A pairwise likelihood approach for longitudinal data with missing observations in both response and covariates

Missing observations occur commonly in longitudinal studies, and it has been documented that biased results could arise if such a feature is not properly accounted for in the analysis. A large body of methods handle missingness arising either from response components or covariate variables, but relatively little attention has been directed to addressing missingness in both response and covariate variables simultaneously. The sparsity of the research on this topic is partially attributed to substantially increased complexity of modeling and computational difficulty. In particular, the likelihood method may become infeasible in handling high dimensional data. This paper explores pairwise likelihood methods to handle longitudinal data with missing observations in both response and covariate variables. A unified framework based on bivariate normal distributions is invoked to accommodate various types of missing data patterns, including non-ignorable and non-monotone missingness. The performance of the proposed methods is assessed under a variety of circumstances. In particular, issues on efficiency and robustness are investigated. Longitudinal survey data from the Waterloo Smoking Prevention Project are analyzed with the proposed methods.