization Methods
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The 4th ICTMC & 38th Annual Meeting of SCT

10. The 4th ICTMC & 38th Annual Meeting of SCT
Average P-Values
Four Randomization Methods
Minimization Methods
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The 4th ICTMC & 38th Annual Meeting of SCT

11. The 4th ICTMC & 38th Annual Meeting of SCT
Significance of Imbalance
Four Randomization Methods
Minimization Methods
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The 4th ICTMC & 38th Annual Meeting of SCT

12. The 4th ICTMC & 38th Annual Meeting of SCT
Example
Sample size = 1520;
Two treatment arms 1:1 ratio
Sites = 15
Covariate = four category ( I = 15%, II = 35%, III = 30%, IV = 20%)
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The 4th ICTMC & 38th Annual Meeting of SCT

13. The 4th ICTMC & 38th Annual Meeting of SCT
Summary
Imbalance decreases when sample size increases (plateau ~ 600)
Stratified permuted blocks and minimization methods with lower imbalance
(Imbalance: Stratified < Minimization < Permuted blocks < Simple)
Minimization methods performs better when strata cells are sparse
(Imbalance: Deterministic < 15% rule < 1/3 rule < Imbalance Score)
Imbalance is consistent with p-values and proportion of significance (p<0.05)
Tables and programs are available
Contact :
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The 4th ICTMC & 38th Annual Meeting of SCT

14. The 4th ICTMC & 38th Annual Meeting of SCT
Disclaimer
The views expressed in this report are those of the authors and do not necessarily reflect the position or policy of the U.S. Department of Veterans Affairs or the United States Government.
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The 4th ICTMC & 38th Annual Meeting of SCT

15. The 4th ICTMC & 38th Annual Meeting of SCT
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