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Estimating the effect of treatment in a proportional hazards model in the presence of non‐compliance and contamination

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  • Jack Cuzick
  • Peter Sasieni
  • Jonathan Myles
  • Jonathan Tyrer

Abstract

Summary. Methods for adjusting for non‐compliance and contamination, which respect the randomization, are extended from binary outcomes to time‐to‐event analyses by using a proportional hazards model. A simple non‐iterative method is developed when there are no covariates, which is a generalization of the Mantel–Haenszel estimator. More generally, a ‘partial likelihood’ is developed which accommodates covariates under the assumption that they are independent of compliance. A key feature is that the proportion of contaminators and non‐compliers in the risk set is updated at each failure time. When covariates are not independent of compliance, a full likelihood is developed and explored, but this leads to a complex estimator. Estimating equations and information matrices are derived for these estimators and they are evaluated by simulation studies.

Suggested Citation

  • Jack Cuzick & Peter Sasieni & Jonathan Myles & Jonathan Tyrer, 2007. "Estimating the effect of treatment in a proportional hazards model in the presence of non‐compliance and contamination," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 565-588, September.
    • Handle: RePEc:bla:jorssb:v:69:y:2007:i:4:p:565-588
    DOI: 10.1111/j.1467-9868.2007.00600.x
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    Cited by:

    1. Stephens Alisa & Keele Luke & Joffe Marshall, 2016. "Generalized Structural Mean Models for Evaluating Depression as a Post-treatment Effect Modifier of a Jobs Training Intervention," Journal of Causal Inference, De Gruyter, vol. 4(2), pages 1-17, September.
    2. Linbo Wang & Eric Tchetgen Tchetgen & Torben Martinussen & Stijn Vansteelandt, 2023. "Instrumental variable estimation of the causal hazard ratio," Biometrics, The International Biometric Society, vol. 79(2), pages 539-550, June.
    3. Torben Martinussen & Stijn Vansteelandt & Eric J. Tchetgen Tchetgen & David M. Zucker, 2017. "Instrumental variables estimation of exposure effects on a time‐to‐event endpoint using structural cumulative survival models," Biometrics, The International Biometric Society, vol. 73(4), pages 1140-1149, December.
    4. Bo Wei & Limin Peng & Mei‐Jie Zhang & Jason P. Fine, 2021. "Estimation of causal quantile effects with a binary instrumental variable and censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 559-578, July.
    5. Shuwei Li & Limin Peng, 2023. "Instrumental variable estimation of complier causal treatment effect with interval‐censored data," Biometrics, The International Biometric Society, vol. 79(1), pages 253-263, March.
    6. VanderWeele Tyler J, 2011. "Principal Stratification -- Uses and Limitations," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-14, July.
    7. Govert E. Bijwaard & Andrew M. Jones, 2024. "Regression discontinuity design with principal stratification in the mixed proportional hazard model: an application to the long-run impact of education on longevity," Empirical Economics, Springer, vol. 67(1), pages 197-223, July.
    8. Abualbishr Alshreef & Nicholas Latimer & Paul Tappenden & Ruth Wong & Dyfrig Hughes & James Fotheringham & Simon Dixon, 2019. "Statistical Methods for Adjusting Estimates of Treatment Effectiveness for Patient Nonadherence in the Context of Time-to-Event Outcomes and Health Technology Assessment: A Systematic Review of Method," Medical Decision Making, , vol. 39(8), pages 910-925, November.
    9. Shengli An & Peter Zhang & Hong-Bin Fang, 2023. "Subgroup Identification in Survival Outcome Data Based on Concordance Probability Measurement," Mathematics, MDPI, vol. 11(13), pages 1-10, June.
    10. Anna M. Wilke & Donald P. Green & Jasper Cooper, 2020. "A placebo design to detect spillovers from an education–entertainment experiment in Uganda," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1075-1096, June.
    11. Hui Nie & Jing Cheng & Dylan S. Small, 2011. "Inference for the Effect of Treatment on Survival Probability in Randomized Trials with Noncompliance and Administrative Censoring," Biometrics, The International Biometric Society, vol. 67(4), pages 1397-1405, December.
    12. Ditte Nørbo Sørensen & Torben Martinussen & Eric Tchetgen Tchetgen, 2019. "A causal proportional hazards estimator under homogeneous or heterogeneous selection in an IV setting," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 639-659, October.
    13. Stephens Alisa & Joffe Marshall & Keele Luke, 2016. "Generalized Structural Mean Models for Evaluating Depression as a Post-treatment Effect Modifier of a Jobs Training Intervention," Journal of Causal Inference, De Gruyter, vol. 4(2), pages 1, September.
    14. L. Altstein & G. Li, 2013. "Latent Subgroup Analysis of a Randomized Clinical Trial through a Semiparametric Accelerated Failure Time Mixture Model," Biometrics, The International Biometric Society, vol. 69(1), pages 52-61, March.
    15. Bijwaard, G.E.; & Jones, A.M.;, 2019. "Education and life-expectancy and how the relationship is mediated through changes in behaviour: a principal stratification approach for hazard rates," Health, Econometrics and Data Group (HEDG) Working Papers 19/05, HEDG, c/o Department of Economics, University of York.

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