Effect size estimates from umbrella designs: Handling patients with a positive test result for multiple biomarkers using random or pragmatic subtrial allocation

Umbrella trials have been suggested to increase trial conduct efficiency when investigating different biomarker-driven experimental therapies. An overarching platform is used for patient screening and subsequent subtrial allocation according to patients' biomarker status. Two subtrial allocation schemes for patients with a positive test result for multiple biomarkers are (i) the pragmatic allocation to the eligible subtrial with the currently fewest included patients and (ii) the random allocation to one of the eligible subtrials. Obviously, the subtrials compete for such patients which are consequently underrepresented in the subtrials. To address questions of the impact of an umbrella design in general as well as with respect to subtrial allocation and analysis method, we investigate an umbrella trial with two parallel group subtrials and discuss generalisations. First, we analytically quantify the impact of the umbrella design with random allocation on the number of patients needed to be screened, the biomarker status distribution and treatment effect estimates compared to the corresponding gold standard of an independent parallel group design. Using simulations and real data, we subsequently compare both allocation schemes and investigate weighted linear regression modelling as possible analysis method for the umbrella design. Our results show that umbrella designs are more efficient than the gold standard. However, depending on the biomarker status distribution in the disease population, an umbrella design can introduce differences in estimated treatment effects in the presence of an interaction between treatment and biomarker status. In principle, weighted linear regression together with the random allocation scheme can address this difference though it is difficult to assess if such an approach is applicable in practice. In any case, caution is required when using treatment effect estimates derived from umbrella designs for e.g. future trial planning or meta-analyses.