Trial Name

A short identifier for your trial. Your downloaded files will be labeled with this name.

Participant Count

The number of participants per generated recruitment list. If the randomization is not stratified, this is the total number of participants in the trial. If the randomization is stratified, this is the number of participants per downloaded stratum file. You will have the option to stratify the randomization further down the tool.

Example: If Participant Count = 100 for a randomization that is not stratified, you will receive a single list for 100 participants. However, if Participant Count = 100 and participants are stratified into N groups, you will receive N lists of 100 arm assignments each (100*N participants total).

End of Randomization

This option controls whether the randomized recruitment list concludes with exact counts of participants in each trial arm.

By default: Exact counts are not required; imbalances within the MTI value are permitted through the end of randomization. This decreases the risk of selection bias, as the final participants are assigned just as randomly as the preceding ones.

Alternatively, depending on your trial design, you might opt to switch this setting such that each trial arm concludes with an exact count of participants. This may be useful for very small trials — for instance, a trial of 12 participants which requires exactly 4 participants to treatment and 8 participants to placebo — though we offer no guidance as to which trial designs might be applicable. Enabling this setting is left to your discretion and judgement regarding your trial's design.

Please note that if you change this setting and require exact counts in each arm, the number in the Participant Count field must be evenly divisible by the sum of the arm ratio values. So a 2-arm 1:1 trial with exact counts in each arm must have a Participant Count divisible by 2 (since 1+1 = 2); likewise a 3-arm 2:1:1 trial with exact counts in each arm must have a Participant Count divisible by 4 (since 2+1+1 = 4).

Customize Trial Arms

Default setting: 2-arm trial allocated 1:1, arms labeled "Arm 1" and "Arm 2."

Number of Trial Arms

The number of arms to which participants may be assigned. The tool supports 2-arm, 3-arm, and 4-arm trials.

Arm Name

For each arm, you may provide a unique name, such as "Treatment" or "Control." Otherwise, default text (e.g., "Arm 2") will be used to identify the arm assignment in the delivered files.

Arm Allocation Ratio

The ratio used to allocate participants into each arm with respect to the other arms. For example, for a 4:1 trial, you would select 4 for one of the arms and 1 for the other. The tool supports integer values 1 to 4. The default setting is to assign arms equally on a 1:1 ratio.

Customize Stratification

Default setting: Do not stratify participant recruitment. Provide one recruitment list for all participants.

Edit this section only if you want to stratify the randomization into independent recruitment lists. For example, this might be requested if participants are recruited at multiple sites, and each site requires its own recruitment list; or if participants sharing relevant demographic or health characteristics are randomized independently to ensure they aren't all assigned to the same arm; or other similar scenarios.

If you request a stratified randomization, an independent randomized recruitment list will be generated for each stratum that results when the stratifying variables are crossed. So for 2 stratifying variables where variable #1 describes 4 groups and variable #2 describes 2 groups, 8 independent recruitment lists will be generated (4 groups by 2 groups = 8 groups).

The tool supports up to 100 independent randomization strata. If you require more than 100 strata, consider submitting multiple requests. So if participants are divided into 120 strata, you might submit one request for the first 60 strata and a second request for the next 60 strata.

Number of Stratification Variables

The number of variables used to stratify participants. For example, if participants are stratified by age and recruitment site, the number of stratification variables is 2 (age and site), regardless of how many groups exist within each variable.

Categorical Variable Name

Enter a unique name identifying this stratifying variable, for example "Age Group" or "Site."

Number of Categories Described By This Variable

For each stratifying variable, specify the number of groups described by this variable. For example, if the variable is "Site" and there are 5 recruitment sites, select 5.

Category Names

For each group described by a stratifying variable, you may provide a label identifying the group. Due to text length restrictions in the final output, this field is limited to 5 characters. For example, in a trial with 2 recruitment sites, one in New York City and the other in London, you might decide to enter "NYC" and "Lond" in these fields.

Customize MTI method

Randomization Method

You have the option to change the MTI randomization method used to determine probabilities of arm assignments throughout the randomized sequence. Default methods are the asymptotic maximal procedure (if exact counts in each arm are not required) or the maximal procedure (if exact counts in each arm are required). Each of the available MTI methods is described in brief on the Learn About Randomization page.

• Maximal Procedure

  This procedure is automatically selected if you've indicated that your trial requires exact counts in each arm (see End of Randomization above).

  Under-assigned arms are favored by a balance-forcing probability that depends both on the current magnitude of arm imbalance and on the location of the participant within the randomized list. For this tool, as the sequence approaches its conclusion, the force towards balanced arms increases, until, at the last allocation, complete balance is forced and the targeted numbers per arm are achieved.

