Optimal Randomization Designs for Large Multicenter Clinical Trials — From the NIH StrokeNet Experience

Abstract

From 2016 to 2021, the National Institutes of Health StrokeNet initiated ten multicenter randomized controlled clinical trials. Optimal subject randomization designs are demanded with four critical properties: 1) protection of treatment assignment randomness, 2) achievement of the desired treatment allocation ratio, 3) balancing of baseline covariates, and 4) ease of implementation. For acute stroke trials, it is necessary to minimize the time between eligibility assessment and treatment initiation. This article reviews the randomization designs for three trials currently enrolling in StrokeNet, the Statins In Intracerebral Hemorrhage trial (SATURN), the Multi-arm Optimization of Stroke Thrombolysis trial (MOST), and the Recombinant Factor VIIa for Hemorrhagic Stroke Trial (FASTEST). Randomization methods utilized in these trials include minimal sufficient balance, block urn design, big stick design, and step-forward randomization. Their advantages and limitations are reviewed and compared to traditional stratified permuted block design and minimization.

Graphical Abstract

CHALLENGES FOR SUBJECT RANDOMIZATION IN CLINICAL TRIALS

Desired Properties for Randomization Designs

Randomization design defines the probabilities of each subject being assigned to each arm. These probabilities are calculated based on the target allocation ratio, the enrollment sequence of the subject, the treatment distribution of previously enrolled subjects, and the baseline profile for previous subjects as well as the current subject when balancing of baseline covariates is needed. There are four essential properties required to optimize subject randomization designs in clinical trials: 1) random treatment assignment, 2) accurate treatment allocation, 3) balanced baseline covariates, and 4) ease of implementation.

Random treatment assignment

Random treatment assignment is the theoretical basis for statistical inferences of clinical trial results and the practical foundation for preventing selection bias.⁴ It can be measured by the proportion of deterministic assignments and the correct guess probability.⁵ A treatment assignment is considered deterministic if there is only one arm available for the subject to be randomized. A high proportion of deterministic assignments or high correct guess probability may induce selection bias when investigators adjust subject recruitment based upon their knowledge of upcoming treatment assignments.

Treatment allocation accuracy

Treatment allocation accuracy measures the amount by which the achieved allocation ratio in the trial differs from the target allocation ratio specified by the study design. For two-arm equal-allocation trials, the target allocation is 1:1. The treatment allocation accuracy can be assessed by the difference between the two arm sizes. For multi-arm and/or unequal allocation trials, the distance between the target allocation ratio and achieved allocation ratio is a generic format of treatment allocation accuracy measurement. For example, in a three-arm study with response adaptive randomization, if the target allocation ratio for the next 30 days is 0.2564: 0.3154: 0.4282, and the treatment distribution of the $N$ subjects enrolled in this period is $N_1:N_2:N_3$, the treatment allocation accuracy can be measured by $\sqrt{{\left(\frac{N_1}{N}-0.2564\right)}^2+{\left(\frac{N_2}{N}-0.3154\right)}^2+{\left(\frac{N_3}{N}-0.4282\right)}^2}$. It is important to recognize that the commonly used permuted block design cannot target allocations with large integers or decimals due to the limitation on block sizes. In this case, the target allocation ratio needs be simplified. For example, allocation 0.2564: 0.3154: 0.4282 may be simplified as 5: 6: 9. Such simplification will reduce the trial efficiency. Randomization designs capable of accurately targeting any treatment allocation ratio are needed, especially for Bayesian adaptive trials with response adaptive randomization.

Covariate imbalance

A balanced subject baseline across treatment groups is critical for the acceptance of trial results.⁶ Covariate imbalance is defined as the variation in covariate distributions among treatment arms. Depending on the type of the covariate (categorical or continuous) and the target allocation ratio of the trial, different methods can be used to evaluate the covariate imbalance. Table 2 shows an example of categorical covariate imbalance calculation in a two-arm trial with 2:1 allocation. Since the randomization algorithm assigns a treatment arm but not a covariate category for each subject, it is more common to evaluate treatment imbalance within each covariate category as opposed to covariate imbalance within each treatment arm.

