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Using auxiliary data for parameter estimation with non‐ignorably missing outcomes

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  • Joseph G. Ibrahim
  • Stuart R. Lipsitz
  • Nick Horton

Abstract

We propose a method for estimating parameters in generalized linear models when the outcome variable is missing for some subjects and the missing data mechanism is non‐ignorable. We assume throughout that the covariates are fully observed. One possible method for estimating the parameters is maximum likelihood with a non‐ignorable missing data model. However, caution must be used when fitting non‐ignorable missing data models because certain parameters may be inestimable for some models. Instead of fitting a non‐ignorable model, we propose the use of auxiliary information in a likelihood approach to reduce the bias, without having to specify a non‐ignorable model. The method is applied to a mental health study.

Suggested Citation

  • Joseph G. Ibrahim & Stuart R. Lipsitz & Nick Horton, 2001. "Using auxiliary data for parameter estimation with non‐ignorably missing outcomes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 361-373.
    • Handle: RePEc:bla:jorssc:v:50:y:2001:i:3:p:361-373
    DOI: 10.1111/1467-9876.00240
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    Citations

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    Cited by:

    1. Dan Jackson & Ian R. White & Morven Leese, 2010. "How much can we learn about missing data?: an exploration of a clinical trial in psychiatry," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(3), pages 593-612, July.
    2. Liang, Hua, 2008. "Generalized partially linear models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 880-895, May.
    3. Wang Miao & Eric J. Tchetgen Tchetgen, 2016. "On varieties of doubly robust estimators under missingness not at random with a shadow variable," Biometrika, Biometrika Trust, vol. 103(2), pages 475-482.
    4. Bindele, Huybrechts F. & Nguelifack, Brice M., 2019. "Generalized signed-rank estimation for regression models with non-ignorable missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 14-33.
    5. Baojiang Chen & Xiao-Hua Zhou, 2011. "Doubly Robust Estimates for Binary Longitudinal Data Analysis with Missing Response and Missing Covariates," Biometrics, The International Biometric Society, vol. 67(3), pages 830-842, September.
    6. Lei Wang & Wei Ma, 2021. "Improved empirical likelihood inference and variable selection for generalized linear models with longitudinal nonignorable dropouts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 623-647, June.
    7. Shonosuke Sugasawa & Kosuke Morikawa & Keisuke Takahata, 2022. "Bayesian semiparametric modeling of response mechanism for nonignorable missing data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 101-117, March.
    8. Yoshiharu Takagi & Yutaka Kano, 2019. "Bias reduction using surrogate endpoints as auxiliary variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 837-852, August.
    9. 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.

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