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A new group-sequential phase II/III clinical trial design Nigel Stallard and Tim Friede Warwick Medical School, Univers

A new group-sequential phase II/III clinical trial design Nigel Stallard and Tim Friede Warwick Medical School, University of Warwick, UK n.stallard@warwick.ac.uk. A new group-sequential phase II/III clinical trial design. Outline Seamless phase II/III design Background 2.1 Notation

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A new group-sequential phase II/III clinical trial design Nigel Stallard and Tim Friede Warwick Medical School, Univers

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  1. A new group-sequential phase II/III clinical trial design Nigel Stallard and Tim Friede Warwick Medical School, University of Warwick, UK n.stallard@warwick.ac.uk

  2. A new group-sequential phase II/III clinical trial design Outline • Seamless phase II/III design • Background 2.1 Notation 2.2 Standard group-sequential approach (k1 = 1) 2.3 Selection of best treatment at first look (k2= … = kn = 1) 3. k2, …, knpre-specified case 3.1 Strong control of FWER 4. k2, …, kndata dependent case 4.1 Error rate control 4.2 Simulation study 5. Conclusions

  3. Interim 1 T0 T1 T2  Tk1 Interim 2 T0 T(1)  T(k2) Interim n etc. Superiority? Superiority? Select treatments  Futility? Futility? 1. Seamless phase II/III design Start T0 T1 T2  Tk1 T0: Control Treatment T1,…, Tk1 Experimental Treatments Aim: control FWER in strong sense

  4. 2. Background 2.1 Notation i measures superiority of Ti over T0 Test H0i: i  0 vs. HAi : i > 0 Let Zij be stagewise test statistic for H0i at stage j Sij be cumulative test statistic for H0i at stage j Number of treatments at each stage, k1, …, kn Monitor Sij: reject H0i at look j if Sij  uj Find boundaries with Pr(reject any true H0i by look j)  *(j) for specified *(1)  …  *(n) = 

  5. 2.2 Standard group-sequential approach (k1 = 1) (Jennison and Turnbull, 2000)  measures superiority of T1 over T0 Test H0:  0 vs. HA:  > 0 Obtain null distribution of S numerically using S1 (first look) is normal S1 ~ N (0, I1) Sj (subsequent looks) has Sj – Sj–1 = Zj ~ N (0, Ij – Ij–1) sum of truncated normals and normal increment density given by convolutions of normal densities Hence find boundaries to satisfy spending function

  6. 2.3 Selection of best treatment at first look (k2= … = kn = 1)(Stallard and Todd, 2003) Let Z1max = max{Zi1} UnderH0 if I11 = … = Ik1 = : I1 Obtain distribution of S1max= Z1maxunder global null hypothesis as in Dunnett test; density is given by

  7. Continue with best treatment, T(1), only Let S1max= Z1max Monitor Sjmax:= S1max + …+ Z(1)j Increments in S1maxare normal; under H0(1) Sjmax – Sj–1max = Z(1)j ~ N (0, Ij– Ij–1) Density given via convolutions as in standard case Use distribution ofSjmaxto give boundary to satisfy spending function for monitoring Sjmax Reject H0(1)at look jif Sjmax  uj

  8. 3. k2, …, knpre-specified case Let Zjmax = max{Zij} Sjmaxbe sum of Zjmax Obtain distribution of Sjmax(given prespecified k1, …, kn) under global null hypothesis Find boundary to control type I error rate for monitoring Sjmax Use this boundary to monitor Sij i.e. reject H0iat look jif Sij  uj Test is conservative as Sjmaxst max{Sij} (sum of maxima is > maximum of sums)

  9. 3.1 Strong control of FWER Consider test of H0K: i = 0  i  K  {1, …, k1}  control error rate for H0K Hence control I error rate for H0i in strong sense by CTP (Markus et al., 1976) Note: can select any treatments since Sijst Sjmax (Jennison and Turnbull, 2006)

  10. 4.1 Error rate control 4. k2, …, kndata dependent case FWER is strongly controlled for pre-specified k1, …, kn In practice may wish to have k1, …, kn data-dependent Proposal: use u1, …, unas above Error rate can be inflated (neither weak nor strong control) Example: k1 = 2, n = 2, I1 = I2/2,  = *(2) = 0.025, *(1) = 0 Define conditional error functions probability of rejectingH0 given stage 1 data (Z1,1, Z2,1) CE1(Z1,1, Z2,1) fork2 = 1 (depends only on max{Z1,1, Z2,1}) CE2(Z1,1, Z2,1) fork2 = 2