Table 2. Example of Categorical Baseline Covariate Imbalance Calculation.

Two-arm 2:1 allocation trial

			Target Allocation		Achieved Allocation		Treatment Imbalance within Covariate Category
	Treatment Allocation Ratio		0.667	0.333	0.650	0.350
		Sum	Active	Control	Active	Control
Covariate Category Ratio	Total	60	40	20	39	21
0.4	Female	24	16	8	13	11	−3*
0.6	Male	36	24	12	26	10	2
Covariate Imbalance within Treatment Arm					−2.6**	2.6

^*:Treatment imbalance in female subjects: female active achieved –female active target = 13 – 16 = −3.

^**:Covariate imbalance in active arm = 0.6 female active – 0.4 male active = 0.6 x 13 – 0.4 * 26 = −2.6.

Different statistical tests can be used to descriptively quantify the level of baseline covariate imbalances. The t-test can be used to compare the means of a continuous covariate between two arms. The Pearson’s chi-squared test can be used to assess the imbalance of a categorical covariate. A small p-value of such tests indicates a serious imbalance in the covariate. We recognize that testing for the homogeneity of baseline covariates at the end of the trial is strongly discouraged because of the concerns for the invalid interpretation and misuse of the results of such tests.^7,8 We use the p-values of these tests during the trial in the randomization algorithm as a quantitative measure for covariate imbalances only. If preferred, other measures for imbalances can also be considered.⁹ Most randomization designs do not have the capacity to balance continuous baseline covariates, such as the time from stroke onset to treatment and age. These important covariates have often been dichotomized when used in the randomization algorithm, which dilutes the covariate information and reduces the efficiency of balancing. Advanced randomization designs capable of balancing both categorical and continuous baseline covariates are desirable.

It is hard to satisfy all the demands of an optimal randomization design simultaneously because of the competing nature among them. Complete random treatment assignment provides the highest allocation randomness but may result in an undesirable variation in treatment allocation accuracy and serious imbalances in baseline covariates. Any effort to increase treatment allocation accuracy or to control baseline covariate imbalance will reduce allocation randomness.¹⁰ Furthermore, protecting treatment allocation accuracy and balancing baseline covariates do not always point to the same treatment assignment. When competing demands occur, decision rules specified in the randomization algorithm are needed.

Challenges to Traditional Randomization Methods

Stratified permuted block design is the most common method for balancing baseline covariates in clinical trials.¹¹ It is easy to implement and has been endorsed by the Statistical Principles for Clinical Trials.¹² Permuted block design can be illustrated with a urn model. Consider a two-arm equal-allocation trial using permuted block design with a block size of 6. The urn starts from 6 balls, 3 white balls for the active arm and 3 black balls for the control arm. When a subject is ready for randomization, a ball is randomly drawn from the urn without replacement, and the subject is assigned accordingly. When the urn is empty, a new block starts with 3 balls for each arm. Recent research has revealed three limitations of permuted block design. First, it has a high proportion of deterministic assignment, which occurs towards the end of each block when the balls left in the urn are of the same color. With a block size of 6, it is expected that 25% of treatment assignments will be deterministic.¹³ Second, it can only target allocation ratios with small integers, such as 1:1, 2:3, or 1:2:3. Permuted block design controls treatment imbalance by the block size. It also requires the block size be a multiple of the sum of allocation elements in integer format to ensure perfect balance at the end of the block. For allocation 1:2:3, the smallest block size is 6. For allocation 5:6:9, the smallest block size is 20. A large block size may be needed to target the treatment allocation accurately, but this could simultaneously increase the treatment imbalance within the block. Finally, permuted block design can balance categorical baseline covariates by stratified randomization only. The number of total strata equals the product of the number of categories of each covariate. Consider a multicenter trial with 50 sites and additional 3 baseline covariates: sex (female vs. male), age group (<60 vs. ≥60), and disease severity level (moderate vs. severe), the total number of strata will be 50 × 2 × 2 × 2 = 400. If the sample size of the trial is 1200, the average number of subjects within each stratum is 3, which nullifies all efforts at imbalance control. Stratified permuted block design is therefore applicable only for trials with one or two categorical baseline covariates, each having few categories.¹⁴

