IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v14y2018i2p16n3.html
   My bibliography  Save this article

Maximum Likelihood Estimation in a Semicontinuous Survival Model with Covariates Subject to Detection Limits

Author

Listed:
  • Bernhardt Paul W.

    (Villanova University, Villanova, PA, USA)

Abstract

Semicontinuous data are common in biological studies, occurring when a variable is continuous over a region but has a point mass at one or more points. In the motivating Genetic and Inflammatory Markers of Sepsis (GenIMS) study, it was of interest to determine how several biomarkers subject to detection limits were related to survival for patients entering the hospital with community acquired pneumonia. While survival times were recorded for all individuals in the study, the primary endpoint of interest was the binary event of 90-day survival, and no patients were lost to follow-up prior to 90 days. In order to use all of the available survival information, we propose a two-part regression model where the probability of surviving to 90 days is modeled using logistic regression and the survival distribution for those experiencing the event prior to this time is modeled with a truncated accelerated failure time model. We assume a series of mixture of normal regression models to model the joint distribution of the censored biomarkers. To estimate the parameters in this model, we suggest a Monte Carlo EM algorithm where multiple imputations are generated for the censored covariates in order to estimate the expectation in the E-step and then weighted maximization is applied to the observed and imputed data in the M-step. We conduct simulations to assess the proposed model and maximization method, and we analyze the GenIMS data set.

Suggested Citation

  • Bernhardt Paul W., 2018. "Maximum Likelihood Estimation in a Semicontinuous Survival Model with Covariates Subject to Detection Limits," The International Journal of Biostatistics, De Gruyter, vol. 14(2), pages 1-16, November.
    • Handle: RePEc:bpj:ijbist:v:14:y:2018:i:2:p:16:n:3
    DOI: 10.1515/ijb-2017-0058
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/ijb-2017-0058
    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-2017-0058?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. Bernhardt, Paul W. & Wang, Huixia Judy & Zhang, Daowen, 2014. "Flexible modeling of survival data with covariates subject to detection limits via multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 81-91.
    2. Zhou Xiao-Hua & Wanzhu Tu, 1999. "Comparison of Several Independent Population Means When Their Samples Contain Log-Normal and Possibly Zero Observations," Biometrics, The International Biometric Society, vol. 55(2), pages 645-651, June.
    3. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz, 1999. "Monte Carlo EM for Missing Covariates in Parametric Regression Models," Biometrics, The International Biometric Society, vol. 55(2), pages 591-596, June.
    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. Norah Alyabs & Sy Han Chiou, 2022. "The Missing Indicator Approach for Accelerated Failure Time Model with Covariates Subject to Limits of Detection," Stats, MDPI, vol. 5(2), pages 1-13, May.
    2. Gerda Claeskens & Fabrizio Consentino, 2008. "Variable Selection with Incomplete Covariate Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1062-1069, December.
    3. Liang, Hua & Su, Haiyan & Zou, Guohua, 2008. "Confidence intervals for a common mean with missing data with applications in an AIDS study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 546-553, December.
    4. Meng Yuan & Chunlin Wang & Boxi Lin & Pengfei Li, 2022. "Semiparametric inference on general functionals of two semicontinuous populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 451-472, June.
    5. Jiang, Wei & Josse, Julie & Lavielle, Marc, 2020. "Logistic regression with missing covariates—Parameter estimation, model selection and prediction within a joint-modeling framework," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    6. Yang, Yan & Simpson, Douglas, 2010. "Unified computational methods for regression analysis of zero-inflated and bound-inflated data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1525-1534, June.
    7. Wang, Chunlin & Marriott, Paul & Li, Pengfei, 2017. "Testing homogeneity for multiple nonnegative distributions with excess zero observations," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 146-157.
    8. Hongbin Zhang & Lang Wu, 2018. "A non‐linear model for censored and mismeasured time varying covariates in survival models, with applications in human immunodeficiency virus and acquired immune deficiency syndrome studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1437-1450, November.
    9. Samiran Sinha & Krishna K. Saha & Suojin Wang, 2014. "Semiparametric approach for non-monotone missing covariates in a parametric regression model," Biometrics, The International Biometric Society, vol. 70(2), pages 299-311, June.
    10. Schelin, Lina & Sjöstedt-de Luna, Sara, 2014. "Spatial prediction in the presence of left-censoring," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 125-141.
    11. Lee, Min Cherng & Mitra, Robin, 2016. "Multiply imputing missing values in data sets with mixed measurement scales using a sequence of generalised linear models," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 24-38.
    12. Han, Cong, 2003. "A note on optimal designs for a two-part model," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 343-351, December.
    13. Zhou, Xiao-Hua & Tu, Wanzhu, 2000. "Interval estimation for the ratio in means of log-normally distributed medical costs with zero values," Computational Statistics & Data Analysis, Elsevier, vol. 35(2), pages 201-210, December.
    14. Chen, Qingxia & Ibrahim, Joseph G. & Chen, Ming-Hui & Senchaudhuri, Pralay, 2008. "Theory and inference for regression models with missing responses and covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1302-1331, July.
    15. Nicholas J. Horton & Nan M. Laird, 2001. "Maximum Likelihood Analysis of Logistic Regression Models with Incomplete Covariate Data and Auxiliary Information," Biometrics, The International Biometric Society, vol. 57(1), pages 34-42, March.
    16. Tonghui Yu & Liming Xiang & Huixia Judy Wang, 2021. "Quantile regression for survival data with covariates subject to detection limits," Biometrics, The International Biometric Society, vol. 77(2), pages 610-621, June.
    17. Regier Michael D. & Moodie Erica E. M., 2016. "The Orthogonally Partitioned EM Algorithm: Extending the EM Algorithm for Algorithmic Stability and Bias Correction Due to Imperfect Data," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 65-77, May.
    18. James Y. Dai & Michael LeBlanc & Charles Kooperberg, 2009. "Semiparametric Estimation Exploiting Covariate Independence in Two-Phase Randomized Trials," Biometrics, The International Biometric Society, vol. 65(1), pages 178-187, March.
    19. Lan Huang & Ming-Hui Chen & Joseph G. Ibrahim, 2005. "Bayesian Analysis for Generalized Linear Models with Nonignorably Missing Covariates," Biometrics, The International Biometric Society, vol. 61(3), pages 767-780, September.
    20. Nanhua Zhang & Roderick J. Little, 2012. "A Pseudo-Bayesian Shrinkage Approach to Regression with Missing Covariates," Biometrics, The International Biometric Society, vol. 68(3), pages 933-942, September.

    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:14:y:2018:i:2:p:16: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.