Recommended when the aim of the study is to assess the treatment effect in both the entire population and in the biomarker-positive subpopulation but not in the biomarker-negative subpopulation.

1. If there is significant confidence that the biomarker is predictive, the sample size estimation is aimed at having a sufficient number of biomarker-positive individuals to enable the treatment effect in the biomarker positive subgroup to be detected.
2. If there is no confidence in the predictive value of the biomarker, the sample size estimation is aimed at having a sufficient number of patients to detect a treatment effect in the overall study population.

• Same formula proposed for marker stratified designs could be considered to achieve sufficient power in each biomarker-defined subgroup simultaneously.
• In order to control the overall type I error rate of the designs at the overall level of significance α it is required to allocate this overall α between the test for the biomarker-positive subgroup and the test for the biomarker-negative. Consequently, for biomarker-positive subgroup the reduced significance level α₁=α-α₂ can be used whereas the reduced significance level α₂=α-α₁ can be used for biomarker-negative subgroup.

Advantages

• Can control the overall type I error α.
• Can require smaller sample size as compared to the subgroup-specific designs, especially when we assume that the novel treatment equally benefits both biomarker-defined subgroups.

Limitations

• Can be overly conservative because of the correlation between the test of treatment effect in the overall study population and in the biomarker subgroups.
• Cannot control the probability of rejecting the null hypothesis of no treatment effect in the biomarker-negative subgroup when the treatment benefit is restricted to biomarker-positive patients. Consequently, there is a high risk of inappropriately recommending the novel treatment for biomarker-negative patients due to the large treatment effect in the biomarker-positive subgroup.

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