Abstract: In a clinical trial, treatment effects of multiple
endpoints can be either of overlapping (partially or completely) or of
non-overlapping nature, in the sense that a single or a group of multiple
endpoints is jointly able to explain or not able to explain a part or whole of
the treatment effect of an endpoint of interest. This information is useful in
assessing the total benefit of a treatment for a set of multiple endpoints of a
trial. An easy-to-understand measure for this purpose is the proportion of the
treatment effect (PTE) of a clinical endpoint explained by the treatment effects
of other endpoint(s) of interest. Conventionally, it is estimated by the ratio
of two statistics. However, this ratio estimate has been statistically
challenging for some applications as it can produce a wide confidence interval
beyond the interval and even the point estimate
may fall outside this interval. This article presents a bootstrapping based
measure using linear models and a simple bootstrapping based measure that avoid the weakness of
the conventional PTE measure. The former is a conditional probability measure
involving PTE and the latter one is an association measure between the induced
treatment effects of a clinical endpoint versus the part of it that is explained
by other endpoint(s) of interest. These measures can help in understanding the
nature of the treatment effects of multiple endpoints of a clinical trial, for
finding whether some of these treatment effects are of overlapping nature or of
independent nature in adding to the treatment benefit.
Keywords and phrases: PTE measure, multiple endpoints, association measures, surrogate endpoints, marginal model, conditional model, bootstrapping methods, meta-analysis.
