The general objective of the proposed research is to develop a battery of statistical methods for specific application to the design and statistical monitoring of complex clinical trials in cancer. In many of these clinical trials, the principal outcomes include measures of morbidity as well as mortality, and sometimes these measurements are recorded over time on each patient. The main research topic (1) focuses on the sequential monitoring of a Gaussian process which may not have independent increments. The test statistics used for the comparison of two groups of patients based upon either survival time or a series of repeated measures, when computed repeatedly during data monitoring, form a Gaussian process which is not necessarily Brownian Motion. Therefore, the classical group sequential methods can not be applied directly. To monitor such processes, we propose to use the Lan-DeMets approach with a surrogate measure for information. We first consider (a) the implementation of a group sequential design in clinical trials when the response variable is time-to-event. In this case we will search for the most appropriate surrogate information for the Wilcoxon statistic, and then consider other two-sample linear rank statistics as well. In (b), we will consider the case of longitudinal data where the response variable is . measured repeatedly over time, and where such data are analyzed using linear or nonlinear models. We would like to investigate the effect of modelling on the choice of surrogate information. Two additional proposed topics are: (2) Uses of conditional power in a two-stage design; (3) Implication of Halperin's definition of the multiple comparison problem. Additional research topics will be identified as work proceeds on these projects, and in response to the discussions with our collaborators.
