Longitudinal data analysis in the modeling of unbalanced repeated measurements

Longitudinal studies are designs that involve repeated measurements of the same individuals over a period. They are used in clinical trials to assess the repeated variables' change on average population over time and the covariates' effects on that average change. Unequal number of measurements per subject causes extensive deliberations on the analysis of longitudinal data. The sequences of measurements from units within the study are incomplete, in the sense that intended measurements are not obtained. To handle the resulting unbalanced data structures, reasons for missingness and/or its relation to the research questions need to be considered. In this thesis firstly, for the balanced longitudinal data with irregularly spaced follow-ups, three longitudinal data methodologies were illustrated, i.e. random effects models with linear mixed models (LMM), Gaussian marginal models with spatial autocorrelation (SpA) and marginal models with generalized estimation equations (GEE). Steps of model building and parameter estimations under each model were presented. After figuring out the nature of balanced data; to create missingness, missing data generation scenarios were determined for each missing data mechanisms (MCAR, MAR and MNAR). For comparison purposes, three methodologies were repeated with available case approach onto three artificial incomplete longitudinal data sets. In addition to the available case approach, complete case analysis is also adopted when the missingness mechanism is MCAR. It turns out that for balanced longitudinal data, likelihood-based methods are similar to GEE with almost identical regression coefficients and slightly smaller standard errors. In that sense, GEE is robust against possible misspecification of within subject associations and has a simpler implementation of fitting marginal model. Likelihood-based methods provided parameter estimates with higher precision and are more elaborate in model building. Essential distinction between likelihood-based methods is that mixed models, in particular, use known covariance structure for unbalanced data while Gaussian marginal model with SpA has different classes of covariance structure derived from spatial statistics. When missingness mechanism is random, by means of reconstructing data and/or extending standart procedures, GEE and likelihood-based techniques resulted in parallel results with the ones retrieved from complete balanced data. When missingness mechanism is not random, likelihood-based techniques yielded some discrepancies on model selection steps and yielded biased parameter estimates. GEE analysis cannot be adapted onto MNAR data set. Lastly complete case analysis approach was applied to the data with cases having all measurements. Since this method suffers from loss of information, it resulted in biased estimates due to the reduction in sample size. Keywords: longitudinal studies, unbalanced data, covariance structure, model fitting, repeated measures