1. In the first stage of the design,   biomarker-negative individuals and  biomarker-positive individuals are recruited. An interim analysis is undertaken with its results determining how the design proceeds.

2. If the number of responses to the novel treatment in the biomarker-negative group, in the first stage  , meets or exceeds a cutoff of  , then Nun additional unselected individuals are accrued during the second stage (including   biomarker-negative responders and   biomarker-positive responders). If   is less than   but the number of responses in the biomarker-positive group in the first stage, , meets or exceeds a cutoff of  , then the design enrolls  , additional biomarker-positive individuals during the second stage (including   responders). If   is less than   and  is less than   then the trial stops. Consequently, when the second stage is terminated, a total of N+ and N− biomarker-positive and biomarker-negative individuals, respectively, will have been enrolled, whilst a total of   (biomarker-positive group) and   (biomarker-negative group) responders will have been observed.

3. In the case where unselected individuals continued to be accrued during the second stage, the total number of responders in the biomarker-negative subgroup,  , is compared to a cutoff, k− whilst the total number of responders in the biomarker-positive subgroup,  , is compared to a cutoff, k+. If  , then we conclude that the experimental treatment is beneficial in the unselected population; if   and   then we conclude that the treatment is beneficial only in the biomarker-positive population; if   and  , then we conclude no treatment benefit. In the case where only biomarker-positive patients continued to be accrued during the second stage,  , is compared to a cutoff,  . If   then we conclude treatment is beneficial in the biomarker-positive subgroup; otherwise we conclude no treatment benefit. The trial stage- and subgroup-specific sample sizes  , , Nun,  and cutoffs  ,  , k−, k+,   are determined so that they control the probability of correct conclusions in the biomarker-positive and unselected patient groups.

    

Note:

Jones and Holmgren (2007) have used the values 34, 34, 32 and 36 for  ,, N^un, and   respectively and the values 2, 1, 4, 4 and 5 for  , , k⁻, k⁺ and   respectively. As stated by Jones and Holmgren (2007) values for the cutoffs   and   (equal to 2 and 1 respectively) are obtained from the first stage of the optimal Simon two-stage design. Additionally, in the case where there is preliminary efficacy of the experimental treatment in the unselected population during the first stage of the trial, the study enters the second stage where the values of k⁻ and k⁺ for decision making need to be defined. Assuming the total number of biomarker-positive subjects (N⁺) enrolled by the end of the second stage is fixed at its expected value given a known prevalence, the aforementioned values (k⁻ and k⁺) can be acquired as the minimum values needed for exclusion of the null value from the (1 −  α ) × 100% exact Blythe-Still-Casella confidence interval where  α ≤0.05; these values can be found using the StatXact software package. However, if the observed total number of biomarker-positive subjects is much different from the expected value, then the cut-offs (k⁻ and k⁺) can be changed using the confidence interval approach aiming to preserve the desired operating features of the design. Moreover, the value of   needed also during the second stage of the trial for decision making can be acquired using either the confidence interval approach or through the calculation of exact binomial probabilities.

Advantages

• May augment the efficiency of the trial as it allows for early understanding that a particular experimental treatment is beneficial in a specific biomarker defined subgroup.
• Straightforward and simple strategy with reasonable operating characteristics.

Limitations

• Requires the pre-specification of appropriate response rates in both biomarker-positive and biomarker-negative subgroups which may be difficult.
• Does not allow early termination of the trial for efficacy in biomarker defined subgroups during the first stage of the trial.

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