Model selection of generalized estimating equations with multiply imputed longitudinal data

Abstract

Longitudinal data often encounter missingness with monotone and/or intermittent missing patterns. Multiple imputation (MI) has been popularly employed for analysis of missing longitudinal data. In particular, the MI-GEE method has been proposed for inference of generalized estimating equations (GEE) when missing data are imputed via MI. However, little is known about how to perform model selection with multiply imputed longitudinal data. In this work, we extend the existing GEE model selection criteria, including the "quasi-likelihood under the independence model criterion" (QIC) and the "missing longitudinal information criterion" (MLIC), to accommodate multiple imputed datasets for selection of the MI-GEE mean model. According to real data analyses from a schizophrenia study and an AIDS study, as well as simulations under nonmonotone missingness with moderate proportion of missing observations, we conclude that: (i) more than a few imputed datasets are required for stable and reliable model selection in MI-GEE analysis; (ii) the MI-based GEE model selection methods with a suitable number of imputations generally perform well, while the naive application of existing model selection methods by simply ignoring missing observations may lead to very poor performance; (iii) the model selection criteria based on improper (frequentist) multiple imputation generally performs better than their analogies based on proper (Bayesian) multiple imputation.

Generalized Estimating Equations in Longitudinal Data Analysis: A Review and Recent Developments

“…Until now, novel methodologies are still needed and being developed due to the increasing usage and potential Advances in Statistics 7 theoretical constraints of GEE as well as new challenges emerging from practical applications in clinical trials or biomedical studies. In addition, current research of interest related to GEE also includes a robust and optimal model selection criterion of GEE under missing at random (MAR) or missing not at random (MNAR) [93,94], sample size/power calculation for correlated sparse or overdispersion count data or longitudinal data with small sample [57][58][59][60], GEE with improved performance under the situations with informative cluster size and/or MAR and/or small sample size [95][96][97][98], and GEE for high-dimensional longitudinal data [99]. Although GEE has attractive features, flexible application, and easy implementation in software, the application in practice should be cautious depending on the context of study design or data structure and the goals of research interest.…”

Childhood polybrominated diphenyl ether (PBDE) exposure and neurobehavior in children at 8 years

“…We estimated βs and 95% confidence intervals (CIs) for BDE-28, -47, -99, -100, -153, and ΣPBDEs with separate multiple informant models for each of the 100 imputed datasets. Final estimates for PBDEs were an average of the 100 results from imputed datasets (Beunckens et al, 2008; Shen and Chen, 2013) and are presented for ages 1, 2, 3, 5, and 8 years, because several interaction terms between PBDEs (continuous) and age (categorical) were statistically significant ( p <0.10).…”

Variable selection in the presence of missing data: imputation‐based methods

“…Their strategies do not work for high-dimensional data with n < p. Similar strategies have also been adopted for analysis of longitudinal data in the presence of missing data, where generalized estimating equations (GEE) 24 for longitudinal data analysis are used. Shen and Chen 25 focused on the model selection criteria by extending the quasi-likelihood under the independence model criterion (QIC) 26 and the missing longitudinal information criterion (MLIC), 27 to the context of MI when a specific model was applied across L MI datasets. Specifically, they proposed to use the average QIC or MLIC values across all L imputed datasets to conduct variable selection.…”