IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2504.02096.html
   My bibliography  Save this paper

Estimation of the complier causal hazard ratio under dependent censoring

Author

Listed:
  • Gilles Crommen
  • Jad Beyhum
  • Ingrid Van Keilegom

Abstract

In this work, we are interested in studying the causal effect of an endogenous binary treatment on a dependently censored duration outcome. By dependent censoring, it is meant that the duration time ($T$) and right censoring time ($C$) are not statistically independent of each other, even after conditioning on the measured covariates. The endogeneity issue is handled by making use of a binary instrumental variable for the treatment. To deal with the dependent censoring problem, it is assumed that on the stratum of compliers: (i) $T$ follows a semiparametric proportional hazards model; (ii) $C$ follows a fully parametric model; and (iii) the relation between $T$ and $C$ is modeled by a parametric copula, such that the association parameter can be left unspecified. In this framework, the treatment effect of interest is the complier causal hazard ratio (CCHR). We devise an estimation procedure that is based on a weighted maximum likelihood approach, where the weights are the probabilities of an observation coming from a complier. The weights are estimated non-parametrically in a first stage, followed by the estimation of the CCHR. Novel conditions under which the model is identifiable are given, a two-step estimation procedure is proposed and some important asymptotic properties are established. Simulations are used to assess the validity and finite-sample performance of the estimation procedure. Finally, we apply the approach to estimate the CCHR of both job training programs on unemployment duration and periodic screening examinations on time until death from breast cancer. The data come from the National Job Training Partnership Act study and the Health Insurance Plan of Greater New York experiment respectively.