• Asymptotic Maximal Procedure

  This procedure is the default if you've indicated that your trial does not require exact counts in each arm (see End of Randomization above).

  Under-assigned arms are favored by a balance-forcing probability that depends solely on the current magnitude of arm imbalance. Exact balance is not forced at the end of the sequence. This slightly decreases the risk of selection bias as compared to the maximal procedure, because under the asymptotic maximal procedure the final participants are assigned just as randomly as the preceding ones.

• Chen's Procedure

  In Chen's procedure, a balance-forcing probability is applied to the under-assigned arm, much in the same way that balance-forcing is applied in the maximal and asymptotic maximal procedures.

  If you select Chen's procedure, you will also select the balance-forcing probability applied to the under-assigned arm. For instance, suppose you chose 60% (which is the default option). If the tool randomly assigns the first participant to Arm 2, then the second participant has a 60% chance of assignment to Arm 1, as this arm is presently under-assigned. When the arms are balanced, no balance-forcing probability is applied.

  In this tool, Chen's procedure is available only for 2-arm trials with 1:1 allocation.

• Big Stick

  In the Big Stick method, no balance-forcing probability is applied unless the imbalance between the arms reaches the MTI value. When the arm imbalance is within the MTI value, arm assignments are completely random. The tradeoff is that this permits reaching the maximum imbalance more frequently.

  In this tool, the Big Stick method is available only for 2-arm trials with 1:1 allocation.

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Technical Details of the Above Options

Maximal Procedure: This procedure is based on the concept that at any point in the randomization process, all future allocation sequences are equally likely. This greatly reduces the overall predictability of arm assignments as compared to other procedures. Approaches to constructing randomized sequences using the maximal procedure are described in the literature. [1][2]

Asymptotic Maximal Procedure: This procedure is based on the asymptotic nature of the imbalance-dependent arm assignment probabilities observed in randomized sequences generated using the maximal procedure. When a randomized sequence is generated with the maximal procedure, as the participant count in the sequence increases, the calculated arm assignment probabilities approach asymptotic values. [3] In practice, for this tool, when the asymptotic maximal procedure is selected, participants are assigned to arms according to probabilities equal to those found at some depth into a maximal procedure-generated sequence, and which approximate the true asymptotic values. However, unlike the maximal procedure, under asymptotic maximal the probabilities are frozen at these values and used throughout the entire randomized sequence.

Chen's Procedure: Compared to the maximal and asymptotic maximal procedures, this procedure is simpler in that, for arm imbalances within the MTI value, the balance-forcing probability is constant throughout the randomization process (whereas with maximal and asymptotic maximal the probabilities change as the arms become more or less imbalanced). As with all MTI procedures, the imbalance between arms is constrained by the chosen MTI value. Chen's procedure with a balance-forcing probability of 50% is equivalent to the Big Stick method.

Big Stick: This procedure is equivalent to Chen's procedure with a balance-forcing probability of 50%. Although allocations for arm imbalances within the MTI value are more random than Chen's procedure, the maximum imbalance is reached more often, increasing the frequency of deterministic allocations.

MTI

The MTI is a value representing the maximum tolerated imbalance between the trial arms at any point during the randomization process. It restricts how imbalanced the arms may become as participants are assigned. Some degree of imbalance is necessary.

A higher MTI value results in allocation sequences which are more random and thus less susceptible to selection bias. However, higher MTI values may result in greater imbalance between the arms. Conversely, lower MTI values guarantee tighter balance between the arms, but the generated allocation sequences are less random and more susceptible to selection bias. The choice of MTI is left to the investigator.

The default MTI in this tool is MTI = 3 for trial arms with equal allocation (e.g., 1:1). The tool allows for MTI values equal to 2, 3, 4 or 5.

Trials with unequal allocation ratios: If the trial is designed with unequal allocation between the arms (e.g., 4:1), the tool interprets the MTI value with respect to the largest arm (i.e., the arm with the highest allocation ratio value). So, if your trial has unequal allocation, you will see higher values available for the MTI as compared to the MTI values in 1:1 trial designs. Specifically, available MTI values are R*(2,3,4,5), where R is the allocation ratio value for the largest arm. For example, in a 2-arm 4:1 trial, the tool allows for MTI equal to 8, 12, 16 or 20, and when calculating the arm imbalance, each participant in the smaller arm is equivalent to 4 participants in the larger arm.

Trials with stratified randomization: If your trial's randomization is stratified, the MTI is applied to participants within each stratum. For example, if your randomization is stratified into 3 groups and you select MTI = 2, then the imbalance between arms will never exceed 2 participants within each group, but across both groups the maximum imbalance could reach 6 participants.