Markov chain marginal bootstrap for generalized estimating equations

Longitudinal data are characterized by repeated measures over time on each subject. The generalized estimating equations (GEE) approach (Liang and Zeger, 1996) has been widely used for the analysis of longitudinal data. The ordinary GEE approach can be robustified through the use of truncated robust estimating functions. Statistical inference on the robust GEE is often based on the asymptotic normality of the estimators, and the asymptotic variance-covariance of the regression parameter estimates can be obtained from a sandwich formula. However, this asymptotic variance-covariance matrix may depend on unknown error density functions. Direct estimation of this matrix can be difficult and unreliable since it depends quite heavily on the nonparametric density estimation. Resampling methods provide an alternative way for estimating the variance of the regression parameter estimates. In this thesis, we extend the Markov chain marginal bootstrap (MCMB) (He and Hu, 2002) to statistical inference for robust GEE estimators with longitudinal data, allowing the estimating functions to be non-smooth and the responses correlated within subjects. By decomposing the problem into one-dimensions and solving the marginal estimating equations at each step instead of solving a p--dimensional system of equations, the MCMB method renders more control to the problem and offers advantages over traditional bootstrap methods for robust GEE estimators where the estimating equation may not be easy to solve. Empirical investigations show favorable performance of the MCMB method in accuracy and reliability compared with the traditional way of inference by direct estimation of the asymptotic variance-covariance.