Generalized partially linear mixed-effects models incorporating mismeasured covariates

In this article we consider a semiparametric generalized mixed-effects model, and propose combining local linear regression, and penalized quasilikelihood and local quasilikelihood techniques to estimate both population and individual parameters and nonparametric curves. The proposed estimators take into account the local correlation structure of the longitudinal data. We establish normality for the estimators of the parameter and asymptotic expansion for the estimators of the nonparametric part. For practical implementation, we propose an appropriate algorithm. We also consider the measurement error problem in covariates in our model, and suggest a strategy for adjusting the effects of measurement errors. We apply the proposed models and methods to study the relation between virologic and immunologic responses in AIDS clinical trials, in which virologic response is classified into binary variables. A dataset from an AIDS clinical study is analyzed.     

Approximate Bayesian shrinkage estimation

A Bayesian shrinkage estimate for the mean in the generalized linear empirical Bayes model is proposed. The posterior mean under the empirical Bayes model has a shrinkage pattern. The shrinkage factor is estimated by using a Bayesian method with the regression coefficients to be fixed at the maximum extended quasi-likelihood estimates. This approach develops a Bayesian shrinkage estimate of the mean which is numerically quite tractable. The method is illustrated with a data set, and the estimate is compared with an earlier one based on an empirical Bayes method. In a special case of the homogeneous model with exchangeable priors, the performance of the Bayesian estimate is illustrated by computer simulations. The simulation result shows as improvement of the Bayesian estimate over the empirical Bayes estimate in some situations.     

Some Methods for Estimation in a Negative-Binomial Model

To clarify the advantage of using the quasilikelihood method, lack of robustness of the maximum likelihood method was demonstrated for the negative-binomial model. Efficiency calculations of the method of moments and the pseudolikelihood method in the estimation of extra-Poisson parameters in a negative-binomial model were carried out. Especially when the overdispersion parameter is small, both methods are relatively highly efficient and the pseudolikelihood estimate is more efficient than the method of moments estimate. Two examples of the quasilikelihood analyses of count data with overdispersion are given. The bootstrap method also is applied to the data to illustrate the advantage of the method of moments or pseudolikelihood method in the estimation of the standard errors of the mean parameter estimates under the negative-binomial model.