Estimating equations approaches to nuisance parameters and outcome-dependent sampling problems for marginal regression models and generalized linear mixed models when outcomes are correlated

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  • March 20, 2019
Creator
  • By, Kunthel
    • Affiliation: Gillings School of Global Public Health, Department of Biostatistics
Abstract
  • For marginal regression models having cluster-specific intercepts, the number of model parameters grows with the sample size so that GEE is not feasible. A solution is to impose a mixing distribution on the intercepts which leads to generalized linear mixed models (GLMMs) whose parameters have different interpretations than marginal models. When GLMM assumptions are not met, parameter estimates are generally biased. A simple procedure for constructing estimating equations is proposed that enables consistent estimation of parameters associated with cluster-varying covariates and is applicable regardless of whether the cluster-specific intercept is treated as fixed or random. The proposed procedure is shown to work for the identity and log links but not for the logit link. Connections to conditional likelihoods, the Cox model, projected score, and adjusted profile likelihoods are discussed. It is shown that our estimating equations can be implemented with minimal programming effort using existing software. We show that a connection exists between biased sampling based on cluster totals and regression models with cluster-specific intercepts. This connection leads naturally to our estimation procedure. Regression parameters associated with cluster-varying covariates can be consistently estimated using our estimating function even when sampling rates are unknown. An estimation procedure based on the double-pair design and an estimating function for a 1-1 matching design are shown to be special cases of our procedure. Risk ratio estimation is possible for case-control studies when family members are chosen as controls.
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  • In Copyright
Note
  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biostatistics."
Advisor
  • Qaqish, Bahjat
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Place of publication
  • Chapel Hill, NC
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  • Open access
Date uploaded
  • March 18, 2013

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