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A robust joint modeling approach for longitudinal data with informative dropouts

Author

Listed:
  • Weiping Zhang

    (University of Science and Technology of China)

  • Feiyue Xie

    (University of Science and Technology of China)

  • Jiaxin Tan

    (University of Science and Technology of China)

Abstract

This article proposes a robust method for analysing longitudinal continuous responses with informative dropouts and potential outliers by using the multivariate t-distribution. We specify a dropout mechanism and a missing covariate distribution and incorporate them into the complete data log-likelihood. Unlike the existing approaches which mainly focus on the inference of regression mean and dropouts process, our approach aims to reveal the dynamics in the location function, marginal scale function and association by joint parsimonious modeling the location and dependence structure. A parametric fractional imputation algorithm is developed to speed up the computation associated with the EM algorithm for maximum likelihood estimation with missing data. The resulting estimators are shown to be consistent and asymptotically normally distributed. Data examples and simulations demonstrate the effectiveness of the proposed approach.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:4:d:10.1007_s00180-020-00972-6
    DOI: 10.1007/s00180-020-00972-6
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    References listed on IDEAS

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    1. Ibrahim, Joseph G. & Zhu, Hongtu & Tang, Niansheng, 2008. "Model Selection Criteria for Missing-Data Problems Using the EM Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1648-1658.
    2. 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.
    3. 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.
    4. Geert Verbeke & Geert Molenberghs & Herbert Thijs & Emmanuel Lesaffre & Michael G. Kenward, 2001. "Sensitivity Analysis for Nonrandom Dropout: A Local Influence Approach," Biometrics, The International Biometric Society, vol. 57(1), pages 7-14, March.
    5. Jae Kwang Kim, 2011. "Parametric fractional imputation for missing data analysis," Biometrika, Biometrika Trust, vol. 98(1), pages 119-132.
    6. Joseph Ibrahim & Geert Molenberghs, 2009. "Missing data methods in longitudinal studies: a review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 1-43, May.
    7. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    8. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    9. Joseph Ibrahim & Geert Molenberghs, 2009. "Rejoinder on: Missing data methods in longitudinal studies: a review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 68-75, May.
    10. Amy L. Stubbendick & Joseph G. Ibrahim, 2003. "Maximum Likelihood Methods for Nonignorable Missing Responses and Covariates in Random Effects Models," Biometrics, The International Biometric Society, vol. 59(4), pages 1140-1150, December.
    11. Fan, Jianqing & Huang, Tao & Li, Runze, 2007. "Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 632-641, June.
    12. Weiping Zhang & Chenlei Leng, 2012. "A moving average Cholesky factor model in covariance modelling for longitudinal data," Biometrika, Biometrika Trust, vol. 99(1), pages 141-150.
    13. Weiping Zhang & Chenlei Leng & Cheng Yong Tang, 2015. "A joint modelling approach for longitudinal studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 219-238, January.
    14. Jason Roy & Xihong Lin, 2005. "Missing Covariates in Longitudinal Data with Informative Dropouts: Bias Analysis and Inference," Biometrics, The International Biometric Society, vol. 61(3), pages 837-846, September.
    15. Fan, Jianqing & Wu, Yichao, 2008. "Semiparametric Estimation of Covariance Matrixes for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1520-1533.
    16. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    17. Mohsen Pourahmadi, 2007. "Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance--Correlation Parameters," Biometrika, Biometrika Trust, vol. 94(4), pages 1006-1013.
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    Cited by:

    1. Zhan Liu & Chun Yip Yau, 2022. "A propensity score adjustment method for longitudinal time series models under nonignorable nonresponse," Statistical Papers, Springer, vol. 63(1), pages 317-342, February.

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