1. Elaine M Pascoe, Darsy Darssan, Liza A Vergara
Use of minimization in multi-centre clinical trials - when to not add randomization
Elaine M Pascoe, Darsy Darssan, Liza A Vergara
Australasian Kidney Trials Network
The University of Queensland

2. Overview Covariate adaptive randomization Minimization example
Minimization issues
Simulation study
Results
Conclusions

3. Covariate adaptive randomization
Aim to balance treatments on prognostic factors
Prognostic factor imbalance
Potentially confounds estimate of treatment effect
Balance across treatments desirable for pre-specified sub-group analyses
Dynamic allocation
Minimization is a well-known example
Introduced by Taves (1974)
Generalization by Pocock & Simon (1975)
Achieves excellent prognostic factor and overall treatment balance

4. Minimization example – 3 factors
Treatments allocated: 50 patients
Next patient: 65 yrs, male, Site 1
Factor
Level
Treatment A
Treatment B
Age
<60 13 15
≥60 12 10
Gender
Female 5 6
Male 20 19
Centre
Site 1 2 4
Site 2
Site 3 11
Characteristics
Treatment A
Treatment B
Age ≥ 60 12 10
Gender = male 20 19
Centre = Site 1 2 4
Sums 34 33
Allocate Treatment B
[Update allocation look-up table]

5. Minimization – risk of selection bias
Potential predictability of next treatment allocation
Add/increase random component
ICH-E9 Statistical Principles for Clinical Trials (p. 10)
Methods
Add to each allocation (p<1.0 & p>0.5)
Increase the maximum tolerated imbalance (MTI)
Overgeneralized claims of risk
Double-blinded, multi-centre trials with central allocation of treatments (Pocock, 1983; Scott et al., 2002; Taves, 2010)

6. Consequences of more randomness
Overall treatment imbalance increases
Brown et al., 2005; Zhao et al., 2015
Prognostic factor, including study centre, imbalances increase
May promote less efficient use of resources in multi-centre trials
Increase need for medication re-supply
Increase in number of unused kits at sites

7. Simulations - context Multi-centre, two treatments
Sequential enrolment of 500 patients
28 sites of variable size
1x60 (12%), 7x25 (5%), 9x20 (4%), 6x10 (2%), 5x5 (1%)
Minimization variables: study site plus 3 binary prognostic factors
Central allocation system
Medication supply and re-supply
Ship 8 kits at start-up (4 of each treatment)
Re-supply 8 kits when there is only one remaining for at least one of the treatments
There will be at least 2 kits remaining at the site (1xA, 1xB)
There could be up to 5 kits (1xA,4xB or vice versa)

8. Simulations – scenarios & outcomes
9 allocation probabilities
p=0.6, 0.65, 0.7, 0.75, 0.80, 0.85, 0.90, 0.95, 1.0
4 maximum tolerated imbalance (MTI) levels:
0, 1, 2, 3
Simple random allocation (SRA) as reference point
37 scenarios
Outcomes
Overall number of low stock warnings (re-supplies)
Total number of unused kits at sites
Efficiency relative to stratification by site with permuted blocks

9. Simulations – technical details
1000 runs per scenario
Each patient had
Differential probability of belonging to each site: 1-12%
50/50 chance of belonging to each level of prognostic factor 1
45/55 chance of belonging to each level of prognostic factor 2
40/60 chance of belonging to each level of prognostic factor 3

10. Results - re-supplies Allocation probability MTI 0.60 0.65 0.70 0.75
0.80
0.85
0.90
0.95
1.00
Raw counts 68 67 66 65 64 63 62 1 2 69 3
Efficiency relative to stratification by site (52 re-supplies)
1.31
1.29
1.27
1.25
1.23
1.21
1.19
1.33
SRA: 70 (2.3), 1.33

11. Results – unused kits at sites
Allocation probability
MTI
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Raw counts
272
262
253
245
239
234
229
226
222 1
271
263
254
246
241
237
232 2
273
256
249
244
236
233
231 3
265
257
252
247
240
Efficiency relative to stratification by site (140 unused kits)
1.94
1.87
1.81
1.75
1.71
1.67
1.64
1.61
1.59
1.88
1.76
1.72
1.69
1.66
1.95
1.83
1.78
1.74
1.65
1.89
1.84
1.8
SRA: 285 (18), 2.07

12. Conclusions Adding a random component to minimisation
Increases overall treatment imbalance
Increases prognostic factor imbalance across treatments
Increases requirement for medication re-supply
Increases unused stock at sites
When to not add randomization?
Selection bias is highly unlikely & resources are scarce
Not necessary for double-blinded multi-centre trials with central allocation of treatments
Early days re: operational/logistical perspective
Perhaps not the right (or best) question

13. References
Brown, S., Thorpe, H., Hawkins, K., and Brown J. (2005). Minimization – reducing predictability for multi-centre trials whilst retaining balance within centre. Statistics in Medicine ICH E9 Expert Working Group (1999). Harmonised Tripartite Guideline: Statistical principles for clinical trials. Pocock, S. J. (1983). Clinical Trials: A Practical Perspective. Wiley: New York Pocock, S. J. and Simon, R. (1975). Sequential treatment assignment with balancing for prognostic factors in controlled clinical trials. Biometrics Scott, N. W., McPherson, G. C., Ramsay, C. R. and Campbell, M. K. (2002). The method of minimization for allocation to clinical trials: a review. Controlled Clinical Trials Taves, D. R. (1974). Minimization: a new method of assigning patients to treatment and control groups . Clinical pharmacology and therapeutics Taves, D. R. (2010). The use of minimization in clinical trials. Contemporary Clinical Trials Zhao, W., Mu, Y., Tayama, D., and Yeatts, S. D. (2015). Comparison of statistical and operational properties of subject randomization procedures for large multicentre clinical trial treating medical emergencies. Contemporary Clinical Trials