Longitudinal data consists of repeated measurements taken over time for each experimental unit or subject, and is frequently observed in clinical trials. Often, in longitudinal trials, observations of a given subject may terminate before the end of the study. The experimental unit (or subject) engaged in such an event is often referred to as a drop-out. Drop-outs, or missing observations, are common and frequently unavoidable phenomena associated with longitudinal trials even in well-designed experiments, and it is an important issue in the analysis of longitudinal data. In the presence of drop-outs, analysis and interpretation of longitudinal data using standard methods that do not take into account the drop-out events may lead to erroneous statistical analysis and flawed conclusions. In recent years, significant attention has been paid in the literature to treating this problem, focusing primarily on building an appropriate model for the drop-out mechanism. In the present work, monotone drop-out events and balanced design are considered. Following some previous work in this area, the proposed model consists of two parts: the measurement process and the drop-out process. A multivariate linear regression model with two-stage random effects was applied to the measurement process, while a semiparametric logistic regression with a linear combination of thin-plate basis functions was implemented for the drop-out process. Both models were simultaneously estimated via a hybrid Markov Chain Monte Carlo (MCMC) method. Several variations of the model describing the drop-out process were considered, and comparisons were made between their relative performances. The applications of the models illustrate the effect of current and past measurements on the likelihood of drop-out, and the models are used to provide practical interpretation of the underlying drop-out mechanism.
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