Jones and Holmgren (2007) presented a biomarker-adaptive parallel two-stage design to evaluate a treatment that it is thought to have different response in different subgroups defined by a prespecified biomarker positive versus negative. The idea is to run two parallel two-stage designs, one in each of the groups (biomarker-positive and biomarker-negative), and then to run an adaptive parallel design. Thus, the design begins with two parallel studies, one conducted in $N_{1}^{-}$ biomarker-negative subjects and the other conducted in $N_{1}^{+}$ biomarker-positive subjects. If the number of responses in the biomarker-negative group in the first stage, $X_{1}^{-}$, is equal or greater than a threshold $k_{1}^{-}$, the design continues to enroll $N^{un}$ unselected subjects during the second stage.
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To conclude about the efficacy of the treatment, the total responses are compared with the relative thresholds if unselected patients continued to be enrolled during the second stage or $Χ_{Τ}^{+}$ is compared against the threshold $k_{2}^{+}$ if only biomarker-positive subjects were enrolled in the second stage. The trial stage- and group-specific samples sizes $N_{1}^{-}$, $N_{1}^{+}$, $N^{un}$, $N_{2}^{-}$ and thresholds $k_{1}^{-}$, $k_{1}^{+}$, $k^{-}$, $k^{+}$, $k_{2}^{+}$ are determined so that they control the probability of correct conclusions in the biomarker-positive and unselected patient groups. The adaptive design can result in a reduction of expected sample size compared with the nonadaptive two parallel designs. Howevere, both adaptive and nonadaptive designs require specification of appropriate benchmark response rates in each of the biomarker-defined subgroups, which may be difficult to specify. See also MacShane et al.
To conclude about the efficacy of the treatment, the total responses are compared with the relative thresholds if unselected patients continued to be enrolled during the second stage or $Χ_{Τ}^{+}$ is compared against the threshold $k_{2}^{+}$ if only biomarker-positive subjects were enrolled in the second stage. The trial stage- and group-specific samples sizes $N_{1}^{-}$, $N_{1}^{+}$, $N^{un}$, $N_{2}^{-}$ and thresholds $k_{1}^{-}$, $k_{1}^{+}$, $k^{-}$, $k^{+}$, $k_{2}^{+}$ are determined so that they control the probability of correct conclusions in the biomarker-positive and unselected patient groups. The adaptive design can result in a reduction of expected sample size compared with the nonadaptive two parallel designs. Howevere, both adaptive and nonadaptive designs require specification of appropriate benchmark response rates in each of the biomarker-defined subgroups, which may be difficult to specify. See also MacShane et al.