  11. k2 = 1 CE1(Z1,1, Z2,1) CE1(Z1,1, Z2,1)f(Z1,1, Z2,1)dZ1,1dZ2,1 =  Type I error rate = 0.025

  12. k2 = 2 CE2(Z1,1, Z2,1) CE2(Z1,1, Z2,1)f(Z1,1, Z2,1)dZ1,1dZ2,1   Type I error rate = 0.01654

  13. Data-dependent k2to maximise type I error rate k2 = argmax{CEk(Z1,1, Z2,1)} Error rate max{CEk(Z1,1, Z2,1)} f(Z1,1, Z2,1)dZ1,1dZ2,1 Exceeds  if CE2(Z1,1, Z2,1)} > CE1(Z1,1, Z2,1)} at any (Z1,1, Z2,1) Type I error rate = 0.02501

  14. Practicaltreatment selection rule (Kelly et al., 2005) Drop treatment Tiif Sij < max{Sij} –  Ij  = 0.1

  15. Error rate does not exceed 0.025 for any < 0.025

  16. 4.2 Simulation study k1 = 2, n = 2, 32 patients per arm in each stage Drop treatment Ti if Sij < max{Sij} –  Ij  = 0  drop worst,  =   continue with both Estimate type I error rates pr(reject any H0i; H0) Estimate power pr(reject H01; H02) for range of 1 values pr(reject H01 or H02) for range of 1 values and 2= 0.5 Compare with other methods

  17. Simulated type I error rates for range of  values Class. Dunnett (), Adap. Dunnett (), Comb. Test (), Gp-seq ()

  18. Simulated power for range 1 values using both tmts ( = ) 2 = 0 2 = 0.5 1 1 Class. Dunnett (), Adap. Dunnett (), Comb. Test (), Gp-seq ()

  19. Simulated power for range 1 values using best tmt ( = 0) 2 = 0 2 = 0.5 1 1 Class. Dunnett (), Adap. Dunnett (), Comb. Test (), Gp-seq ()

  20. Simulated power for range 1 values using  = 1 2 = 0 2 = 0.5 1 1 Class. Dunnett (), Adap. Dunnett (), Comb. Test (), Gp-seq ()

  21. 5. Conclusions Group-sequential approach allows selection of >1 treatment extending Stallard and Todd (2003) method allows reduction of number of treatments over several stages does not allow further adaptations gives stopping boundaries in advance - can construct repeated c.i.’s (Jennison & Turnbull, 1989) strongly controls FWER for pre-specified k1, …, kn appears to control FWER with selection rule simulated

  22. Choice of approach to maximise power depends on choice treatment selection rule true effectiveness of experimental treatments Single effective treatment, small  - group-sequential method can be (slightly) more powerful Several effective treatments, large  - adaptive Dunnett test can be more powerful

  23. References Stallard, N., Friede, T. Flexible group-sequential designs for clinical trials with treatment selection. Statistics in Medicine, 27, 6209-6227, 2008. Friede, T., Stallard, N. A comparison of methods for adaptive treatment selection. Biometrical Journal, 50, 767-781, 2008. Bauer P, Kieser M. Combining different phases in the development of medical treatments within a single trial. Stat. Med., 18, 1833-1848, 1999. Dunnett CW. A multiple comparison procedure for comparing several treatments with a control. JASA, 50, 1096-1121, 1955. Jennison C, Turnbull BW. Interim analyses: the repeated confidence interval approach. JRSS(B), 51, 305-361, 1989. Jennison C, Turnbull BW. Confirmatory seamless phase II/III clinical trials with hypothesis selection at interim: opportunities and limitations. Biom. J., 48, 650-655, 2006. Kelly PJ, Stallard N, Todd S. An adaptive group sequential design for phase II/III clinical trials that select a single treatments from several. J. Biopharm. Stat., 15, 641-658, 2005. Koenig F, Brannath W, Bretz F, Posch M. Adaptive Dunnett test for treatment selection. Stat. Med., 27, 1612-1625, 2008. Marcus R, Peritz E, Gabriel KR. On closed testing procedures with special reference to ordered analysis of variance. Biometrika, 63, 655-660, 1976. Stallard N, Todd S. Sequential designs for phase III clinical trials incorporating treatment selection. Stat. Med., 2003, 22, 689-703, 2003.

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