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Conditional estimation for generalized linear models when covariates are subject-specific parameters in a mixed model
Erning Li1, Daowen Zhang, Marie Davidian
1Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, USA.
Biometrics
|March 23, 2004
Summary
This study introduces new statistical methods for analyzing longitudinal data, improving generalized linear model (GLM) inference without assuming random effect distributions. This enhances the reliability of results in health studies.
Area of Science:
- Biostatistics
- Longitudinal Data Analysis
- Statistical Modeling
Background:
- Generalized linear models (GLM) are used to analyze relationships between primary endpoints and longitudinal data.
- Subject-specific random effects in linear mixed models are often used for longitudinal measurements.
- Naive imputation methods can lead to biased inference in these models.
Purpose of the Study:
- To develop robust statistical estimators for GLM parameters in longitudinal studies.
- To address bias in inference caused by subject-specific random effects.
- To propose methods that do not rely on parametric assumptions about random effects distributions.
Main Methods:
- Adapting the Stefanski and Carroll (1987) strategy.
- Developing novel estimators for GLM parameters.
- Utilizing methods that ensure consistent inference regardless of the random effects distribution.
Main Results:
- The proposed estimators yield consistent inference without distributional assumptions on random effects.
- The methods reduce bias compared to naive imputation techniques.
- Simulations and a bone mineral density study demonstrate the effectiveness of the approach.
Conclusions:
- The developed methods offer a reliable alternative for analyzing longitudinal data within a GLM framework.
- These techniques provide unbiased and consistent inference, crucial for observational health studies.
- The approach is applicable to various continuous response longitudinal profiles.