IDEAS home Printed from https://ideas.repec.org/p/bep/mchbio/1026.html
   My bibliography  Save this paper

Survival Analysis USing Auxiliary Variables Via Nonparametric Multiple Imputation

Author

Listed:
  • Chiu-Hsieh Hsu

    (University of Michigan Biostatistics)

  • Jeremy Taylor

    (University of Michigan)

  • Susan Murray

    (University of Michigan Biostatistics)

Abstract

We develop an approach, based on multiple imputation, that estimates the marginal survival distribution in survival analysis using auxiliary variables to recover information for censored observations. To conduct the imputation, we use two working proportional hazards models to define an imputing risk set. One model is for the event times and the other for the censoring times. Based on the imputing risk set, two nonparametric multiple imputation models are considered: a risk set imputation, and a Kaplan-Meier imputation. For both methods a future event or censoring time is imputed for each censoring observation. In a situation with a categorical auxiliary variable, we show that with a large number of imputes the estimates from the Kaplan-Meier imputation method correspond to the weighted Kaplan-Meier estimator. We also show that the Kaplan-Meier imputation-based method is robust to misspecification of either one of the two working models. In a simulation study with time independent and time dependent auxiliary variables, we show that the use of multiple imputation methods can improve the efficiency of estimators and reduce bias due to dependent censoring. The Kaplan-Meier imputation method is shown to outperform the risk-set imputation approach. We apply the approach to AIDS clinical trial data comparing ZDV and placebo, in which CD4 count in the time-dependent auxiliary variable.

Suggested Citation

  • Chiu-Hsieh Hsu & Jeremy Taylor & Susan Murray, 2004. "Survival Analysis USing Auxiliary Variables Via Nonparametric Multiple Imputation," The University of Michigan Department of Biostatistics Working Paper Series 1026, Berkeley Electronic Press.
    • Handle: RePEc:bep:mchbio:1026
    Note: oai:bepress.com:umichbiostat-1026
    as

    Download full text from publisher

    File URL: http://www.bepress.com/cgi/viewcontent.cgi?article=1026&context=umichbiostat
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Taylor, Jeremy M. G. & Murray, Susan & Hsu, Chiu-Hsieh, 2002. "Survival estimation and testing via multiple imputation," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 221-232, July.
    2. 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.
    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. Rachel Axelrod & Daniel Nevo, 2023. "A sensitivity analysis approach for the causal hazard ratio in randomized and observational studies," Biometrics, The International Biometric Society, vol. 79(3), pages 2743-2756, September.
    2. Yanyao Yi & Ting Ye & Menggang Yu & Jun Shao, 2020. "Cox regression with survival‐time‐dependent missing covariate values," Biometrics, The International Biometric Society, vol. 76(2), pages 460-471, June.
    3. Michael Rosenblum & Nicholas P. Jewell & Mark van der Laan & Stephen Shiboski & Ariane van der Straten & Nancy Padian, 2009. "Analysing direct effects in randomized trials with secondary interventions: an application to human immunodeficiency virus prevention trials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(2), pages 443-465, April.
    4. Douglas E. Schaubel & Guanghui Wei, 2011. "Double Inverse-Weighted Estimation of Cumulative Treatment Effects Under Nonproportional Hazards and Dependent Censoring," Biometrics, The International Biometric Society, vol. 67(1), pages 29-38, March.
    5. Romin Pajouheshnia & Noah A. Schuster & Rolf H. H. Groenwold & Frans H. Rutten & Karel G. M. Moons & Linda M. Peelen, 2020. "Accounting for time‐dependent treatment use when developing a prognostic model from observational data: A review of methods," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(1), pages 38-51, February.
    6. Greg DiRienzo, 2004. "Nonparametric Comparison of Two Survival-Time Distributions in the Presence of Dependent Censoring," Harvard University Biostatistics Working Paper Series 1000, Berkeley Electronic Press.
    7. Tala Al-Rousan & Jeffrey A Sparks & Mary Pettinger & Rowan Chlebowski & JoAnn E Manson & Andrew M Kauntiz & Robert Wallace, 2018. "Menopausal hormone therapy and the incidence of carpal tunnel syndrome in postmenopausal women: Findings from the Women’s Health Initiative," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-15, December.
    8. A. G. DiRienzo, 2003. "Nonparametric Comparison of Two Survival-Time Distributions in the Presence of Dependent Censoring," Biometrics, The International Biometric Society, vol. 59(3), pages 497-504, September.
    9. Shuxi Zeng & Elizabeth C. Lange & Elizabeth A. Archie & Fernando A. Campos & Susan C. Alberts & Fan Li, 2023. "A Causal Mediation Model for Longitudinal Mediators and Survival Outcomes with an Application to Animal Behavior," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(2), pages 197-218, June.
    10. Shen, Pao-sheng, 2009. "An inverse-probability-weighted approach to the estimation of distribution function with doubly censored data," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1269-1276, May.
    11. Geneletti, Sara & Mason, Alexina & Best, Nicky, 2011. "Adjusting for selection effects in epidemiologic studies: why sensitivity analysis is the only “solution”," LSE Research Online Documents on Economics 31520, London School of Economics and Political Science, LSE Library.
    12. Shen, Pao-sheng, 2010. "Semiparametric estimation of survival function when data are subject to dependent censoring and left truncation," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 161-168, February.
    13. Susmita Datta & Jennifer Le-Rademacher & Somnath Datta, 2007. "Predicting Patient Survival from Microarray Data by Accelerated Failure Time Modeling Using Partial Least Squares and LASSO," Biometrics, The International Biometric Society, vol. 63(1), pages 259-271, March.
    14. Qingxia Chen & Fan Zhang & Ming-Hui Chen & Xiuyu Julie Cong, 2020. "Estimation of treatment effects and model diagnostics with two-way time-varying treatment switching: an application to a head and neck study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 685-707, October.
    15. Bella Vakulenko‐Lagun & Jing Qian & Sy Han Chiou & Nancy Wang & Rebecca A. Betensky, 2022. "Nonparametric estimation of the survival distribution under covariate‐induced dependent truncation," Biometrics, The International Biometric Society, vol. 78(4), pages 1390-1401, December.
    16. Shirin Moghaddam & John Newell & John Hinde, 2022. "A Bayesian Approach for Imputation of Censored Survival Data," Stats, MDPI, vol. 5(1), pages 1-19, January.
    17. Andrew Ying & Eric J. Tchetgen Tchetgen, 2023. "Structural cumulative survival models for estimation of treatment effects accounting for treatment switching in randomized experiments," Biometrics, The International Biometric Society, vol. 79(3), pages 1597-1609, September.
    18. Jincheng Shen & Lu Wang & Jeremy M. G. Taylor, 2017. "Estimation of the optimal regime in treatment of prostate cancer recurrence from observational data using flexible weighting models," Biometrics, The International Biometric Society, vol. 73(2), pages 635-645, June.
    19. Pao-sheng Shen, 2010. "Nonparametric analysis of doubly truncated data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 835-853, October.
    20. Chiu-Hsieh Hsu & Jeremy Taylor & Susan Murray, 2004. "Multiple Imputation For Interval Censored Data With Auxiliary Variables," The University of Michigan Department of Biostatistics Working Paper Series 1025, Berkeley Electronic Press.

    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:bep:mchbio:1026. 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: Christopher F. Baum (email available below). General contact details of provider: http://www.bepress.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.