A Phase II Clinical Trial Design for Associated Co-primary Efficacy and Toxicity Outcomes with Baseline Covariates

  • Kristian BrockEmail author
  • Lucinda Billingham
  • Christina Yap
  • Gary Middleton
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 296)


The experimental design presented here is motivated by a phase II clinical trial called PePS2, investigating the efficacy and safety of an immunotherapy called pembrolizumab in a specific subgroup of lung cancer patients. Previous trials have shown that the probability of efficacy is correlated with particular patient variables. There are clinical trial designs that investigate co-primary efficacy and toxicity outcomes in phase II, but few that incorporate covariates. We present here the approach we developed for PePS2, latterly recognised to be a special case of a more general method originally presented by Thall, Nguyen and Estey. Their method incorporates covariates to conduct a dose-finding study but has been scarcely used in trials. Dose-finding is not required in PePS2 because a candidate dose has been widely tested. Starting from the most general case, we introduce our method as a novel refinement appropriate for use in phase II, and evaluate it using a simulation study. Our method shares information across patient cohorts. Simulations show it is more efficient than analysing the cohorts separately. Using the design in PePS2 with 60 patients to test the treatment in six cohorts determined by our baseline covariates, we can expect error rates typical of those used in phase II trials. However, we demonstrate that care must be taken when specifying the models for efficacy and toxicity because more complex models require greater sample sizes for acceptable simulated performance.


Covariate Efficacy Phase ii Toxicity Trial 


  1. 1.
    Borghaei, H., Paz-Ares, L., Horn, L., Spigel, D.R., Steins, M., Ready, N.E., et al.: Nivolumab versus docetaxel in advanced non-squamous non-small-cell lung cancer. N. Engl. J. Med. 373, 123–135 (2015)CrossRefGoogle Scholar
  2. 2.
    Braun, T.M.: The bivariate continual reassessment method: extending the CRM to phase I trials of two competing outcomes. Control. Clin. Trials. 23, 240–256 (2002)CrossRefGoogle Scholar
  3. 3.
    Brutti, P., Gubbiotti, S., Sambucini, V.: An extension of the single threshold design for monitoring efficacy and safety in phase II clinical trials. Stat. Med. 30, 1648–1664 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bryant, J., Day, R.: Incorporating toxicity considerations into the design of two-stage phase II clinical trials. Biometrics. 51, 1372–1383 (1995)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Carpenter, B., Gelman, A., Hoffman, M.D., Lee, D., Goodrich, B., et al.: Stan: a probabilistic programming language. J. Stat. Softw. 76, 1–32 (2017)CrossRefGoogle Scholar
  6. 6.
    Conaway, M., Petroni, G.: Designs for phase II trials allowing for a trade-off between response and toxicity. Biometrics. 52, 1375–1386 (1996)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cook, R., Farewell, V.: Guidelines for monitoring efficacy and toxicity responses in clinical trials. Biometrics. 50, 1146–1152 (1994)CrossRefGoogle Scholar
  8. 8.
    Eisenhauer, E.A., Therasse, P., Bogaerts, J., Schwartz, L.H., Sargent, D., et al.: New response evaluation criteria in solid tumours: revised RECIST guideline (version 1.1). Eur. J. Cancer. 45 228–2DD47 (2009)Google Scholar
  9. 9.
    Garon, E.B., Rizvi, N.A., Hui, R., Leighl, N., Balmanoukian, A.S., et al.: Pembrolizumab for the treatment of nonsmall-cell lung cancer. N. Engl. J. Med. 372, 2018–2028 (2015)CrossRefGoogle Scholar
  10. 10.
    Herbst, R.S., Baas, P., Kim, D., Felip, E., Perez-Gracia, J.L., et al.: Pembrolizumab versus docetaxel for previously treated, PD-L1-positive, advanced non-small-cell lung cancer (KEYNOTE-010): a randomised controlled trial. Lancet. 387, 1540–1550 (2016)CrossRefGoogle Scholar
  11. 11.
    Jin, H.: Alternative designs of phase II trials considering response and toxicity. Contemp. Clin. Trials. 109, 525–536 (2007)CrossRefGoogle Scholar
  12. 12.
    Konopleva, M., Thall, P.F., Arana Yi, C., Borthakur, G., Coveler, A., et al.: Phase I/II study of the hypoxia-activated prodrug PR104 in refractory/relapsed acute myeloid leukemia and acute lymphoblastic leukemia. Haematologica. 100, 927–934 (2015)CrossRefGoogle Scholar
  13. 13.
    Schiller, J.H., Harrington, D., Belani, C.P., Langer, C., Sandler, A., et al.: Comparison of four chemotherapy regimens for advanced non-small-cell lung cancer. N. Engl. J. Med. 346, 92–98 (2002)CrossRefGoogle Scholar
  14. 14.
    Thall, P.F., Simon, R.M., Estey, E.H.: New statistical strategy for monitoring safety and efficacy in single-arm clinical trials. J. Clin. Oncol. 14, 296–303 (1996)CrossRefGoogle Scholar
  15. 15.
    Thall, P.F., Sung, H.G.: Some extensions and applications of a Bayesian strategy for monitoring multiple outcomes in clinical trials. Stat. Med. 17, 1563–1580 (1998)CrossRefGoogle Scholar
  16. 16.
    Thall, P.F., Cook, J.D.: Dose-finding based on efficacy-toxicity trade-offs. Biometrics. 60, 684–693 (2004)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Thall, P.F., Nguyen, H.Q., Estey, E.: Patient-specific dose finding based on bivariate outcomes and covariates. Biometrics. 64, 1126–1136 (2008)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Yao, Y., Vehtari, A., Simpson, D., Gelman, A.: Using stacking to average Bayesian predictive distributions. Bayesian Anal. 13, 917–1007 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Zhang, W., Sargent, D.J., Mandrekar, S.: An adaptive dose-finding design incorporating both toxicity and efficacy. Stat. Med. 25, 2365–2383 (2006)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kristian Brock
    • 1
    Email author
  • Lucinda Billingham
    • 1
  • Christina Yap
    • 1
  • Gary Middleton
    • 1
  1. 1.University of BirminghamBirminghamUK

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