Minimization was originally proposed by Taves in 1974, as an alternative to stratified permuted block design, to balance multiple categorical baseline covariates.¹⁵ It assigns the subject to the arm with the smallest sum of previously enrolled subject numbers in all covariate categories associated with the current subject. Shown in Table 3 is an example of treatment assignment using minimization for the 23^rd subject in a two-arm equal-allocation trial with sex, age group and clinical site as baseline covariates. In this example, the subject is assigned to the active arm, because it has a smaller sum of marginal subject counts than the control arm.

Table 3. Example of Minimization Assignment.

Two-Arm Equal-Allocation Trial with Three Covariates

For the 23^rd Subject (Male, Age Group ≥60, Site #2)

First 22 subjects’ allocation in each baseline covariate category								Sum of Subjects in associated categories	Treatment Assignment
Arm	Sex		Age Group		Clinical Site
	Female	Male	<60	≥60	Site #1	Site #2	Site #3
Active	7	5	3	8	4	5	3	18	←
Control	4	6	2	9	4	4	2	19

Pocock and Simon proposed a more general version of the minimization method, which allows unequal allocations, weights for covariate importance, and a biased coin probability for treatment assignment.¹⁶ However, in practice, Taves’ minimization is used more often because of its simplicity in implementation. Minimization method has two limitations. First, it can balance categorical covariates only. Second, it carries an underlying philosophy of zero-tolerance for baseline covariate imbalance, which reduces treatment allocation randomness.¹⁷

The low allocation randomness of traditional randomization methods and the use of vulnerable implementation methods have led to concerns of selection bias for many clinical trials, including the NINDS rt-PA Stroke Study.¹⁸ This trial used a permuted block design with various block sizes stratified by clinical center and time from onset to treatment (0 to 90 or 91 to 180 minutes).¹⁹ The randomization design was implemented with sealed envelopes. The Food and Drug Administration (FDA) clinical review identified that 13 subjects were randomized out of sequence and 18 were randomized from the wrong stratum. These 31 randomization errors changed treatment assignments for 22 subjects. Of these 22, twenty-one subjects should have received Active but instead received placebo, and only one should have received placebo and instead received Active. This result led to the concern of selection bias, as these errors did not appear to occur at random.¹⁸ The study also reported the distributions of 11 baseline covariates. Clinical center and time from stroke onset to treatment were well balanced because both are stratification factors for randomization. Among the other 9 covariates, age and weight had serious imbalance with p-value of 0.029 and 0.011 respectively.⁹ The low treatment allocation randomness of the permuted block design and the small number of covariates allowed by the stratification could have been avoided, had a better alternative to the stratified permuted block design been used and implemented with a secure centralized randomization system for the rt-PA Stroke Study.

BETTER ALTERNATIVES TO STRATIFIED PERMUTED BLOCK DESIGN AND MINIMIZATION

Restricted Randomization Methods with Maximum Tolerated Imbalance

When a stratified permuted block design is applied in a sequentially enrolling multicenter clinical trial, at a given timepoint (such as interim analysis or end of the study), the number of subjects in the last block in each stratum is a random variable. Block-end perfect balance is neither feasible nor necessary. Berger et al. defined a concept of randomization designs that controls the maximum tolerated imbalance (MTI).²⁰ Several restricted randomization designs can be classified as MTI procedure, including big stick design,²¹ maximal procedure²⁰ and block urn design.²²

The big stick design uses complete random assignments by default and deterministic assignments when the MTI threshold is reached.²¹ The maximal procedure maximizes the number of feasible treatment assignment sequences under the conditions of the MTI and the sequence length, and therefore increases the treatment assignment randomness. The maximal procedure gives all feasible sequences the same probability, which is a superior property for statistical analyses of trial results.²⁰ If one sequence is used for the entire study, the sequence length equals the sample size. When randomization is stratified, one treatment assignment sequence is needed for each stratum with the sequence length equals the size of the stratum. In sequentially enrolling trials, the size of each covariate stratum remains unknown until the end of the study, making the implementation of the maximal procedure hard. This issue has been resolved by a modified version, named as asymptotic maximal procedure, which removes the sequence length condition and simplifies the implementation.²³

