Is 1:1 Always Most Powerful? Why Careful Determination of Allocation Ratios Matters in Trial Design

TL;DR

This paper challenges the default use of 1:1 allocation in randomized trials, demonstrating that unequal ratios can enhance power and benefit participants, especially when outcome variances differ.

Contribution

It provides theoretical insights and case studies showing the advantages of optimized unequal allocation strategies over traditional equal randomization.

Findings

Unequal allocation can maintain or improve statistical power.

Optimized ratios increase the number of patients receiving better treatments.

Power gains are observed in both binary and continuous outcome trials.

Abstract

The principle of allocating an equal number of patients to each arm in a randomized controlled trial remains widely believed to be optimal for maximising statistical power. However, this long-held belief only holds true if the treatment groups have equal outcome variances, a condition that is often not met or, is simply not assessed in practice. This paper reasserts the fact that a departure from a 1:1 ratio can maintain or improve statistical power while increasing the benefits to participants. The benefit is particularly self-evident for binary and time-to-event endpoints, where variances are determined by the assumed success or event rates. To illustrate this, we present two case studies: a small-scale metastatic melanoma trial with a binary endpoint and a larger trial evaluating virtual reality for pain reduction with a continuous endpoint. Our simulations compare equal randomisation, preplanned fixed unequal randomisation, and response-adaptive randomisation targeting Neyman allocation. Results show that unequal allocation can increase the proportion of patients receiving the superior treatment without reducing power, with modest power gains observed in both binary and continuous settings, highlighting the practical relevance of optimised allocation strategies across trial types and sizes.