Ofner, IMI Determining the Parameter Settings of Different Randomization Methods for Specific Study Designs Petra Ofner-Kopeinig, Maximilian Errath and Andrea Berghold Institute for Medical Informatics, Statistics and Documentation Medical University of Graz, Austria

Ofner, IMI Motivating Example 200 patients to be included into the study Stratified by –Gender (male, female) –Treatment history (past, recent, none) Which randomization method should be used?

Ofner, IMI Randomization Methods Complete randomization Biased Coin (Efron) Big Stick (Soares & Wu) Minimization (Taves; Pocock & Simon) Urn Design (Wei) Permuted Block Randomization (Matts & Lachin) …

Ofner, IMI Randomization Methods Allocation of treatment at random Achieve treatment group balance Potential for Selection Bias

Ofner, IMI Choice of Randomization Method Smallest treatment imbalance at the end of the study Maximum imbalance ever achieved over the course of the study Compare different parameter settings of the methods

Ofner, IMI Definition of Imbalance Two treatment groups: relative frequency of the absolute differences between groups Different treatment group sizes: differences between expected and observed frequencies More than 2 treatment groups: maximum of differences between expected and observed frequencies

Ofner, IMI Randomizer – Simulation Tool Developed at the Institute for Medical Informatics, Statistics and Documentation, Medical University Graz Web based software for randomization of multi- center clinical trials Trial Management

Ofner, IMI Simulation tool The simulation tool can be used for: Generation of static randomization lists Validation –FDA-Guidelines –GCP-compliant  AGES Pharmed Simulation of different study designs

Ofner, IMI Simulation tool

Ofner, IMI Simulations Complete randomization Urn design with different parameters –Ud011 (initial urn = 0, with replacement, balls to add = 1) –Ud002 (initial urn = 0, without replacem balls to add = 2) Permuted block randomization with different block lengths –Pb6 (block length = 6) –Pb20 (block length = 20) 1000 Trials

Ofner, IMI Complete Randomization Balance behaviour can not be controlled in any way Big differences between treatment groups are possible Stratified Randomization: Randomization is done within subgroups, that means for small patient numbers

Ofner, IMI Urn Design (1) Generalization of the Biased Coin Method. UD ( ,  ), with or without replacement –  = initial urn –  = balls to add Inital urn contains for 2 treatments  white und  red balls. Drawing a red ball means allocation of treatment X, drawing a white ball allocation of treatment Y. After each drawing the ball is replaced to the urn or not and  balls of the opposite colour are added to the urn. For each randomization step this procedure is repeaded.  > 0;  = 0  corresponds to complete randomization

Ofner, IMI Urn Design (2)  = 0,  > 0: no difference in imbalance for any   /   0: ud approaches cr  /    : urn randomization preserves balance within small strata

Ofner, IMI Permuted Block Randomization M blocks containing m = n/M patients M and n/M are positive integers Within block i, m/2 patients are assigned to treatment A, m/2 patients are assigned to treatment B Randomization is performed within blocks Maximum imbalance m/2 Randomizer: length of blocks must be a multiple of the number of treatments

Ofner, IMI Example patients -Patients are stratified by gender (male, female) and their treatment history (none, past, recent) -Distribution of factors is not known, we expect a uniform distribution

Ofner, IMI Simulated Means and Variances of the Treatment Group Imbalance at study end MethodMeanVariance Cr,5005,0076 Pb6,5002,0004 Pb20,5000,0010 Ud011,5006,0025 Ud002,5003,0010

Ofner, IMI Example patients -Patients are stratified by gender (male, female) and their treatment history (none, past, recent) -Distribution of strata is known Treatment history nonepastrecent GenderFemale Male

Ofner, IMI Simulated Means and Variances of the Treatment Group Imbalance MethodMeanVariance Cr,5025,0138 Pb6,5011,0023 Pb20,5007,0066 Ud011,4997,0050 Ud002,4998,0022

Ofner, IMI

Summary Effects of imbalances on power are small unless imbalance is considered substantial (0.6 or 0.7 to one of the two groups) For trials with n > 200 substantial treatment imbalances are unlikely with complete randomization or urn design. Stratified block randomization: can result in treatment imbalances in the trial due to incomplete blocks in some strata. Urn design: balls to add / initial urn determines to what degree balance is enforced Multicenter studies

Ofner, IMI References Efron, B., Forcing a sequential experiment to be balanced, Biometrika 57: , 1971 Lachin J.M., Statistical Properties of Randomization in Clinical Trials, Controlled Clinical Trials 9: (1988)) Lachin, J.M., Properties of Simple Randomization in Clinical Trials, Controlled Clinical Trials 9: , 1988 Matts, J.P., Lachin, J.M., Properties of Permuted-Block Randomization in Clinical Trials, Controlled Clinical Trials 9: , 1988 Wei, L.J., Lachin, J.M., Properties of the Urn Randomization in Clinical Trials, Controlled Clinical Trials 9: , 1988 Taves, D.R., Minimization: a new method of assigning patients to treatment and control groups, Clinical Pharmacol. Ther. 15: , 1974 Pocock, S.J., Simon, R., Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial, Biometrics 31, , 1975 Soares, J.F., Wu, C.F.J., Some Restricted Randomization Rules in Sequential Designs, Communications in Statistics: Theory and Methods 17, , 1983 …

Ofner, IMI