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Marginal regression analysis of longitudinal data with time‐dependent covariates: a generalized method‐of‐moments approach

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  • Tze Leung Lai
  • Dylan Small

Abstract

Summary. We develop a new approach to using estimating equations to estimate marginal regression models for longitudinal data with time‐dependent covariates. Our approach classifies time‐dependent covariates into three types—types I, II and III. The type of covariate determines what estimating equations can be used involving the covariate. We use the generalized method of moments to make optimal use of the estimating equations that are made available by the covariates. Previous literature has suggested the use of generalized estimating equations with the independent working correlation when there are time‐dependent covariates. We conduct a simulation study that shows that our approach can provide substantial gains in efficiency over generalized estimating equations with the independent working correlation when a time‐dependent covariate is of types I or II, and our approach remains consistent and comparable in efficiency with generalized estimating equations with the independent working correlation when a time‐dependent covariate is of type III. We apply our approach to analyse the relationship between the body mass index and future morbidity among children in the Philippines.

Suggested Citation

  • Tze Leung Lai & Dylan Small, 2007. "Marginal regression analysis of longitudinal data with time‐dependent covariates: a generalized method‐of‐moments approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 79-99, February.
    • Handle: RePEc:bla:jorssb:v:69:y:2007:i:1:p:79-99
    DOI: 10.1111/j.1467-9868.2007.00578.x
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    References listed on IDEAS

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    1. Annie Qu & Bruce G. Lindsay, 2003. "Building adaptive estimating equations when inverse of covariance estimation is difficult," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 127-142, February.
    2. Bouis, Howarth E. & Haddad, Lawrence James, 1990. "Effects of agricultural commercialization on land tenure, household resource allocation, and nutrition in the Philippines:," Research reports 79, International Food Policy Research Institute (IFPRI).
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    Cited by:

    1. Martha Skup & Hongtu Zhu & Heping Zhang, 2012. "Multiscale Adaptive Marginal Analysis of Longitudinal Neuroimaging Data with Time-Varying Covariates," Biometrics, The International Biometric Society, vol. 68(4), pages 1083-1092, December.
    2. Geronimi, J. & Saporta, G., 2017. "Variable selection for multiply-imputed data with penalized generalized estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 103-114.
    3. Elsa Vazquez & Jeffrey R. Wilson, 2021. "Partitioned method of valid moment marginal model with Bayes interval estimates for correlated binary data with time-dependent covariates," Computational Statistics, Springer, vol. 36(4), pages 2701-2718, December.
    4. Benjamin French & Patrick J. Heagerty, 2009. "Marginal Mark Regression Analysis of Recurrent Marked Point Process Data," Biometrics, The International Biometric Society, vol. 65(2), pages 415-422, June.
    5. Denis Heng-Yan Leung & Dylan S. Small & Jing Qin & Min Zhu, 2013. "Shrinkage Empirical Likelihood Estimator in Longitudinal Analysis with Time-Dependent Covariates—Application to Modeling the Health of Filipino Children," Biometrics, The International Biometric Society, vol. 69(3), pages 624-632, September.

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