IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v83y2021i1d10.1007_s13571-019-00222-w.html
   My bibliography  Save this article

Statistical Modeling of Longitudinal Data with Non-Ignorable Non-Monotone Missingness with Semiparametric Bayesian and Machine Learning Components

Author

Listed:
  • Yu Cao

    (Virginia Commonwealth University)

  • Nitai D. Mukhopadhyay

    (Virginia Commonwealth University)

Abstract

In longitudinal studies, outcomes are measured repeatedly over time and it is common that not all the patients will be measured throughout the study. For example patients can be lost to follow-up (monotone missingness) or miss one or more visits (non-monotone missingness); hence there are missing outcomes. In the longitudinal setting, we often assume the missingness is related to the unobserved data, which is non-ignorable. Pattern-mixture models (PMM) analyze the joint distribution of outcome and patterns of missingness in longitudinal data with non-ignorable non-monotone missingness. Existing methods employ PMM and impute the unobserved outcomes using the distribution of observed outcomes, conditioned on missing patterns. We extend the existing methods using latent class analysis (LCA) and a shared-parameter PMM. The LCA groups patterns of missingness with similar features and the shared-parameter PMM allows a subset of parameters to be different between latent classes when fitting a model. We also propose a method for imputation using distribution of observed data conditioning on latent class. Our model improves existing methods by accommodating data with small sample size. In a simulation study our estimator had smaller mean squared error than existing methods. Our methodology is applied to data from a phase II clinical trial that studies quality of life of patients with prostate cancer receiving radiation therapy.

