IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v11y2015i1p23-50n3.html
   My bibliography  Save this article

Conditional Transformation Models for Survivor Function Estimation

Author

Listed:
  • Möst Lisa

    (LMU München, Institut für Statistik, München, Germany)

  • Hothorn Torsten

    (Institut für Sozial- und Präventivmedizin, Universität Zürich, Abteilung Biostatistik Hirschengraben 84, Zürich CH-8001, Switzerland)

Abstract

In survival analysis, the estimation of patient-specific survivor functions that are conditional on a set of patient characteristics is of special interest. In general, knowledge of the conditional survival probabilities of a patient at all relevant time points allows better assessment of the patient’s risk than summary statistics, such as median survival time. Nevertheless, standard methods for analysing survival data seldom estimate the survivor function directly. Therefore, we propose the application of conditional transformation models (CTMs) for the estimation of the conditional distribution function of survival times given a set of patient characteristics. We used the inverse probability of censoring weighting approach to account for right-censored observations. Our proposed modelling approach allows the prediction of patient-specific survivor functions. In addition, CTMs constitute a flexible model class that is able to deal with proportional as well as non-proportional hazards. The well-known Cox model is included in the class of CTMs as a special case. We investigated the performance of CTMs in survival data analysis in a simulation that included proportional and non-proportional hazard settings and different scenarios of explanatory variables. Furthermore, we re-analysed the survival times of patients suffering from chronic myelogenous leukaemia and studied the impact of the proportional hazards assumption on previously published results.

Suggested Citation

  • Möst Lisa & Hothorn Torsten, 2015. "Conditional Transformation Models for Survivor Function Estimation," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 23-50, May.
    • Handle: RePEc:bpj:ijbist:v:11:y:2015:i:1:p:23-50:n:3
    DOI: 10.1515/ijb-2014-0006
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/ijb-2014-0006
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/ijb-2014-0006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Thomas H. Scheike & Torben Martinussen, 2004. "On Estimation and Tests of Time‐Varying Effects in the Proportional Hazards Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 51-62, March.
    2. Michael Schemper & Robin Henderson, 2000. "Predictive Accuracy and Explained Variation in Cox Regression," Biometrics, The International Biometric Society, vol. 56(1), pages 249-255, March.
    3. Honore, Bo & Khan, Shakeeb & Powell, James L., 2002. "Quantile regression under random censoring," Journal of Econometrics, Elsevier, vol. 109(1), pages 67-105, July.
    4. Holger Dette & Stanislav Volgushev, 2008. "Non‐crossing non‐parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627, July.
    5. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    6. Schmid, Matthias & Hothorn, Torsten, 2008. "Boosting additive models using component-wise P-Splines," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 298-311, December.
    7. Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
    8. James M. Robins & Dianne M. Finkelstein, 2000. "Correcting for Noncompliance and Dependent Censoring in an AIDS Clinical Trial with Inverse Probability of Censoring Weighted (IPCW) Log-Rank Tests," Biometrics, The International Biometric Society, vol. 56(3), pages 779-788, September.
    9. Donglin Zeng & D. Y. Lin, 2006. "Efficient estimation of semiparametric transformation models for counting processes," Biometrika, Biometrika Trust, vol. 93(3), pages 627-640, September.
    10. Torsten Hothorn & Thomas Kneib & Peter Bühlmann, 2014. "Conditional transformation models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 3-27, January.
    11. Kani Chen, 2002. "Semiparametric analysis of transformation models with censored data," Biometrika, Biometrika Trust, vol. 89(3), pages 659-668, August.
    12. Wang, Huixia Judy & Wang, Lan, 2009. "Locally Weighted Censored Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1117-1128.
    13. Peng, Limin & Huang, Yijian, 2008. "Survival Analysis With Quantile Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 637-649, June.
    14. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    15. Spierdijk, Laura, 2008. "Nonparametric conditional hazard rate estimation: A local linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2419-2434, January.
    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. Lin, Guixian & He, Xuming & Portnoy, Stephen, 2012. "Quantile regression with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 797-812.
    2. Peng, Limin, 2012. "Self-consistent estimation of censored quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 368-379.
    3. Xie, Shangyu & Wan, Alan T.K. & Zhou, Yong, 2015. "Quantile regression methods with varying-coefficient models for censored data," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 154-172.
    4. Miguel A Delgado & Andrés García-Suaza & Pedro H C Sant’Anna, 2022. "Distribution regression in duration analysis: an application to unemployment spells [Lecture notes in statistics: Proceedings]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 675-698.
    5. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2019. "Weighted quantile regression for censored data with application to export duration data," Statistical Papers, Springer, vol. 60(4), pages 1161-1192, August.
    6. Pang, Lei & Lu, Wenbin & Wang, Huixia Judy, 2012. "Variance estimation in censored quantile regression via induced smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 785-796.
    7. Chen, Songnian, 2023. "Two-step estimation of censored quantile regression for duration models with time-varying regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 1310-1336.
    8. Fan, Yanqin & Liu, Ruixuan, 2018. "Partial identification and inference in censored quantile regression," Journal of Econometrics, Elsevier, vol. 206(1), pages 1-38.
    9. Jad Beyhum & Lorenzo Tedesco & Ingrid Van Keilegom, 2022. "Instrumental variable quantile regression under random right censoring," Papers 2209.01429, arXiv.org, revised Feb 2023.
    10. Ying Cui & Limin Peng, 2022. "Assessing dynamic covariate effects with survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 675-699, October.
    11. Jiang, Rong & Qian, Weimin & Zhou, Zhangong, 2012. "Variable selection and coefficient estimation via composite quantile regression with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 308-317.
    12. Wang, Qihua & Tong, Xingwei & Sun, Liuquan, 2012. "Exploring the varying covariate effects in proportional odds models with censored data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 168-189.
    13. Akram Yazdani & Hojjat Zeraati & Mehdi Yaseri & Shahpar Haghighat & Ahmad Kaviani, 2022. "Laplace regression with clustered censored data," Computational Statistics, Springer, vol. 37(3), pages 1041-1068, July.
    14. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2013. "Global Bahadur Representation For Nonparametric Censored Regression Quantiles And Its Applications," Econometric Theory, Cambridge University Press, vol. 29(5), pages 941-968, October.
    15. Xiaoyi Wen & Jinfeng Xu, 2022. "Generalized Accelerated Failure Time Models for Recurrent Events," Mathematics, MDPI, vol. 10(15), pages 1-14, July.
    16. Jung-Yu Cheng & Shinn-Jia Tzeng, 2014. "Quantile regression of right-censored length-biased data using the Buckley–James-type method," Computational Statistics, Springer, vol. 29(6), pages 1571-1592, December.
    17. Tao Hu & Baosheng Liang, 2021. "A New Class of Estimators Based on a General Relative Loss Function," Mathematics, MDPI, vol. 9(10), pages 1-19, May.
    18. Shuang Ji & Limin Peng & Yu Cheng & HuiChuan Lai, 2012. "Quantile Regression for Doubly Censored Data," Biometrics, The International Biometric Society, vol. 68(1), pages 101-112, March.
    19. Worku Biyadgie Ewnetu & Irène Gijbels & Anneleen Verhasselt, 2024. "Two-piece distribution based semi-parametric quantile regression for right censored data," Statistical Papers, Springer, vol. 65(5), pages 2775-2810, July.
    20. Chen, Songnian, 2018. "Sequential estimation of censored quantile regression models," Journal of Econometrics, Elsevier, vol. 207(1), pages 30-52.

    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:bpj:ijbist:v:11:y:2015:i:1:p:23-50:n:3. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.