The block urn design uses the same urn model as the permuted block design. However it adds a set of balanced balls back to the urn as long as the number of balls for each arm does not exceed the number of balls with which it started. For example, in a two-arm equal-allocation trial with a block size of 6, two balls, one for each arm, are added to the urn when both arms have less than 3 balls in the urn.²² These MTI methods significantly reduce the proportion of deterministic assignments. For two-arm equal-allocation trials, with the MTI of 3 (equivalent to a block size of 6), big stick design, maximal procedure, and block urn design have 16.7%, 7.3% and 5.9% deterministic assignments, respectively,²⁴ much lower than 25% with permuted block design.

Minimal Sufficient Balance

Minimal sufficient balance was proposed to maximize allocation randomness while controlling baseline covariate imbalances within pre-specified tolerated levels.⁹ It evaluates the imbalance among treatment arms for each covariate, either continuous or categorical, by the p-value of a test, prior to the treatment assignment of the current subject. When the imbalance exceeds the maximum tolerated level and a biased-coin assignment can meaningfully reduce the imbalance for that covariate, a vote is registered for the treatment assignment in favor of reducing the imbalance. After imbalances are assessed for all baseline covariates, votes are summarized with optional weights reflecting the priority of different covariates. The voting weight represents the priority level of different covariates and should be specified based on clinical considerations before the trial started. For example, in a stroke prevention trial, baseline stroke severity and age are confounding factors. A treatment assignment may reduce the imbalance in baseline stroke severity but increase the imbalance in age, or vice versa. The principal investigator may choose to balance baseline stroke severity first by requesting a higher weight in the randomization algorithm. If one arm receives more weighted votes than other arm(s), this arm will receive an allocation probability higher than the target allocation probability. Otherwise, a complete random assignment with the target allocation probability is used. Minimal sufficient balance can effectively balance many baseline covariates, both continuous and categorical types, and is applicable to two or multi-arm trials with equal or unequal allocations. Most importantly, minimal sufficient balance abandons minimization’s zero-tolerance rule toward covariate imbalance and acts only when the imbalance is serious.

Figure 1 compares the relative pros and cons of traditional randomization methods and four advanced randomization methods. Block urn design shares all properties of the permuted block design, except its higher allocation randomness. It is a better alternative to the permuted block design in trials with equal or simple unequal allocations like 1:2 or 1:2:3 and 1 or 2 categorical baseline covariates. For two-arm equal-allocation trials, big stick design is a good choice due to its simplicity of implementation. If baseline covariate balancing is not needed, asymptotic maximal procedure can be considered for trials with fixed allocations. Minimal sufficient balancing requires customized programming to implement, but it performs better than minimization in all other respects. It is applicable to two or multi-arm trials and able to accurately target equal, unequal, and response adaptive allocations. It can balance many baseline covariates of any types, categorical, ordinal, or continuous. Most importantly, minimal sufficient balance provides a high level of treatment allocation randomness, and therefore, protects the credibility of the trial results.

Figure 1.

Relative Pros and Cons of Randomization Methods

Step-forward Randomization

Trials treating medical emergencies like acute stroke require careful procedural consideration to minimize the time between eligibility confirmation and treatment initiation, as this affects both the safety and efficacy of the intervention. In addition to obtaining authorization for Exception from Informed Consent (21CFR50.24, 1996),²⁵ strategies to eliminate the time delay caused by a centralized subject randomization process are necessary. Step-forward randomization²⁶ was proposed and first implemented in the Albumin in Acute Stroke trial (NCT00235495)²⁷ in 2006. Step-forward randomization is an implementation method for centralized subject randomization designs. It performs randomization of the next subject at the site immediately after the enrollment and acute treatment of the current subject at the same site. In a drug study, with concealment and masking, the site puts a “use next” label on the drug kit assigned to the next subject and stores it in a readily available location until the next subject arrives. The randomization algorithm considers the treatment distribution information of previously enrolled subjects and current “use next” assignments at all sites. If imbalance in a categorical baseline covariate, such as age group, needs to be controlled, one “use next” assignment will be used for each covariate category at each site.