Suggested Citation

  • Gilles Crommen & Jad Beyhum & Ingrid Van Keilegom, 2025. "Estimation of the complier causal hazard ratio under dependent censoring," Papers 2504.02096, arXiv.org.
  • Handle: RePEc:arx:papers:2504.02096
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2504.02096
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. German Blanco & Xuan Chen & Carlos A. Flores & Alfonso Flores-Lagunes, 2020. "Bounds on Average and Quantile Treatment Effects on Duration Outcomes Under Censoring, Selection, and Noncompliance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 901-920, October.
    2. Deresa, Negera Wakgari & Van Keilegom , Ingrid, 2020. "Flexible parametric model for survival data subject to dependent censoring," LIDAM Reprints ISBA 2020043, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    4. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    5. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    6. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    7. Sujica, Aleksandar & Van Keilegom, Ingrid, 2018. "The copula-graphic estimator in censored nonparametric location-scale regression models," Econometrics and Statistics, Elsevier, vol. 7(C), pages 89-114.
    8. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    9. 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.
    10. Bijwaard, Govert E. & Ridder, Geert, 2005. "Correcting for selective compliance in a re-employment bonus experiment," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 77-111.
    11. Jad Beyhum & Lorenzo Tedesco & Ingrid Van Keilegom, 2024. "Instrumental variable quantile regression under random right censoring," The Econometrics Journal, Royal Economic Society, vol. 27(1), pages 21-36.
    12. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    13. Munir Hiabu & Simon M.S. Lo & Ralf A. Wilke, 2025. "Identifiability and estimation of the competing risks model under exclusion restrictions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 79(1), February.
    14. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    15. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 152(2), pages 104-119, October.
    16. Gilles Crommen & Jad Beyhum & Ingrid Van Keilegom, 2024. "An instrumental variable approach under dependent censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 473-495, June.
    17. Jad Beyhum & Samuele Centorrino & Jean-Pierre Florens & Ingrid Van Keilegom, 2024. "Instrumental Variable Estimation of Dynamic Treatment Effects on a Duration Outcome," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 732-742, April.
    18. Zucker, David M., 2005. "A PseudoPartial Likelihood Method for Semiparametric Survival Regression With Covariate Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1264-1277, December.
    19. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    20. Rivest, Louis-Paul & Wells, Martin T., 2001. "A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 138-155, October.
    21. Jad Beyhum & Jean-Pierre Florens & Ingrid Van Keilegom, 2022. "Nonparametric Instrumental Regression With Right Censored Duration Outcomes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1034-1045, June.
    22. Brigham R. Frandsen, 2019. "Testing Censoring Point Independence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 496-505, July.
    23. Negera Wakgari Deresa & Ingrid Van Keilegom, 2024. "Copula Based Cox Proportional Hazards Models for Dependent Censoring," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 1044-1054, April.
    24. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    25. Jialiang Li & Jason Fine & Alan Brookhart, 2015. "Instrumental variable additive hazards models," Biometrics, The International Biometric Society, vol. 71(1), pages 122-130, March.
    26. Deresa, Negera Wakgari & Van Keilegom, Ingrid, 2020. "A multivariate normal regression model for survival data subject to different types of dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    27. Lo, Simon M.S. & Wilke, Ralf A., 2017. "Identifiability Of The Sign Of Covariate Effects In The Competing Risks Model," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1186-1217, October.
    28. C Czado & I Van Keilegom, 2023. "Dependent censoring based on parametric copulas," Biometrika, Biometrika Trust, vol. 110(3), pages 721-738.
    29. Brigham R. Frandsen, 2015. "Treatment Effects With Censoring and Endogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1745-1752, December.
    30. Jad Beyhum & Jean-Pierre Florens & Ingrid van Keilegom, 2022. "Nonparametric Instrumental Regression With Right Censored Duration Outcomes," Post-Print hal-04042903, HAL.
    31. Jad Beyhum & Jean-Pierre Florens & Ingrid Keilegom, 2023. "A nonparametric instrumental approach to confounding in competing risks models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 709-734, October.
    32. Gerard J. van den Berg & Petyo Bonev & Enno Mammen, 2020. "Nonparametric Instrumental Variable Methods for Dynamic Treatment Evaluation," The Review of Economics and Statistics, MIT Press, vol. 102(2), pages 355-367, May.
    33. Xuelin Huang & Nan Zhang, 2008. "Regression Survival Analysis with an Assumed Copula for Dependent Censoring: A Sensitivity Analysis Approach," Biometrics, The International Biometric Society, vol. 64(4), pages 1090-1099, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gilles Crommen & Jad Beyhum & Ingrid Van Keilegom, 2024. "An instrumental variable approach under dependent censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 473-495, June.
    2. Jad Beyhum & Lorenzo Tedesco & Ingrid Van Keilegom, 2022. "Instrumental variable quantile regression under random right censoring," Papers 2209.01429, arXiv.org, revised Feb 2023.
    3. Negera Wakgari Deresa & Ingrid Van Keilegom, 2025. "Semiparametric transformation models for survival data with dependent censoring," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(3), pages 425-457, June.
    4. Lorenzo Tedesco & Jad Beyhum & Ingrid Van Keilegom, 2023. "Instrumental variable estimation of the proportional hazards model by presmoothing," Papers 2309.02183, arXiv.org.
    5. Jad Beyhum & Jean-Pierre FLorens & Ingrid Van Keilegom, 2020. "Nonparametric instrumental regression with right censored duration outcomes," Papers 2011.10423, arXiv.org.
    6. Beyhum, Jad & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2020. "Nonparametric Instrumental Regression with Right Censored Duration Outcomes," TSE Working Papers 20-1164, Toulouse School of Economics (TSE).
    7. Jad Beyhum & Jean-Pierre Florens & Ingrid Van Keilegom, 2021. "A nonparametric instrumental approach to endogeneity in competing risks models," Papers 2105.00946, arXiv.org.
    8. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    9. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    10. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
    11. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    12. German Blanco & Xuan Chen & Carlos A. Flores & Alfonso Flores-Lagunes, 2020. "Bounds on Average and Quantile Treatment Effects on Duration Outcomes Under Censoring, Selection, and Noncompliance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 901-920, October.
    13. Huber, Martin & Mellace, Giovanni, 2012. "Relaxing monotonicity in the identification of local average treatment effects," Economics Working Paper Series 1212, University of St. Gallen, School of Economics and Political Science.
    14. Muller, Christophe, 2018. "Heterogeneity and nonconstant effect in two-stage quantile regression," Econometrics and Statistics, Elsevier, vol. 8(C), pages 3-12.
    15. Manuel Arellano & Stéphane Bonhomme, 2017. "Quantile Selection Models With an Application to Understanding Changes in Wage Inequality," Econometrica, Econometric Society, vol. 85, pages 1-28, January.
    16. Joshua D. Angrist, 2004. "Treatment effect heterogeneity in theory and practice," Economic Journal, Royal Economic Society, vol. 114(494), pages 52-83, March.
    17. Gracious M. Diiro & Abdoul G. Sam & David Kraybill, 2017. "Heterogeneous Effects of Maternal Labor Market Participation on the Nutritional Status of Children: Empirical Evidence from Rural India," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 10(3), pages 609-632, September.
    18. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    19. Peter Hull & Michal Kolesár & Christopher Walters, 2022. "Labor by design: contributions of David Card, Joshua Angrist, and Guido Imbens," Scandinavian Journal of Economics, Wiley Blackwell, vol. 124(3), pages 603-645, July.
    20. Lo, Simon M.S. & Wilke, Ralf A. & Emura, Takeshi, 2024. "A semiparametric model for the cause-specific hazard under risk proportionality," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2504.02096. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.