Dynamic Central Randomization

Randomization and the management of trial supplies is a critical factor in clinical research. In this white paper we review several major randomization approaches currently used in clinical trials. We also describe the dynamic central randomization (DCR) method that was defined, tested and implemented as part of Fountayn’s eClinical solution. The new method was designed to achieve balance at the study level and the site (center) level as well. Different from other randomization methods, DCR takes into account the inventory conditions and supply management to reduce the waste of drugs and minimize the shipment cost. After simulation testing DCR was implemented and demonstrated that the DCR method performed as planned achieving site and center balance and resulting in a significant savings of study costs by maximizing the use of available study trial supplies.

Introduction

Randomization is a procedure used in clinical trials to manage the allocation of supplies to individual subjects. Fundamental to its design is that participants are allocated to treatment and control groups at random, thereby minimizing selection bias and maximizing the precision of treatment effect estimates. The aim of randomization is to produce comparable groups and provide a basis for an assumption-free statistical test of the equality of treatments.

The definition of some terms used here along with other commonly used ones in clinical trials can be found in [7]

Randomization Methods

The randomization methods widely used in clinical trials commonly conducted today can be classified into two main approaches: static randomization and dynamic randomization.

Static Randomization

Permuted Block Randomization

Stratified Randomization

Simple Randomization

Stratified Permuted Block Randomization

Zelen’s Balanced Block Randomization [4]

Dynamic Randomization

Um Randomization

Minimization

Response-Adaptive Allocation

Static Randomization

1. SIMPLE RANDOMIZATION is the most basic method of random treatment assignment. It can be thought of as tossing a coin for each trial participant, A being allocated with “heads”, B with “tails”. However, it is not usually performed using a real coin-toss, as issues of concealment, validation and reproducibility arise. Simple randomization is usually implemented using a sequence of random numbers typically from a computer-generated sequence. In a large trial (at least 1000 subjects), simple randomization provides balance in the number of patients allocated to each treatment group in the trial, however for smaller  studies the numbers allocated to each group may not be well balanced.

2. PERMUTED BLOCK RANDOMIZATION is a predefined randomization sequence composed of permuted blocks where each block balances treatment in multiples of the desired allocation ratio. For example, in a trial involving two treatments with the allocation ratio 1:1, a block has equal numbers of A’s and B’s with the order of treatments within the block being randomly permuted. A block of size four has six different possible arrangements of two A’s and two B’s. A random number sequence is used to choose a particular block, which sets the allocation order for the first four subjects. Similarly, the treatment group is allocated to the next four patients in the order specified by the next randomly selected block. The process is then repeated. Permuted block randomization ensures treatment group numbers are evenly balanced at the end of each block. Blocked randomization has been used in smaller studies to maintain good balance.

3. ZELEN’S BALANCED BLOCK RANDOMIZATION [4]: In Zelen’s balanced blocked randomization subjects are allocated to treatments from a central list unless the center (or site) imbalance is equal to or larger than a certain magnitude, at which point the allocation is forced to reduce the magnitude of the imbalance. The forcing can be applied either deterministically or with a certain probability.

4. STRATIFIED PERMUTED BLOCK RANDOMIZATION: This method allocates a block rather than a treatment each time to a site for a particular stratum. The subjects enrolling into the same stratum/site are randomized using the available numbers in the block until the block is filled. One advantage of this method is that it allows new, unplanned sites to join the study. Unfortunately if there are a large number of incomplete blocks it usually indicates an imbalance at the study level.

Stratified Randomization

Stratified randomization is a randomization method that groups patients into strata according to clinical features (prognostic factors) that are believed to influence outcome. A set of permuted blocks is generated for each combination of prognostic factors. For example, in a hypothetical trial, suitable stratification factors might be gender and risk factor. A set of permuted blocks is then generated for women with high risk factors and another set for women with low risk factors and so on. Stratification can add to the credibility of a trial, as it ensures treatment balance on these known prognostic factors, allowing for easy interpretation of outcomes without adjustment. However care must be taken as over-stratification, a large number of strata in comparison to the number of patients, will result in many strata containing few patients and thereby resulting in substantial imbalance. In multi-institutional trials the institution is also considered as a stratification factor.

1. URN RANDOMIZATION was first defined by Wei [8] [9] [10]. In urn randomization the assignment of probabilities is adapted to the degree of imbalance in relation to the number of patients already entered into the trial. For example in a two-treatment trial with no stratifying factors at each iteration a ball is randomly drawn from an urn that contains a number of balls in two colors (e.g., white and red). If the color of the ball is white, treatment A is assigned; otherwise, treatment B is allocated. Then a predefined number of balls in opposite color are added to the urn. The randomization is performed continuously by running the iterations.