RANDOMIZATION METHODS USED IN STROKENET TRIALS

Randomization Algorithm for a Two-Arm Equal-Allocation Trial with five Baseline Covariates

Statins In Intracerebral Hemorrhage (SATURN, NCT03936361) is a multi-center, pragmatic, prospective, randomized, open-label, blinded end-point assessment phase 3 trial funded by NINDS. The SATURN trial aims to determine whether continuation vs. discontinuation of statin drugs after spontaneous lobar intracerebral hemorrhage (ICH) is the best strategy; and whether the decision to continue/discontinue statins should be influenced by an individual's Apolipoprotein-E (APOE) genotype. A planned maximum of 1456 patients presenting within 7 days of a spontaneous lobar intracerebral hemorrhage while taking statins from approximately 140 sites in the United States, Canada and Europe will be randomized with equal allocation to one of two treatment strategies: discontinuation vs. continuation of statin therapy. The objective of SATURN randomization is to maximize treatment allocation randomness while containing the overall treatment imbalance within pre-specified thresholds and preventing serious imbalances in five categorical baseline covariates. Stratified permuted block design is not applicable for this study because the total number of strata, i.e., the product of the 5 covariate category numbers, exceeds 3000. Minimization was not used because of its low allocation randomness.

As shown in Figure 2a, customized randomization algorithm was developed for the SATURN trial. The goal of the burn-in period is to contain the overall treatment imbalance within the limit δ₁. Block urn design is selected for the burn-in period due to its higher allocation randomness (R1 in Figure 2a). After the burn-in period, when the overall treatment imbalance reaches the maximum tolerated level of δ₂, a deterministic assignment to the smaller arm is used (R2 in Figure 2a). Otherwise, minimal sufficient balance is applied to prevent serious imbalances in the 5 categorical baseline covariates. If a covariate has serious imbalance, a weighted vote is registered for the smaller arm. The weight reflects the relative importance of the covariate. After imbalances in all 5 covariates are checked, if one arm received more votes than the other arm, a biased coin probability in favor of that arm is used for the treatment assignment (R3 in Figure 2a). If no covariate has serious imbalance, or the two arms receive equal number of votes, a complete random assignment is made (R0 in Figure 2a). The performance of this randomization algorithm is affected by several parameters, including the overall treatment imbalance limits within and after the burn-in period, the p-value threshold indicating serious imbalances, voting weights for each baseline covariate, and the biased coin probability used in the minimal sufficient balance. Based on the parameters used, SATURN is expected to have 6.3% deterministic assignments, 25% assignments with a biased coin probability varying from of 0.6 to 0.8, and 68.7% complete random assignments.^9,22,24

Figure 2.

Subject Randomization Algorithms for Two StrokeNet Trials

Randomization Algorithm for a Three-Arm Drug Trial with Response Adaptive Allocations

Multi-arm Optimization of Stroke Thrombolysis (MOST, NCT03735979) is a three-arm response adaptive randomized controlled phase 3 trial funded by NINDS. The primary objective of the trial is to determine if argatroban or eptifibatide results in improved 90-day modified Rankin Scale scores as compared with placebo in acute ischemic stroke patients treated with standard of care thrombolysis within three hours of symptom onset.²⁸ The study plans to randomize a maximum of 1200 subjects from more than 100 sites in the United States. The trial started with a balanced three-arm burn-in period of 150 subjects followed by a response adaptive randomization phase of 350 subjects with the target allocation updated periodically based on a Bayesian response adaptive design. Starting with the 501^st subject, the trial will have a fixed equal allocation with possible termination of one treatment arm. The objectives of subject randomization in the MOST study are: 1) to accurately achieve target allocations, including response adaptive allocations in decimal format, 2) to prevent serious imbalance in the continuous covariates of baseline NIHSS score and age, and 3) to protect allocation randomness.

