How to Choose α and β in a Simon Two-Stage Design

Introduction

After deciding p₀, the response rate considered clinically unacceptable, and p₁, the response rate considered clinically promising, the next step is choosing α and β.

Many researchers use α = 0.05 and β = 0.20 because these values are common in published studies. They are sensible defaults, but they are not universal rules. The right choices depend on the consequences of making the wrong decision, the available patient population, and the objectives of your Phase II trial.

What Is α?

α (alpha) is the Type I error rate. It is the probability of concluding that a treatment is promising when its true response rate is only p₀—the response rate considered clinically unacceptable.

In practical terms, α measures the risk of advancing an ineffective treatment. For example, if p₀ = 20% and α = 0.05, a treatment with a true 20% response rate has at most a 5% chance of being incorrectly recommended for further study under the design’s Type I error definition.

A smaller α makes the study more conservative because stronger evidence is required before a treatment is declared promising. Lower α reduces false positives but usually increases the required sample size.

What Is β?

β (beta) is the Type II error rate. It is the probability of rejecting a treatment even though its true response rate is p₁—the response rate considered clinically worthwhile.

For example, if p₁ = 40% and β = 0.20, a treatment with a true 40% response rate has a 20% chance that the design will incorrectly conclude it is not promising.

The complement of β is statistical power: Power = 1 − β. Thus, β = 0.20 means 80% power, while β = 0.10 means 90% power. Lower β reduces the chance of missing an effective treatment but generally requires more patients.

Why α and β Matter

Choosing α and β is a balance between scientific confidence and study feasibility. Reducing either error rate usually requires enrolling more patients.

For p₀ = 20% and p₁ = 40%, the exact sample size depends on whether you choose an optimal, minimax, or admissible Simon design. However, the overall trend is consistent: more stringent error requirements generally produce larger designs.

Choosing α and β in Practice

There is no universally correct choice. Consider the consequences of making the wrong decision, the disease context, available treatments, patient population, and the purpose of the study.

Common Choices

The following combinations are useful starting points, not fixed rules. Investigators should justify the selected values in the context of the study.

Regulatory Considerations

Simon two-stage designs are primarily used in Phase II screening studies, where the goal is to determine whether a treatment shows enough promise to justify further investigation.

Unlike confirmatory Phase III trials, there is no universally required choice of α and β for these screening designs. Investigators should justify the values based on the study objectives, clinical context, and acceptable levels of risk. A well-reasoned justification is generally more valuable than simply copying values from previous publications.

Common Mistakes

Assuming α = 0.05 is always required: exploratory studies may reasonably use α = 0.10 when the goal is screening for promising treatments.

Confusing β with power: remember that Power = 1 − β. β = 0.20 means 80% power; β = 0.10 means 90% power.

Reducing both α and β without considering sample size: lower error rates provide stronger evidence but almost always increase the number of required patients.

Choosing α and β before defining p₀ and p₁: define the clinically unacceptable and promising response rates first, then choose error rates that fit the resulting clinical question.

Key Takeaways

α controls the probability of advancing an ineffective treatment.

β controls the probability of missing an effective treatment.

Power = 1 − β.

Lower α and β generally require larger sample sizes.

Choose α and β based on the consequences of false positives and false negatives—not simply because previous studies used those values.

Frequently Asked Questions