# The Epidemiologic Comparison of Two Correlated Relative Risks: A Simple but Efficient Clinical Trial Design for Assessing Risk-Reduction and Treatment Significance

## TL;DR

This paper introduces a clinical trial design that compares two treatments using a shared control group, reducing study time and costs while accurately assessing risk reduction.

## Contribution

A novel method for comparing two correlated relative risks using a shared control group in clinical trials.

## Key findings

- Using shared controls reduces study time and costs in platform trials.
- Multiplicity adjustment is unnecessary on the log-difference scale for three-group designs.
- The method is illustrated with a practical example on LDL-C statin risk reduction.

## Abstract

In the context of platform design, umbrella trials are a type of master protocol in which multiple treatments are randomized and evaluated with respect to a common, referent-control arm. In a simplified (1:1:1), non-adapted case, this is equivalent to the epidemiologic comparison of two correlated relative risks for assessing risk-reduction on the log-difference scale. The use of shared controls has the potential to reduce study time and costs but infers greater complexity to account for the covariance between relative effect estimates (i.e., dependence arising because treatment arms use the same referent group). Multiplicity adjustment is unnecessary on the log-difference scale (three-group design) as this is a single test statistic for interaction. An intuitive, risk-reduction (LDL-C statin) example is presented to illustrate the practical application of this method.