Analysis of repeated measures in clinical trials using summary statistics

This thesis is concerned with statistical methodology for randomized clinical trials with repeated measurements over time, as regards both data analysis and the implications for study design. The inherent within-subject dependencies for repeated measurements necessitate analyses that take account of their covariance structure. There exists a whole battery of methods for analysing repeated measures designs, ranging from very simple (e.g. separate t-tests at each time-point) to very complicated (e.g. multi-level models with arbitrary error structures), but I will focus on "the summary statistic approach" which has recently become increasingly popular. When interest centres around the average response to treatment over time, a logical choice of summary statistic is the mean of each subject's post-randomisation measurements, with appropriate adjustment for pre-treatment measurements. Among the class of "mean summary statistics" analysis of covariance (ANCOVA) is shown to be superior to its competitors. In particular, variance formulae are derived both under a general covariance structure and more specific cases (e.g. compound symmetry) , allowing direct comparisons of efficiency among different summary statistics and repeated measures designs. The importance of precise estimates of the pre-entry levels and the consequences for sample size requirements are emphasized. Some additional topics in relation to mean summary statistics, notably; the bias in estimation if pre-treatment means differ, the choice between additive or multiplicative models, and the summary statistic "area under the curve", are also investigated. For studies with restrictions on the range of baseline measurements the negative consequences incurred by "regression to the mean" are explored, especially regarding the variance for between-group comparisons. For a more general class of true treatment effects over time, the optimal linear summary statistic under any covariance structure is derived. Special interest is devoted to the case of linearly diverging mean treatment curves, where the optimal alternative to the comparison of slopes is defined. Asymptotic relative efficiencies are shown to be a useful tool when contrasting different designs and different summary statistics, both in the planning and reporting of repeated measures clinical trials. Finally, comparisons with other approaches are made, and recommendations given based on the need to balance theoretical considerations with practical matters.