The analysis longitudinal binary data.

Longitudinal data modelling is complicated by the necessity to deal appropriately with the correlation between observations made on the same individual. A thorough examination of popular approaches to longitudinal analysis establishes the essential features of an effective longitudinal model. Building upon an earlier non-robust version proposed by Heagerty [20], our robust marginally specified generalized linear mixed model (ROBMS-GLMM) is successful in exhibiting such features. This type of model is one of the first to allow both population-averaged and individual specific inference. As well, this type of model adopts the flexibility and interpretability of generalized linear models for introducing dependence, but builds regression structure for the marginal mean, allowing valid application with time-independent and time-dependent covariates. These new estimators are obtained as solutions of a robustified likelihood equation involving Huber's least favorable distribution and a collection of weights. Huber's least favorable distribution produces estimates which are resistant to deviations from the random effects distributional assumptions. Innovative weighting strategies enable the ROBMS-GLMM to perform well when faced with outlying observations both in the response and covariates. A simulation study allows us to investigate the sampling properties of the ROBMS-GLMM estimates. We illustrate the methodology with an analysis of a prospective longitudinal study of laryngoscopic endotracheal intubation, a skill which numerous health care professionals are expected to acquire. We also look at data collected on pregnancies and births in Nova Scotia with interest in the smoking habits of the expectant mothers. Psychiatric data concerning an anti-depression drug is also used for demonstrative purposes. The principal goal of our research is to achieve robust inference in longitudinal analyses. Robust model testing strategies and asymptotics properties of the ROBMS-GLMMs are also of interest. A concurrent goal is to investigate and potentially alleviate some of the difficulties with current model fitting software.

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