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Robust analysis of longitudinal data with nonignorable missing responses

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  • Sanjoy Sinha

Abstract

We encounter missing data in many longitudinal studies. When the missing data are nonignorable, it is important to analyze the data by incorporating the missing data mechanism into the observed data likelihood function. The classical maximum likelihood (ML) method for analyzing longitudinal missing data has been extensively studied in the literature. However, it is well-known that the ordinary ML estimators are sensitive to extreme observations or outliers in the data. In this paper, we propose and explore a robust method, which is developed in the framework of the ML method, and is useful for downweighting any influential observations in the data when estimating the model parameters. We study the empirical properties of the robust estimators in small simulations. We also illustrate the robust method using incomplete longitudinal data on CD4 counts from clinical trials of HIV-infected patients. Copyright Springer-Verlag 2012

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  • Sanjoy Sinha, 2012. "Robust analysis of longitudinal data with nonignorable missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 913-938, October.
    • Handle: RePEc:spr:metrik:v:75:y:2012:i:7:p:913-938
    DOI: 10.1007/s00184-011-0359-3
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    References listed on IDEAS

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    1. Dantan Etienne & Proust-Lima Cécile & Letenneur Luc & Jacqmin-Gadda Helene, 2008. "Pattern Mixture Models and Latent Class Models for the Analysis of Multivariate Longitudinal Data with Informative Dropouts," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-26, July.
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    3. John S. Preisser & Bahjat F. Qaqish, 1999. "Robust Regression for Clustered Data with Application to Binary Responses," Biometrics, The International Biometric Society, vol. 55(2), pages 574-579, June.
    4. Roderick J. A. Little, 1988. "Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(1), pages 23-38, March.
    5. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    6. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
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    Cited by:

    1. Yu-Ye Zou & Han-Ying Liang & Jing-Jing Zhang, 2015. "Nonlinear wavelet density estimation with data missing at random when covariates are present," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 967-995, November.
    2. Xia, Ye-Mao & Tang, Nian-Sheng & Gou, Jian-Wei, 2016. "Generalized linear latent models for multivariate longitudinal measurements mixed with hidden Markov models," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 259-275.

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