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Table 1 Overview of program set-ups \( S\left({\hat{\theta}}_2^{s_1},{\hat{\theta}}_2^{s_2}\right) \)

From: Optimal designs for phase II/III drug development programs including methods for discounting of phase II results

Program set-up \( S\left({\hat{\theta}}_2^{s_1},{\hat{\theta}}_2^{s_2}\right) \) Adjustment of the estimate used for decision rule Estimate used for decision rule Adjustment of the estimate used for calculating the number of events for phase III Estimate used for calculating the number of events for phase III
\( S\left({\hat{\theta}}_2^u,{\hat{\theta}}_2^u\right) \) (unadjusted) none (s1 = u) \( {\hat{\theta}}_2^u \) none (s2 = u) \( {\hat{\theta}}_2^u \)
\( S\left({\hat{\theta}}_2^u,{\hat{\theta}}_2^{\lambda}\right) \) (multiplicative) multiplicative (s2 = λ) \( {\hat{\theta}}_2^{\lambda } \)
\( S\left({\hat{\theta}}_2^u,{\hat{\theta}}_2^{\alpha_{CI}}\right) \) (additive) additive (s2 = αCI) \( {\hat{\theta}}_2^{\alpha_{CI}} \)
\( S\left({\hat{\theta}}_2^{\lambda },{\hat{\theta}}_2^{\lambda}\right) \) (multiplicative) multiplicative (s1 = λ) \( {\hat{\theta}}_2^{\lambda } \) multiplicative (s2 = λ) \( {\hat{\theta}}_2^{\lambda } \)
\( S\left({\hat{\theta}}_2^{\alpha_{CI}},{\hat{\theta}}_2^{\alpha_{CI}}\right) \) (additive) additive
(s1 = αCI)
\( {\hat{\theta}}_2^{\alpha_{CI}} \) additive (s2 = αCI) \( {\hat{\theta}}_2^{\alpha_{CI}} \)
  1. Program set-ups are defined by the estimate used for the go/no-go decision (selection s1: “go if \( {\hat{\theta}}_2^{s_1}\ge \kappa \) ”) and by the calculation of the number of events for phase III (selection s2: \( {D}_3\left({\hat{\theta}}_2^{s_2}\right),{s}_2\in \left\{\lambda, {\alpha}_{CI},u\right\} \), where \( {\hat{\theta}}_2^{\lambda }={\hat{\theta}}_2\bullet \lambda \), \( {\hat{\theta}}_2^{\alpha_{CI}}={\hat{\theta}}_2-{z}_{1-{\alpha}_{CI}}\bullet \sqrt{4/{d}_2} \), and \( {\hat{\theta}}_2^u={\hat{\theta}}_2 \) are the multiplicatively adjusted, additively adjusted, and unadjusted treatment effect estimates of phase II).