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Statistics in Biosciences

, Volume 10, Issue 1, pp 202–216 | Cite as

Residual Bootstrap Test for Interactions in Biomarker Threshold Models with Survival Data

  • Parisa Gavanji
  • Bingshu E. ChenEmail author
  • Wenyu Jiang
Article

Abstract

Many new treatments in cancer clinical trials tend to benefit a subset of patients more. To avoid unnecessary therapies and failure to recognize beneficial treatments, biomarker threshold models are often used to identify this subset of patients. We are interested in testing the treatment–biomarker interaction effects in a threshold model with biomarker but an unknown cut point. The unknown cut point causes irregularity in the model, and the traditional likelihood ratio test cannot be applied directly. A test for biomarker–treatment interaction effects is developed using a residual bootstrap method to approximate the distribution of the proposed test statistic. We evaluate the residual bootstrap and the permutation methods through extensive simulation study and find that the residual bootstrap method gives accurate test size, while the permutation method cannot control type I error sometimes in the presence of main treatment effects. The proposed residual bootstrap test can be used to explore potential treatment-by-biomarker interaction in clinical studies. The findings can be applied to guide the follow-up trial design using biomarker as a stratification factor. We apply the proposed residual bootstrap method to data from Breast International Group (BIG) 1-98 randomized clinical trial and show that patients with high Ki-67 level may benefit more from Letrozole treatment.

Keywords

Biomarker Permutation method Residual Bootstrap Survival analysis Biomarker threshold models Treatment-biomarker interaction 

Notes

Acknowledgements

This work was supported in part by the Grants from the Natural Sciences and Engineering Research Council of Canada (NSERC). The computation was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca) and Compute/Calcul Canada. The authors would like to thank the referees and the Editor for their insightful comments and suggestions.

References

  1. 1.
    Aalen OO (1978b) Nonparametric inference for a family of counting processes. Ann Stat 6:701–726MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Barker AD, Sigman CC, Kelloff GJ, Hylton NM, Berry DA, Esserman LJ (2009) I-SPY 2: an adaptive breast cancer trial design in the setting of neoadjuvant chemotherapy. Clin Pharmacol Ther 86(1):97–100CrossRefGoogle Scholar
  3. 3.
    Bonetti M, Gelber RD (2000) A graphical method to assess treatment-covariate interactions using the cox model on subsets of the data. Stat Med 19(19):2595–2609CrossRefGoogle Scholar
  4. 4.
    Chen BE, Jiang W, Tu D (2014) A Hierarchical Bayes model for biomarker subset effects in clinical trials. Computat Stat Data Anal 71:324–334MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jiang W, Freidlin B, Simon R (2007) Biomarker-adaptive threshold design: a procedure for evaluating treatment with possible biomarker-defined subset effect. J Natl Cancer Inst 99(13):1036–1043CrossRefGoogle Scholar
  6. 6.
    Lazar A, Cole B, Bonetti M, Gelber R (2010) Evaluation of treatment-effect heterogeneity using biomarkers measured on a continuous scale: subpopulation treatment effect pattern plot. J Clin Oncol 28(29):4539–44CrossRefGoogle Scholar
  7. 7.
    Luo X, Boyett J (1997) Estimation of a threshold parameter in Cox regression. Commun Stat Theory Methods 26:2329–2346MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Loughin TM (1995) A residual bootstrap for regression parameters in proportional hazards model. J Stat Comput Simul 77:367–384CrossRefGoogle Scholar
  9. 9.
    Nelson W (1972) Theory and applications of hazard plotting for censored failure data. Technometrics 14:945–965CrossRefGoogle Scholar
  10. 10.
    Pons O (2003) Estimation in a Cox regression model with a change-point according to a threshold in a covariate. Ann Stat 31:2442–2463MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Royston P, Altman DG, Sauerbrei W (2006) Dichotomizing continuous predictors in multiple regression: a bad idea. Stat Med 25:127–141MathSciNetCrossRefGoogle Scholar
  12. 12.
    Royston P, Sauerbrei W (2004) A new approach to modeling interactions between treatment and continuous covariates in clinical trials by using fractional polynomials. Stat Med 23(16):2509–2525CrossRefGoogle Scholar
  13. 13.
    Sargent DJ, Conley BA, Allegra C, Collette L (2005) Clinical trial designs for predictive marker validation in cancer treatment trials. J Clin Oncol 23(9):2020–2027CrossRefGoogle Scholar
  14. 14.
    Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  15. 15.
    Simon R (2014) Biomarker based clinical trial design. Chin Clin Oncol 3(3):39Google Scholar
  16. 16.
    Zang Y, Lee JJ (2015) Adaptive clinical trial designs in oncology. Chin Clin Oncol 3(4):1–20Google Scholar

Copyright information

© International Chinese Statistical Association 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada
  2. 2.Department of Public Health Sciences and Canadian Cancer Trials GroupQueen’s UniversityKingstonCanada

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