Statistical methods for handling incomplete longitudinal data with emphasis on discrete outcomes with application.

Abstract

In longitudinal studies, measurements are taken repeatedly over time on the same ex- perimental unit. These measurements are thus correlated. The variances in repeated measures change with respect to time. Therefore, the variations together with the po- tential correlation patterns produce a complicated variance structure for the measures. Standard regression and analysis of variance techniques may result into invalid inference because they entail some mathematical assumptions that do not hold for repeated mea- sures data. Coupled with the repeated nature of the measurements, these datasets are often imbal- anced due to missing data. Methods used should be capable of handling the incomplete nature of the data, with the ability to capture the reasons for missingness in the analysis. This thesis seeks to investigate and compare analysis methods for incomplete correlated data, with primary emphasis on discrete longitudinal data. The thesis adopts the general taxonomy of longitudinal models, including marginal, random e ects, and transitional models. Although the objective is to deal with discrete data, the thesis starts with one continu- ous data case. Chapter 2 presents a comparative analysis on how to handle longitudinal continuous outcomes with dropouts missing at random. Inverse probability weighted generalized estimating equations (GEEs) and multiple imputation (MI) are compared. In Chapter 3, the weighted GEE is compared to GEE after MI (MI-GEE) in the analy- sis of correlated count outcome data in a simulation study. Chapter 4 deals with MI in the handling of ordinal longitudinal data with dropouts on the outcome. MI strategies, namely multivariate normal imputation (MNI) and fully conditional speci cation (FCS) are compared both in a simulation study and a real data application. In Chapter 5, still focussing on ordinal outcomes, the thesis presents a simulation and real data ap- plication to compare complete case analysis with advanced methods; direct likelihood analysis, MNI, FCS and ordinal imputation method. Finally, in Chapter 6, cumulative logit ordinal transition models are utilized to investigate the inuence of dependency of current incomplete responses on past responses. Transitions from one response state to another over time are of interest.