As shown in Figure 2b, the MOST randomization algorithm checks study drug inventory first. Only treatment arms with study drug available at the site are included in the randomization algorithm. If study drug is only available for one arm, a forced assignment to the available arm is used (R1 in Figure 2b). If two or more arms have study drug, the algorithm checks the treatment imbalance among treatment arms with study drug based on number of subjects randomized within the current allocation. If the treatment imbalance exceeds the pre-specified threshold, the current subject will be assigned deterministically to the least represented arm (R2 in Figure 2b). Otherwise, the algorithm performs pair-wise t-tests between arms with study drug to check the imbalance of baseline NIHSS among subjects enrolled in the study. If the biggest imbalance is considered serious and the current subject has a baseline NIHSS score not too close to the median of the two means, a biased coin assignment in favor of reducing the baseline NIHSS imbalance is applied (R3 in Figure 2b). If no action is needed for NIHSS imbalance control, the system checks the imbalance in age. If serious imbalance in age is identified and the current subject’s age is not too close to the median, a biased coin assignment in favor of reducing the age imbalance is used (R4 in Figure 2b). If no action is needed to control treatment imbalance and baseline covariate imbalance, a complete random assignment is applied to the current subject using the target allocation probabilities (R0 in Figure 2b). Based on the values of the parameters used in this randomization algorithm, should all sites maintain sufficient study drug inventory, and the trial reach the maximum sample size without treatment arm termination after the first 500 subjects are enrolled, the MOST randomization algorithm described above will have 3% deterministic assignment, 13% biased coin assignments, and 84% complete random assignments.

Randomization Algorithm for an Emergency Treatment Trial

Recombinant Factor VIIa (rFVIIa) for Hemorrhagic Stroke Trial (FASTEST, NCT03496883) is a global, Phase III, randomized, double-blind controlled trial funded by NINDS. The central hypothesis is that rFVIIa, administered within 120 minutes from stroke onset, will improve outcomes at 180 days as measured by the modified Rankin Scale (mRS) compared to standard therapy. FASTEST plans to enroll 860 subjects from 100 hospital sites and 15 mobile stroke units from 4 regions: the United States, Canada, Japan, and Europe (including Germany, Spain, and the United Kingdom), and randomize them in a 1:1 ratio to receive either rFVIIa or placebo injection. To minimize time-to-treatment, FASTEST uses emergency research consent procedures, including exception from informed consent in the United States,²⁵ and the step-forward randomization,²⁶ so that a study drug kit is identified and ready to be used as soon as a subject is determined to meet eligibility.

Novo Nordisk A/S manufactures and supplies rFVIIa and matching placebo for the FASTEST trial. Central pharmacies in the four regions receive study medication shipments and assemble study drug kits with rFVIIa or placebo plus the histidine solvent in a blinded concealed format. Each drug kit has a globally unique ID. Treatment assignment of drug kits is produced using block urn design²² stratified by region during the process of sequential drug kit label creation. The automated study drug tracking program generates site drug kit shipping requests when any of the following events occur:

1. A site is approved to receive investigational product or is released to enroll.

2. Site study drug inventory is below the minimal level due to a drug kit being administered to a subject or expiration in 21 days.

3. A drug kit is removed from site inventory for any reason prior to being used.

The site minimal inventory is set to 4 for sites with an associated mobile stroke unit and sites with a high enrolling record, and 2 for all other sites. The implementation of the step-forward randomization reduces the time-to-treatment for acute stroke subjects and controls treatment imbalance within each region. Embedded in the computerized site drug shipping request program, the randomization algorithm minimizes the imbalance between the numbers of drug kits (used by subjects or remaining in site inventory) in the two treatment arms. When the total number of sites in the region remains the same, statistical work indicates that the standard deviation of the treatment imbalance in randomized subjects equals the square root of the total number of drug kits in site inventory in the region. As the study progresses and the number of enrolled subjects increases, the treatment imbalance will be bounded by the number of sites, which is expected to be stabilized. For sites enrolling an average of 2 or less subjects per year, it is acceptable to reduce the minimal drug kit inventory from 2 to 1. This will help to reduce the treatment imbalance in enrolled subjects. If progressively site closing is applied toward the end of the study, such as closing underperforming sites earlier, the treatment imbalance could be further narrowed.