Suggested Citation

  • Yu Cao & Nitai D. Mukhopadhyay, 2021. "Statistical Modeling of Longitudinal Data with Non-Ignorable Non-Monotone Missingness with Semiparametric Bayesian and Machine Learning Components," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 152-169, May.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:1:d:10.1007_s13571-019-00222-w
    DOI: 10.1007/s13571-019-00222-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-019-00222-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13571-019-00222-w?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. Jason Roy & Michael J. Daniels, 2008. "A General Class of Pattern Mixture Models for Nonignorable Dropout with Many Possible Dropout Times," Biometrics, The International Biometric Society, vol. 64(2), pages 538-545, June.
    2. A. R. Linero, 2017. "Bayesian nonparametric analysis of longitudinal studies in the presence of informative missingness," Biometrika, Biometrika Trust, vol. 104(2), pages 327-341.
    3. Stijn Vansteelandt & Andrea Rotnitzky & James Robins, 2007. "Estimation of Regression Models for the Mean of Repeated Outcomes Under Nonignorable Nonmonotone Nonresponse," Biometrika, Biometrika Trust, vol. 94(4), pages 841-860.
    4. P. Diggle & M. G. Kenward, 1994. "Informative Drop‐Out in Longitudinal Data Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 49-73, March.
    5. Antonio R. Linero & Michael J. Daniels, 2015. "A Flexible Bayesian Approach to Monotone Missing Data in Longitudinal Studies With Nonignorable Missingness With Application to an Acute Schizophrenia Clinical Trial," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 45-55, March.
    6. Michael J. Daniels, 2002. "Bayesian analysis of covariance matrices and dynamic models for longitudinal data," Biometrika, Biometrika Trust, vol. 89(3), pages 553-566, August.
    7. G. Molenberghs & B. Michiels & M. G. Kenward & P. J. Diggle, 1998. "Monotone missing data and pattern‐mixture models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(2), pages 153-161, June.
    8. Jason Roy, 2003. "Modeling Longitudinal Data with Nonignorable Dropouts Using a Latent Dropout Class Model," Biometrics, The International Biometric Society, vol. 59(4), pages 829-836, 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. Heng Chen & Daniel F. Heitjan, 2022. "Analysis of local sensitivity to nonignorability with missing outcomes and predictors," Biometrics, The International Biometric Society, vol. 78(4), pages 1342-1352, December.
    2. Michael J. Daniels & Minji Lee & Wei Feng, 2023. "Dirichlet process mixture models for the analysis of repeated attempt designs," Biometrics, The International Biometric Society, vol. 79(4), pages 3907-3915, December.
    3. Pourahmadi, Mohsen & Daniels, Michael J. & Park, Trevor, 2007. "Simultaneous modelling of the Cholesky decomposition of several covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 568-587, March.
    4. Miran A. Jaffa & Ayad A. Jaffa, 2019. "A Likelihood-Based Approach with Shared Latent Random Parameters for the Longitudinal Binary and Informative Censoring Processes," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 597-613, December.
    5. A. R. Linero, 2017. "Bayesian nonparametric analysis of longitudinal studies in the presence of informative missingness," Biometrika, Biometrika Trust, vol. 104(2), pages 327-341.
    6. Maria Marino & Marco Alfó, 2015. "Latent drop-out based transitions in linear quantile hidden Markov models for longitudinal responses with attrition," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(4), pages 483-502, December.
    7. Weiping Zhang & Feiyue Xie & Jiaxin Tan, 2020. "A robust joint modeling approach for longitudinal data with informative dropouts," Computational Statistics, Springer, vol. 35(4), pages 1759-1783, December.
    8. Betsy J. Feldman & Sophia Rabe-Hesketh, 2012. "Modeling Achievement Trajectories When Attrition Is Informative," Journal of Educational and Behavioral Statistics, , vol. 37(6), pages 703-736, December.
    9. Joseph W. Hogan & Xihong Lin & Benjamin Herman, 2004. "Mixtures of Varying Coefficient Models for Longitudinal Data with Discrete or Continuous Nonignorable Dropout," Biometrics, The International Biometric Society, vol. 60(4), pages 854-864, December.
    10. David M. Murray & Jonathan L. Blitstein, 2003. "Methods To Reduce The Impact Of Intraclass Correlation In Group-Randomized Trials," Evaluation Review, , vol. 27(1), pages 79-103, February.
    11. Patrick E. B. FitzGerald, 2002. "Extended Generalized Estimating Equations for Binary Familial Data with Incomplete Families," Biometrics, The International Biometric Society, vol. 58(4), pages 718-726, December.
    12. Tony Vangeneugden & Geert Molenberghs & Geert Verbeke & Clarice G.B. Dem�trio, 2011. "Marginal correlation from an extended random-effects model for repeated and overdispersed counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 215-232, September.
    13. Eric J. Tchetgen Tchetgen & Kathleen E. Wirth, 2017. "A general instrumental variable framework for regression analysis with outcome missing not at random," Biometrics, The International Biometric Society, vol. 73(4), pages 1123-1131, December.
    14. Antonio R. Linero, 2022. "Simulation‐based estimators of analytically intractable causal effects," Biometrics, The International Biometric Society, vol. 78(3), pages 1001-1017, September.
    15. Sinha, Sanjoy K. & Kaushal, Amit & Xiao, Wenzhong, 2014. "Inference for longitudinal data with nonignorable nonmonotone missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 77-91.
    16. E. Michael Foster & Grace Y. Fang, 2004. "Alternative Methods for Handling Attrition," Evaluation Review, , vol. 28(5), pages 434-464, October.
    17. Jason Roy & Michael J. Daniels, 2008. "A General Class of Pattern Mixture Models for Nonignorable Dropout with Many Possible Dropout Times," Biometrics, The International Biometric Society, vol. 64(2), pages 538-545, June.
    18. Jung, Hyekyung & Schafer, Joseph L. & Seo, Byungtae, 2011. "A latent class selection model for nonignorably missing data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 802-812, January.
    19. Mette Ejrnæs & Anders Holm, 2006. "Comparing Fixed Effects and Covariance Structure Estimators for Panel Data," Sociological Methods & Research, , vol. 35(1), pages 61-83, August.
    20. Bo Cai & David B. Dunson, 2006. "Bayesian Covariance Selection in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 62(2), pages 446-457, June.

    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:spr:sankhb:v:83:y:2021:i:1:d:10.1007_s13571-019-00222-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.