Group sequential procedures for multiple comparison of rates of change

Group sequential methods find a particular field of application in clinical trials because patient recruitment is by nature sequential. It is important to minimize the number of patients exposed to an inferior treatment. Moreover, the experimenter is required to monitor the data on a few occasions during the trial to check for toxicity or other unsuspected harmful side-effects. These intermediate analyses may reveal a significant superiority of one treatment, resulting in an early termination of the trial, but only a sequential design allows for such early termination. The availability of fast and efficient algorithms for estimating parameters of multivariate distributions (e.g. Expectation Maximization or Newton-Raphson algorithms) and for computing multivariate normal probabilities opens new frontiers by allowing complex but very flexible experimental designs for the comparison of several treatments. Using these powerful tools, together with the concept of spending function, flexible procedures for multiple comparison of treatments have been designed. In 1991, Lee and DeMets (Journal of the American Statistical Association 86, 757-62) proposed a group sequential procedure for comparing the rates of change of two treatments. Our work generalizes their model, a linear mixed effects model with repeated measurements, to several treatments. We derive group sequential procedures for comparing the rates of change of several treatments to a control while controlling the overall significance level, or more generally, comparing general contrasts of changes of several treatments while controlling the overall significance level, and studying and comparing data-dependent allocation rules and strategies for assigning patients to treatments. These procedures and algorithms are applied to real and simulated data. The importance of this work lies in the fact that quite often in clinical trials, we compare the effects of more than one treatment or the effects of different doses of the same treatment. Here we provide flexible procedures for multiple comparisons to the medical experimenter. With these procedures, the number and times of interim analyses need not be specified in advance, missing observations can be handled, and the experimenter can freely choose which treatment effects to test at any time he wishes. The overall significance level of the tests is controlled. Moreover algorithms for the execution of these procedures are provided. This study tries to open avenues of further theoretical and numerical studies in multiple comparisons, a field which has a long history in theoretical and applied statistics and which recently has seen vigorous new developments to which the above-described research contributes.