| Summary: | This thesis discusses issues arising in the analysis of repeated measurement studies with missing data. The first part of the thesis is motivated by a study where continuous and bounded longitudinal data form the outcome of interest. The aim of this study is to investigate the change over time in the outcome variable and factors that influence this change. The analysis is complicated because some patients withdraw from the study, leading to an incomplete data set. We propose a non-linear mixed model that specifies the rate of change and the bounds of the outcome as a function of covariates. This mixed model has advantages over transforming the data and is easy to interpret. We discuss different models for the covariance structure of bounded continuous longitudinal data. To explore the impact of missingness, we perform several sensitivity analyses. Further, we propose a model for informative missingness, taking into account the number and nature of reminders made to contact initial non-responders, and evaluate the impact of missingness on estimates of change. We contrast this model with the traditional selection model, where the missingness process is modelled. Our investigations suggest that using the richer information of the reminder process enables a more accurate choice of covariates which induce missingness, than modelling the missingness process. Regarding the reminder process, we observe that phone calls are most effective. The second part of this thesis is motivated by dose-finding studies, where the number of events per subject within a specified study period form the primary outcome. These studies aim to identify a target dose for which the new drug can be shown to be as effective as a competitor medication. Given a pain-related outcome, we expect many patients to drop out before the end of the study. The impact of missingness on the analysis and models for the missingness process must be carefully considered. The recurrent events are modelled as over-dispersed Poisson process data, with dose as regressor. Additional covariates may be included. Constant and time-varying rate functions are examined. Based on a range of such models, the impact of missingness on the precision of the target dose estimation is evaluated by simulations. Five different analysis methods are assessed: a complete case analysis; two analyses using different single imputation techniques; a direct likelihood analysis; and an analysis using pattern-mixture models. The target dose estimation is robust if the same missingness process holds for the target dose group and the active control group. This robustness is lost as soon as the missingness mechanisms for the active control and the target dose differ. Of the methods explored, the direct-likelihood approach performs best, even when a missing not at random mechanism holds.
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