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

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

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

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]

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)

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

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)

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

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

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

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

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

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 24 3715-3727. 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 31 103-115. 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 23 662-674. Taves, D. R. (1974). Minimization: a new method of assigning patients to treatment and control groups . Clinical pharmacology and therapeutics 15 443-453. Taves, D. R. (2010). The use of minimization in clinical trials. Contemporary Clinical Trials 31 180-184. 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 41 211-218.