Overview

Big Stick Design (BSD) is an adaptive randomization procedure that allows the allocation to drift away from perfect balance up to a predefined Maximum Tolerated Imbalance (MTI). Once the imbalance reaches the MTI, the next subject is deterministically assigned to the under-represented arm. Otherwise, each assignment is made with equal probability.

Big Stick Design provides better allocation concealment than Permuted Block Design (because assignments are less predictable) while still guaranteeing that the final imbalance never exceeds the MTI.

How it works

Let D = (number of subjects in Arm A) − (number of subjects in Arm B).

• If |D| < MTI → assign Arm A or Arm B each with probability 0.5 (for 1:1 allocation).
• If D = +MTI → assign Arm B (force balance).
• If D = −MTI → assign Arm A (force balance).

Example — MTI = 3, 1:1 allocation:

Subject	Random draw	Assignment	Running D
1	0.71	TRT	+1
2	0.33	PBO	0
3	0.88	TRT	+1
4	0.62	TRT	+2
5	0.41	PBO	+1
6	0.91	TRT	+2
7	0.55	TRT	+3 — MTI reached
8	forced	PBO	+2

The imbalance never exceeds 3 at any point.

When to use

Use Big Stick Design when:

• You want stronger allocation concealment than Permuted Block provides (because the "big stick" intervention is less predictable than the end of a fixed block).
• The trial is single-site and simple (no stratification by subject characteristics required).
• You are willing to accept slight final imbalance in exchange for better masking.

For multi-site trials or subject-level stratification, combine with site-based or stratified variants if your platform supports it.

Configuration

In the Randomization app, select Big Stick Design as the algorithm, then configure:

Setting	Description
Type of imbalance evaluation	Count based — absolute difference in number of subjects per group. Ratio based — compares actual vs expected proportions. Cost based — assigns weight to treatment groups.
Study Groups	One row per treatment arm: Label, Code, Weight, Description
MTI Value	Maximum Tolerated Imbalance — the maximum allowed imbalance between arms. For count-based evaluation: 2–4 is typical for a 1:1 trial.
Imbalance level	By Site — evaluate imbalance separately for each site. By Study — evaluate across the entire study.
Imbalance scope	All active subjects — count all enrolled subjects. Exclude Withdrawn Subjects — exclude subjects who have withdrawn from the study.
Force assignment	Toggle — when enabled, forces assignment to the under-represented arm when the MTI is reached.
Soft Randomization Probability	Probability (0–100%) of assigning to the optimal (balancing) arm. Recommended 70–90% for large studies, 100% for small studies. Higher values improve balance but reduce unpredictability.

MTI guidance

Trial size	Typical MTI	Notes
< 50 subjects	2–3	Tight control; slight loss of concealment
50–200 subjects	3–5	Good balance between concealment and balance
> 200 subjects	5–8	Large trials tolerate larger imbalance without meaningful impact on power

Tip: Setting MTI too low (e.g., 1) approaches deterministic assignment and reduces allocation concealment. Setting it too high (e.g., equal to sample size) approaches simple randomization with no balance guarantee.

Comparison with Permuted Block

Property	Permuted Block	Big Stick Design
Allocation concealment	Weaker at block end	Stronger — harder to predict
Maximum imbalance	Block size / 2	MTI
Predictability	Higher (especially small blocks)	Lower
Simplicity	Simple	Slightly more complex
Pre-generatable	Yes	Not meaningfully

Regulatory acceptance

Big Stick Design is described in Soares & Wu (1983) and is recognized in the randomization literature, though less commonly used than Permuted Block. Document the MTI value and procedure in the randomization SOP and protocol. Discuss with your biostatistician before selecting BSD for a confirmatory trial.