Closed testing procedures for group sequential clinical trials with multiple endpoints

A simple approach is given for conducting closed testing in clinical trials with multiple endpoints in which group sequential monitoring is planned. The approach allows a flexible stopping time; the earliest and latest stopping times are described. The paradigm is applicable both to clinical trials with multiple endpoints and to the one-sided multiple comparison problem of several treatments versus a control. The approach leads to enhancements of previous methods and suggestions for new methods. An example of a respiratory disease trial with four endpoints is given.

Classification of the effectiveness of combination treatments

According to FDA regulations, a combination drug is not efficacious unless each component contributes to the claimed effects. For a univariate endpoint, this implies that the combination at specific doses must be superior to each of its components at the same doses. More demanding is the property of synergy, in which the effect of the combination must be superior to the effect expected based on those of its components. If it is equal to those effects, it is additive, and if it is inferior, it is antagonistic. We give regions in the combination dose plane where these concepts are well defined. If the effect of the combination is greater than the greatest effect achievable by any of its components it is therapeutically synergistic. A combination can be antagonistic, yet its components can still contribute to the claimed effects. If it is additive, synergistic or therapeutically synergistic, its components must contribute to the claimed effects. We relate these concepts and provide designs and sequential procedures for determining whether a combination is therapeutically synergistic, synergistic, additive, antagonistic and contributing or antagonistic and non-contributing.

On the design and analysis of randomized clinical trials with multiple endpoints

This paper considers some methods for reducing the number of significance tests undertaken when analyzing and reporting results of clinical trials. Emphasis is placed on designing and analyzing clinical trials to examine a composite hypothesis concerning multiple endpoints and combining this multiple endpoint methodology with group sequential methodology. Four methods for composite hypotheses are considered: an ordinary least squares and a generalized least squares approach both due to O'Brien (1984, Biometrics 40, 1079-1087), a new modification of these, and an approximate likelihood ratio test, due to Tang, Gnecco, and Geller (1989, Biometrika 76, 577-583). These are extended for group sequential use. In particular, simulation is used to generate critical values and sequences of nominal significance levels for the approximate likelihood ratio test, which is not normally distributed. An example is given and the relative merits of the suggested approaches are discussed.