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

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 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

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 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

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 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

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 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

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 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

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 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

The 4th ICTMC & 38th Annual Meeting of SCT Imbalance of Four Randomization Methods 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

The 4th ICTMC & 38th Annual Meeting of SCT Imbalance of Minimization Methods 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

The 4th ICTMC & 38th Annual Meeting of SCT Average P-Values Four Randomization Methods Minimization Methods 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

The 4th ICTMC & 38th Annual Meeting of SCT Significance of Imbalance Four Randomization Methods Minimization Methods 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

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%) 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

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 : Zhibao.Mi@va.gov Eileen.Stock@va.gov 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

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. 9/20/2018 The 4th ICTMC & 38th Annual Meeting of SCT

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