| This manuscript includes three different topics in missing data and causality:;1) Aphasia is the loss of the ability to produce and/or comprehend language due to injury to brain areas responsible for these functions. This study modeled the way aphasic patients process different sentence types, as well as their ability to accomplish tasks using Rasch models. However, several features of the data were found to be inadequately captured by such models. We proposed a full Bayesian approach, exploring a mixture of generalized linear mixed models. The mixture model was a better fit than other models and showed that aphasic patients can be classified into different ability and response profile groups, and that patients utilize different cognitive resources in different comprehension tasks.;2) End-of-life medical expenses are a significant proportion of health care expenditures. These expenditures were studied using cost-of-services from Medicare claims and cause of death from death certificates. In the absence of a unique identifier linking the two datasets, common variables identified unique matches for only 33% of deaths. The remaining cases formed cells with multiple cases. We sampled from the joint posterior distribution of model parameters and the permutations that link cases from the two files within each cell. The procedure generated m datasets which were analyzed independently and results combined using Rubin's multiple imputation rules. Our approach can be applied to other file linking applications.;3) The estimation of population treatment effects is a subject of extensive research. In cases where additional covariates that affect the outcome exist, estimation of the effects is controlled (adjusted) by using a model that combines an indicator for the treatment and a function of the covariates in an additive manner. This model relies on the assumption that the response surfaces of the outcome given the covariates are parallel in both treatment groups. When this assumption is incorrect, the resulting estimate of the treatment effect generally gives unreliable inferences. In observational studies, the effect of this assumption is significant. We propose a three-stage procedure that is based on Rubin's Causal Model. Simulation analyses comparing this procedure to other methods are also conducted. |
