# Response adaptive designs for binary responses: how to offer patient benefit while being robust to time trends?

## TL;DR

This paper evaluates response-adaptive randomisation (RAR) in clinical trials, especially for rare diseases, focusing on controlling type I error inflation caused by patient drift and proposing robust, computationally efficient correction methods.

## Contribution

It analyzes the impact of time trends on RAR in rare disease trials and introduces a robust, computationally cheap RAR design with correction methods for type I error control.

## Key findings

- Type I error inflation depends on the magnitude of time trends.
- Certain correction methods effectively control type I error in RAR.
- Proposed RAR design is robust to multiple time trend scenarios.

## Abstract

Response-adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not feasible or ethically objectionable. In this paper we discuss and address a major criticism of RAR: the undesirable type I error inflation due to unknown time trends in the trial. Time trends can appear because of changes in the characteristics of recruited patients - so-called "patient drift". Patient drift is a realistic concern for clinical trials in rare diseases because these typically recruit patients over a very long period of time. We compute by simulations how large the type I error inflation is as a function of the time trend magnitude in order to determine in which contexts a potentially costly correction is actually necessary. We then assess the ability of different correction methods to preserve type I error in this context and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations of which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the two-armed and the multi-armed case. We further propose a RAR design for multi-armed clinical trials, which is computationally cheap and robust to several time trends considered.