IMPLEMENTATION OF RANDOMIZATION ALGORITHM

To ensure data integrity and trial operation efficiency, eliminate redundant data capture and data discrepancies among silo database systems, StrokeNet implements all clinical trials in an integrated clinical trial management system. This internally developed system provides information support for case report form data management, subject randomization, study supply (such as drug and lab kits) tracking, and other trial operation management tasks.

Figure 3 illustrates the generic procedure for subject randomization implemented for StrokeNet trials. A special case report form is used for subject randomization. When a subject randomization is requested, the site submits the randomization case report form. The system conducts a six-step data validation procedure: 1) the subject has not been previously randomized; 2) the site is currently released to enroll; 3) informed consent is obtained or exception from informed consent is confirmed; 4) all inclusion/exclusion criteria are confirmed as being met; 5) data for all baseline covariates to be used by the randomization algorithm are collected and associated case report forms are submitted; and 6) in drug studies, the site has study drug in inventory for at least one arm.

Figure 3.

Generic subject randomization procedure with trial specific randomization algorithm

Upon passing the data validation, the system calculates the allocation probabilities for assigning the subject to each arm based on 1) the randomization algorithm; 2) the target allocation ratio; 3) the distributions of treatment assignments; 4) distributions of baseline covariates; and 5) study drug inventory at the site (for drug studies). The treatment assignment is made based on the allocation probabilities and the value of a random number between 0 and 1. For example, in a two-arm trial the allocation probabilities obtained from the randomization design are 0.45 and 0.55 for the active and control arms respectively. If the random number obtained in real-time is less than 0.45, the current subject will be assigned to the active arm. Otherwise, the subject will be assigned to the control arm. The integration of the randomization module into the clinical trial management system makes it feasible to retrieve all required information within the central database in real time. The random number generated at the time of subject randomization eliminates the risk of potential selection bias due to intentional or unintentional concealment failures associated with pre-generated randomization lists.

After successful completion of the subject randomization procedure, all data used or generated by the randomization algorithm are archived and locked in the database where they cannot be changed. Edits to baseline covariates after randomization are documented in case report forms where covariate data are collected.

DISCUSSION

The use of advanced randomization designs may require extra implementation and validation efforts. Due to these concerns, investigators may choose to use traditional randomization methods. Closer examination of these advanced randomization designs may alleviate some of the concerns. For example, for two-arm equal-allocation trials, compared to permuted block design, big stick design has a higher allocation randomness and is easier for implementation. Block urn design has the same level of simplicity for implementation as permuted block design but offers much higher allocation randomness. Minimal sufficient balance requires customized programming. This cost is justified by the benefits of high allocation randomness, strong capacity for baseline covariate balancing and accurate targeting of any allocation ratios. For data management centers with a high trial volume load, the experience gained from the development and validation of an advanced randomization design from one trial can be used for subsequent trials, especially when a generic database system structure is used. In recent decades the mean cost per subject in a clinical trial has an average annual increase of 7.5%.²⁹ Meanwhile, information technologies and resources for clinical trial subject randomization have become available and affordable. Using less optimal randomization designs because of computer programming cost concerns is not justifiable.