2. MINIMIZATION is a method that was originally proposed independently by Taves [5] and by Pocock and Simon [6]. It aims to ensure treatment arms are balanced with respect to all prognostic factors as well as for the number of patients in each group. The subject is allocated with a certain probability to a treatment that minimizes the imbalance for each stratifying factor level where the imbalance is evaluated by the weighted sum of ranges or variances in each stratum. Minimization can avoid problems of empty or sparse strata in a small trial and tends to produce more balanced treatment groups compared with restricted and unrestricted randomization.

3. RESPONSE-ADAPTIVE ALLOCATION MINIMIZATION is a method that was originally proposed independently by Taves [5] and by Pocock and Simon [6]. It aims to ensure treatment arms are balanced with respect to all prognostic factors as well as for the number of patients in each group. The subject is allocated with a certain probability to a treatment that minimizes the imbalance for each stratifying factor level where the imbalance is evaluated by the weighted sum of ranges or variances in each stratum. Minimization can avoid problems of empty or sparse strata in a small trial and tends to produce more balanced treatment groups compared with restricted and unrestricted randomization. It is essential to note the allocation methods adopted in the trials have an implication on the statistical analysis. For example, simulations in [11] shows that minimization resulted in conservative levels of significance using Student’s t test and improved the power of the selected hypothesis compared to stratified randomization. However when using data from actual trials [12] simulations run demonstrated that minimization was inferior to stratified allocation and equivalent to simple randomization in reducing alpha and beta errors. Moreover, the simulation showed [13] that minimization may distort p-values but by incorporating covariates in the analysis can alleviate this problem.

Randomization and Trial Supply Management (RTSM) by Fountayn

The randomization in Fountayn’s Randomization and Trial Supply Management (RTSM) is a variant of stratified randomization using forced randomization under situations where assignments alone are not successful.  In other words subjects are allocated treatments from a central list of permuted blocks for each stratum. When a subject comes to a site the stratum is determined for this patient and the next available treatment in the block for the stratum is assigned. However, the assignment may not always be fulfilled at the site due to shortage of drug. In this case, the randomization specification applies the minimization technique choosing one treatment from the inventory that minimizes the imbalance between treatment groups on all stratifying factors. The imbalance can be evaluated at the study level or the site level as the sum of imbalance for each stratum.

In practice treatments involving medications typically have a limited supply at each site due to high cost and/or concerns to minimize waste. While patients may enter any one of the sites at random it is not common but it is possible that a few patients coming to a site in a row are allocated the same treatment, causing one particular treatment/drug to run out of stock. In this case resupply of treatment drugs/medications to their maximal stock levels needs to be done for continuation of the trial.

These factors, inventory conditions and treatment restock, have a significant impact on the study balance and should be considered carefully. Once the inventory falls to a specified amount the resupply routine can automatically be triggered and more drug kits are shipped from the packaging company. Drugs in a supply package are determined based on the drug allocation ratio. Fountayn has experience in actual studies [Cost Savings with Fountayn EDC and RTSM] building a supply package strategy in such way that the drugs in the inventory after resupply follow the allocation ratio and optimize the drug supply.

The foundation for this resupply strategy is that the allocation of next block across all sites has nothing to do with how previous blocks were assigned and the current assignment has no memory of history. In other words, the next recruited patient can be assigned to any one of the treatments and still comply with the allocation ratio. It is therefore reasonable to refill the inventory of a site to make it ready for the next block assignment. For example, a hypothetical clinical trial has two treatment groups (A and B) with allocation ratio 1:1. A block of size four has two A’s and two B’s. The initial supply to each of the two sites is also two A’s and two B’s. Suppose in the randomization of the first block, two A’s were assigned to the first site and two B’s to the second site. At this point, the first site has two B’s left, whereas the second site has two A’s left. Instead of supplying each site with one A and one B, we send two As to the first site and two B’s to the second site. After resupply, both sites are restocked to their initial stage and set for the next randomization.

Fountayn RTSM provides a sophisticated level of flexibility.

Randomization can be set to address the individual needs of your trial.

Summary

As noted in the introduction randomization is a procedure used in clinical trials to manage the allocation of supplies to individual subjects. There are two basic methodologies and several approaches of each method to implement randomization to meet the goals and objectives of clinical trials. Fundamental to any design is that participants are allocated to treatment and control groups at random, thereby minimizing selection bias and maximizing the precision of treatment effect estimates. Fountayn has defined and implemented a dynamic central randomization approach that effectively and efficiently meets the fundamental randomizations needs of clinical trials in a dynamic approach that results in significant study savings by maximizing the use of trial supplies [Cost Savings with Fountayn EDC and RTSM].

References

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