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Joint generalized estimating equations for multivariate longitudinal binary outcomes with missing data: an application to acquired immune deficiency syndrome data

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  • Stuart R. Lipsitz
  • Garrett M. Fitzmaurice
  • Joseph G. Ibrahim
  • Debajyoti Sinha
  • Michael Parzen
  • Steven Lipshultz

Abstract

Summary. In a large, prospective longitudinal study designed to monitor cardiac abnormalities in children born to women who are infected with the human immunodeficiency virus, instead of a single outcome variable, there are multiple binary outcomes (e.g. abnormal heart rate, abnormal blood pressure and abnormal heart wall thickness) considered as joint measures of heart function over time. In the presence of missing responses at some time points, longitudinal marginal models for these multiple outcomes can be estimated by using generalized estimating equations (GEEs), and consistent estimates can be obtained under the assumption of a missingness completely at random mechanism. When the missing data mechanism is missingness at random, i.e. the probability of missing a particular outcome at a time point depends on observed values of that outcome and the remaining outcomes at other time points, we propose joint estimation of the marginal models by using a single modified GEE based on an EM‐type algorithm. The method proposed is motivated by the longitudinal study of cardiac abnormalities in children who were born to women infected with the human immunodeficiency virus, and analyses of these data are presented to illustrate the application of the method. Further, in an asymptotic study of bias, we show that, under a missingness at random mechanism in which missingness depends on all observed outcome variables, our joint estimation via the modified GEE produces almost unbiased estimates, provided that the correlation model has been correctly specified, whereas estimates from standard GEEs can lead to substantial bias.

Suggested Citation

  • Stuart R. Lipsitz & Garrett M. Fitzmaurice & Joseph G. Ibrahim & Debajyoti Sinha & Michael Parzen & Steven Lipshultz, 2009. "Joint generalized estimating equations for multivariate longitudinal binary outcomes with missing data: an application to acquired immune deficiency syndrome data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 3-20, January.
    • Handle: RePEc:bla:jorssa:v:172:y:2009:i:1:p:3-20
    DOI: 10.1111/j.1467-985X.2008.00564.x
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    References listed on IDEAS

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    1. D. R. Cox, 1972. "The Analysis of Multivariate Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 113-120, June.
    2. Garrett M. Fitzmaurice & Stuart R. Lipsitz & Geert Molenberghs & Joseph G. Ibrahim, 2001. "Bias in Estimating Association Parameters for Longitudinal Binary Responses with Drop‐Outs," Biometrics, The International Biometric Society, vol. 57(1), pages 15-21, March.
    3. Stuart R. Lipsitz & Geert Molenberghs & Garrett M. Fitzmaurice & Joseph Ibrahim, 2000. "GEE with Gaussian Estimation of the Correlations When Data Are Incomplete," Biometrics, The International Biometric Society, vol. 56(2), pages 528-536, June.
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    Cited by:

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    2. Thomas Suesse & Ivy Liu, 2013. "Modelling Strategies for Repeated Multiple Response Data," International Statistical Review, International Statistical Institute, vol. 81(2), pages 230-248, August.
    3. G. Inan & R. Yucel, 2017. "Joint GEEs for multivariate correlated data with incomplete binary outcomes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 1920-1937, August.
    4. Clemontina A. Davenport & Arnab Maity & Patrick F. Sullivan & Jung-Ying Tzeng, 2018. "A Powerful Test for SNP Effects on Multivariate Binary Outcomes Using Kernel Machine Regression," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(1), pages 117-138, April.
    5. Manuel Gomes & Edmond S.-W. Ng & Richard Grieve & Richard Nixon & James Carpenter & Simon G. Thompson, 2012. "Developing Appropriate Methods for Cost-Effectiveness Analysis of Cluster Randomized Trials," Medical Decision Making, , vol. 32(2), pages 350-361, March.
    6. Ângela Jornada Ben & Johanna M. Dongen & Mohamed El Alili & Martijn W. Heymans & Jos W. R. Twisk & Janet L. MacNeil-Vroomen & Maartje Wit & Susan E. M. Dijk & Teddy Oosterhuis & Judith E. Bosmans, 2023. "The handling of missing data in trial-based economic evaluations: should data be multiply imputed prior to longitudinal linear mixed-model analyses?," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 24(6), pages 951-965, August.

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