# Adaptive multicenter designs for continuous response clinical trials in the presence of an unknown sensitive subgroup

## TL;DR

This paper proposes adaptive multicenter clinical trial designs that identify sensitive subgroups with continuous responses without prior markers, using mixture models and simple optimization, applicable to real-world drug response studies.

## Contribution

It introduces novel adaptive RCT designs capable of detecting unknown sensitive subgroups based solely on response data, extending to multicenter trials with efficient numerical methods.

## Key findings

- Designs successfully identify sensitive subgroups in simulated scenarios.
- Extension to multicenter trials using Hochberg's step-up procedure.
- Avoids extensive simulations with simple optimization techniques.

## Abstract

The partial effectiveness of drugs is of importance to the pharmaceutical industry. Randomized controlled trials (RCTs) assuming the existence of a subgroup sensitive to the treatment are already used. These designs, however, are available only if there is a known marker for identifying subjects in the subgroup. In this paper we investigate a model in which the response in the treatment group $Z^T$ has a two-component mixture density $(1-p)\mathcal N(\mu^C, \sigma^2)+p\mathcal N(\mu^T, \sigma^2)$ representing the treatment responses of \emph{placebo responders} and \emph{drug responders}. The treatment-specific effect is $\mu = \frac{\mu^T-\mu^C}{\sigma}$ and $p$ is the prevalence of the drug responders in the population. Other patients in the treatment group react as if they had received a placebo. We develop one- and two-stage RCT designs that are able to detect a sensitive subgroup based solely on the responses. We also extend them to a multicenter RCTs using Hochberg's step-up procedure. We avoid extensive simulations and use simple and quick numerical optimization methods.