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Flexible modeling of survival data with covariates subject to detection limits via multiple imputation

Author

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  • Bernhardt, Paul W.
  • Wang, Huixia Judy
  • Zhang, Daowen

Abstract

Models for survival data generally assume that covariates are fully observed. However, in medical studies it is not uncommon for biomarkers to be censored at known detection limits. A computationally-efficient multiple imputation procedure for modeling survival data with covariates subject to detection limits is proposed. This procedure is developed in the context of an accelerated failure time model with a flexible seminonparametric error distribution. The consistency and asymptotic normality of the multiple imputation estimator are established and a consistent variance estimator is provided. An iterative version of the proposed multiple imputation algorithm that approximates the EM algorithm for maximum likelihood is also suggested. Simulation studies demonstrate that the proposed multiple imputation methods work well while alternative methods lead to estimates that are either biased or more variable. The proposed methods are applied to analyze the dataset from a recently-conducted GenIMS study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:81-91
    DOI: 10.1016/j.csda.2013.07.027
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    References listed on IDEAS

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    1. Rigobon, Roberto & Stoker, Thomas M., 2009. "Bias From Censored Regressors," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 340-353.
    2. Roberto Rigobon & Thomas M. Stoker, 2007. "Estimation With Censored Regressors: Basic Issues," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1441-1467, November.
    3. Lee, Sungim & Park, S. H. & Park, Jinho, 2003. "The proportional hazards regression with a censored covariate," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 309-319, February.
    4. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    5. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
    6. Martin, Andrew D. & Quinn, Kevin M. & Park, Jong Hee, 2011. "MCMCpack: Markov Chain Monte Carlo in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i09).
    7. Austin P.C. & Brunner L.J., 2003. "Type I Error Inflation in the Presence of a Ceiling Effect," The American Statistician, American Statistical Association, vol. 57, pages 97-104, May.
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    Cited by:

    1. Bernhardt, Paul W. & Zhang, Daowen & Wang, Huixia Judy, 2015. "A fast EM algorithm for fitting joint models of a binary response and multiple longitudinal covariates subject to detection limits," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 37-53.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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