A balanced baseline profile of key clinical characteristics is critical for the acceptance of trial results amongst the clinical community. From a statistical point of view, under complete randomization, a baseline covariate always has 5% chance of serious imbalance between treatment groups when indicated by a p-value less than 0.05. Should the trial involve five baseline covariates, there will be 1 − 0.95⁵ = 22.6% chance of seeing at least one covariate with a serious imbalance, although this is simply the result of a random procedure. It is not hard to prevent serious imbalances if a certain level of imbalance is tolerated. For example, if imbalances with a p-value of no less than 0.3 are tolerated, it requires about 5% of assignments to be made with a biased coin probability of 0.8, leaving the remaining 95% treatment assignments completely random.⁹

Randomization methods used in a clinical trial may affect the interpretation of statistical analysis results. Whether or not baseline covariates covered by the randomization algorithm should be included in the statistical model has been a hot topic for decades.^7,8,30,31 It is worth noting that the involvement of a baseline covariate in the randomization algorithm varies widely across different randomization designs. With stratified permuted block design, the covariate information is used by the randomization algorithm for all subjects. When the minimal sufficient balance is used to prevent serious imbalance with p-value less than 0.3 for a baseline covariate, only 5% of treatment assignments will be affected by the covariate value. The impact of baseline covariate imbalance on the estimation of the treatment effect is generally trivial,³² but the impact of the covariate itself may or may not exist. If a baseline covariate is clinically justified as a potential confounding factor, it should be included in the model for the estimation of the treatment effect, regardless of whether its distribution across treatment arms is balanced or not.³³

CONCLUSIONS

For trials limited to use pre-generated randomization sequences, big stick design, block urn design and asymptotic maximal procedure are recommended, because they have lower proportion of deterministic assignments under the same maximum tolerated imbalance. Big stick design is defined for two-arm equal-allocation trials. Block urn design and asymptotic maximal procedure are applicable for two or multi-arm trials with equal or unequal allocations.

For trials with potential confounding baseline covariates, such as index stroke severity and age, the minimal sufficient balance design is recommended. It maximizes allocation randomness while prevents serious baseline covariate imbalances and fits almost all target allocation and baseline covariate scenarios.

For trials involving complex study designs, such as burn-in period, response adaptive target allocations, a hierarchy randomization scheme can be used, so that different randomization designs can be applied at different stage of the study to address different requirements with pre-specified priority order. For example, the block urn design can be used for the burn-in period to ensure a near-balanced treatment distribution. After that, the minimal sufficient balance design can be applied to prevent serious imbalances in treatment distribution and baseline covariate distribution.

From the research ethics point of view, there is zero tolerance for selection bias in clinical research. Allocation randomness protects against selection bias, and therefore should be maximized with priority in randomization designs. Small amount of treatment imbalance should be tolerated when the sample size is not small. Perfectly balanced baseline covariates in sequential clinical trials are neither feasible nor needed. It is inappropriate to apply a zero-tolerance policy for baseline covariate imbalance while ignoring its detrimental effects on allocation randomness. Both permuted block design and minimization method have lower allocation randomness, and therefore should be replaced with better alternatives.

Table 1. Randomized controlled clinical trials initiated in NIH StrokeNet from 2016 to 2021.

No.	Trial Title	ClinicalTrials.gov Identifier	Planned Sample Size	EFIC§	Number of Arms	Target Allocation	Categorical Covariates	Continuous Covariates
1	ARCADIA	NCT03192215	1100	No	2	1:1	1	0
2	ASPIRE	NCT03907046	700	No	2	1:1	2	0
3	Defuse3	NCT02586415	476	No	2	1:1	5	0
4	FASTEST	NCT03496883	860	Yes	2	1:1	1	0
5	I-ACQUIRE	NCT03910075	240	No	3	1:1:1	1	0
6	MOST	NCT03735979	1200	No	3	RAR†	0	2
7	SATURN	NCT03936361	1456	No	2	1:1	5	0
8	SleepSMART	NCT03812653	3062	No	2	1:1	3	1
9	TeleRehab	NCT02360488	124	No	2	1:1	1	2
10	TRANSPORT2	NCT03826030	129	No	3	1:1:1	2	1

Note:

EFIC^§ = exception from informed consent

RAR^† = response adaptive randomization

Nonstandard Abbreviations and Acronyms

FASTEST

Recombinant Factor VIIa for Hemorrhagic Stroke Trial

MOST

Multi-arm Optimization of Stroke Thrombolysis trial

MTI

Maximum Tolerated Imbalance

SATURN

Statins In Intracerebral Hemorrhage trial

StrokeNet

Stroke Trials Network funded by NIH/NINDS