Regression analysis of longitudinal data with irregular and informative observation times

In longitudinal data analyses, the observation times are often assumed to be independent of the outcomes. In applications in which this assumption is violated, the standard inferential approach of using the generalized estimating equations may lead to biased inference. Current methods require the correct specification of either the observation time process or the repeated measure process with a correct covariance structure. In this article, we construct a novel pairwise likelihood method for longitudinal data that allows for dependence between observation times and outcomes. This method investigates the marginal covariate effects on the repeated measure process, while leaving the probability structure of the observation time process unspecified. The novelty of this method is that it yields consistent estimator of the marginal covariate effects without specification of the observation time process or the covariance structure of the repeated measures process. Large sample properties of the regression coefficient estimates and a pairwise likelihood ratio test procedure are established. Simulation studies demonstrate that the proposed method performs well in finite samples. An analysis of weight loss data from a web-based program is presented to illustrate the proposed method.

A robust method for finely stratified familial studies with proband-based sampling

This paper presents a robust method to conduct inference in finely stratified familial studies under proband-based sampling. We assume that the interest is in both the marginal effects of subject-specific covariates on a binary response and the familial aggregation of the response, as quantified by intrafamilial pairwise odds ratios. We adopt an estimating function for proband-based family studies originally developed by Zhao and others (1998) in the context of an unstratified design and treat the stratification effects as fixed nuisance parameters. Our method requires modeling only the first 2 joint moments of the observations and reduces by 2 orders of magnitude the bias induced by fitting the stratum-specific nuisance parameters. An analytical standard error estimator for the proposed estimator is also provided. The proposed approach is applied to a matched case-control familial study of sleep apnea. A simulation study confirms the usefulness of the approach.

Generalization of the Mantel-Haenszel Estimating Function for Sparse Clustered Binary Data

We extend the Mantel-Haenszel estimating function to estimate both the intra-cluster pairwise correlation and the main effects for sparse clustered binary data. We propose both a composite likelihood approach and an estimating function approach for the analysis of such data. The proposed estimators are consistent and asymptotically normally distributed. Simulation results demonstrate that the two approaches are comparable in terms of bias and efficiency; however, the estimating equation approach is computationally simpler. Analysis of the Georgia High Blood Pressure survey is used for illustration.