Optimal trial design selection: a comparative analysis between two-arm and three-arm trials incorporating network meta-analysis for evaluating a new treatment

Planning the design of a new trial comparing two treatments already in a network of trials with an a-priori plan to estimate the effect size using a network meta-analysis increases power or reduces the sample size requirements. However, when the comparison of interest is between a treatment already in the existing network (old treatment) and a treatment that hasn’t been studied previously (new treatment), the impact of leveraging information from the existing network to inform trial design has not been extensively investigated. We aim to identify the most powerful trial design for a comparison of interest between an old treatment A and a new treatment Z, given a fixed total sample size. We consider three possible designs: a two-arm trial between A and Z (’direct two-arm’), a two-arm trial between another old treatment B and Z (’indirect two-arm’), and a three-arm trial among A, B, and Z.

We compare the standard error of the estimated effect size between treatments A and Z for each of the three trial designs using formulas. For continuous outcomes, the direct two-arm trial always has the largest power, while for a binary outcome, the minimum variances among the three trial designs are conclusive only when \(p_A(1-p_A) \ge p_B(1-p_B)\). Simulation studies are conducted to demonstrate the potential for the indirect two-arm and three-arm trials to outperform the direct two-arm trial in terms of power under the condition of \(p_A(1-p_A) < p_B(1-p_B)\).

Based on the simulation results, we observe that the indirect two-arm and three-arm trials have the potential to be more powerful than a direct two-arm trial only when \(p_A(1-p_A) < p_B(1-p_B)\). This power advantage is influenced by various factors, including the risk of the three treatments, the total sample size, and the standard error of the estimated effect size from the existing network meta-analysis.

The standard two-arm trial design between two treatments in the comparison of interest may not always be the most powerful design. Utilizing information from the existing network meta-analysis, incorporating an additional old treatment into the trial design through an indirect two-arm trial or a three-arm trial can increase power.