Optimal vs. Minimax Simon Designs: Which Should You Choose?

The Core Difference

Simon's two-stage design is one of the most widely used phase II designs for single-arm oncology trials. When designing a single-arm phase II clinical trial using Simon's two-stage design, one of the first planning decisions is whether to use the optimal design or the minimax design.

Both designs were introduced by Richard Simon and satisfy exactly the same statistical requirements. They use the same values of p0, p1, alpha, and beta.

Because those design parameters are identical, both designs provide the same control of Type I error and statistical power. They satisfy the same error-rate operating characteristics but optimize different objectives.

Everything else, including statistical validity, is identical. The only difference is what each design optimizes.

The optimal design minimizes the expected sample size when the treatment is ineffective, under the null hypothesis. The minimax design minimizes the maximum possible sample size that the trial could require.

Why This Matters

In a two-stage trial, investigators may stop the study early if the treatment shows insufficient activity during Stage 1. Because of that futility rule, the actual number of enrolled patients is often smaller than the maximum planned sample size.

The choice between the optimal and minimax design determines how this early stopping flexibility is used.

The optimal and minimax designs use this flexibility differently. The optimal design aims to reduce the average number of patients enrolled in unsuccessful trials. The minimax design aims to guarantee the smallest possible upper limit on total enrollment.

Neither design is statistically superior. They satisfy the same statistical requirements but optimize different objectives. The choice depends on the ethical and operational priorities of the trial.

Optimal Design

The optimal design is constructed to maximize the benefit of early stopping when the treatment is inactive.

It typically has a higher probability of early termination for futility and a smaller expected sample size under the null hypothesis. The tradeoff is that it may require a slightly larger maximum sample size if the trial continues to Stage 2.

A higher probability of early termination means ineffective treatments are identified sooner, reducing unnecessary patient enrollment.

If most investigational treatments are expected to fail, as is often the case in oncology phase II development, this approach can reduce the average number of patients exposed to ineffective therapies.

What does the Optimal design actually optimize?

A common misconception is that the Optimal design minimizes the expected sample size regardless of the true treatment effect. It does not.

The objective is much more specific: the Optimal design minimizes the expected sample size when the true response rate equals p₀, the response rate that represents an ineffective treatment.

Why p₀? Because if the treatment truly offers no meaningful benefit, we want the trial to stop as early as possible. Enrolling fewer patients in an ineffective study saves time and resources while reducing the number of patients exposed to a treatment that is unlikely to help.

As the true response rate increases above p₀, the expected sample size also changes. When a treatment is more promising, the trial is less likely to stop early for futility and is more likely to continue to the second stage. As a result, the expected sample size generally increases.

This illustrates an important principle: the Optimal design is optimized for one specific scenario, not for every possible true response rate.

This also explains why the Optimal and Minimax designs can recommend different sample sizes even when they satisfy the same Type I error (α) and power (1 − β) requirements. They optimize different objectives, so neither design is universally better. The right choice depends on what you want to optimize for your study.

Minimax Design

The minimax design takes a different perspective. Instead of minimizing average enrollment, it minimizes the largest sample size the study could ever require.

It usually provides the smallest possible maximum sample size among valid Simon designs, but often has a slightly larger expected sample size under the null and somewhat fewer early stops for futility.

This design is especially useful in rare diseases or studies with limited recruitment, where exceeding the planned maximum sample size may not be feasible.

The minimax design is particularly attractive when recruitment is difficult, the available patient population is limited, drug supply is constrained, or sponsors require a strict upper bound on enrollment.

Typical Trade-offs

Although the exact operating characteristics depend on the chosen p0, p1, alpha, and beta values, the overall pattern is consistent.

The optimal design usually has lower expected sample size under the null, higher probability of early stopping, and lower average patient exposure to ineffective treatment. Its maximum total sample size may be slightly larger.

Although the optimal design may require a few more patients in the worst case, it often treats fewer patients overall because early stopping occurs more frequently when the treatment is ineffective.

The minimax design usually has the smallest possible maximum total sample size and the lowest worst-case enrollment. Its expected sample size under the null may be slightly larger because it tends to continue to Stage 2 more often.

A useful way to read candidate designs is to ask whether the trial team is optimizing average exposure in unsuccessful trials or the worst-case enrollment ceiling. That question is usually more informative than asking which design is better in the abstract.

A Conceptual Example

Imagine two Simon two-stage designs that satisfy exactly the same values of p0, p1, alpha, and beta. Both satisfy the same statistical requirements, but their operating characteristics differ.

When to Choose the Optimal Design

The optimal design is often preferred when most candidate treatments are expected to be ineffective and minimizing patient exposure to inactive therapies is an important ethical objective.

It is also a natural choice when recruitment is relatively straightforward and a slightly larger maximum sample size is acceptable.

Because many phase II oncology trials evaluate treatments that ultimately prove inactive, the optimal design is commonly used to reduce average enrollment under the null hypothesis.

When to Choose the Minimax Design

The minimax design is often preferred when recruitment is difficult, the disease is rare, the available patient population is limited, or funding and logistics impose a strict cap on enrollment.

It can also be appropriate when sponsors or study teams need certainty about the maximum study size before committing resources.

In these situations, guaranteeing the smallest possible maximum sample size may outweigh the benefit of a lower expected sample size.

How to Decide

Start by asking whether there is a hard limit on the total number of patients who can be enrolled. If the answer is yes, the minimax design deserves close attention.

Next, consider how difficult recruitment will be and whether the trial's ethical priority is minimizing average exposure to inactive treatment or minimizing the maximum enrollment commitment.

Finally, compare the expected sample size, probability of early termination, and maximum sample size for the candidate designs side by side. BioStatHub generates optimal, minimax, and admissible designs together so these trade-offs can be reviewed before selecting the final design.

In practice, most investigators generate both the optimal and minimax designs, compare ESS, PET, and maximum sample size, and then select the design that best balances ethical and operational considerations. BioStatHub displays these metrics side by side, making it straightforward to justify the final choice in the study protocol.

Reporting Your Choice

Whichever design you select, the study protocol should briefly explain the rationale. This helps reviewers see that the choice reflects ethical and operational priorities rather than statistical validity alone.

For an optimal design, the rationale might state that the design was selected to minimize expected sample size under the null hypothesis while maintaining the desired Type I error rate and power.

For a minimax design, the rationale might state that recruitment was expected to be challenging and minimizing the maximum required sample size was considered a priority.

Key Takeaways

Both the optimal and minimax Simon two-stage designs satisfy the same statistical requirements and provide the same control of Type I error and power for the specified design inputs.

Choose the optimal design when reducing the expected number of patients enrolled in ineffective trials is the primary goal. Choose the minimax design when limiting the maximum possible sample size is the overriding practical consideration.

Neither design is universally better. Once you understand these two extremes, admissible Simon designs are worth exploring because they can provide an attractive compromise between expected sample size and maximum sample size.

Frequently Asked Questions