# Bayesian design and analysis of external pilot trials for complex interventions

## TL;DR

This paper introduces a Bayesian framework for designing and analyzing external pilot trials of complex interventions, enabling more nuanced decision-making by evaluating multiple parameters and trade-offs through a loss function.

## Contribution

It presents a novel Bayesian approach that incorporates a loss function for decision-making, addressing methodological challenges in small-sample, multi-endpoint pilot trials.

## Key findings

- Demonstrated the method on a physical activity intervention in care homes.
- Provided a computational algorithm for estimating operating characteristics.
- Showed improved decision-making flexibility in pilot trial design.

## Abstract

External pilot trials of complex interventions are used to help determine if and how a confirmatory trial should be undertaken, providing estimates of parameters such as recruitment, retention and adherence rates. The decision to progress to the confirmatory trial is typically made by comparing these estimates to pre-specified thresholds known as progression criteria, although the statistical properties of such decision rules are rarely assessed. Such assessment is complicated by several methodological challenges, including the simultaneous evaluation of multiple endpoints, complex multi-level models, small sample sizes, and uncertainty in nuisance parameters. In response to these challenges, we describe a Bayesian approach to the design and analysis of external pilot trials. We show how progression decisions can be made by minimising the expected value of a loss function, defined over the whole parameter space to allow for preferences and trade-offs between multiple parameters to be articulated and used in the decision making process. The assessment of preferences is kept feasible by using a piecewise constant parameterisation of the loss function, the parameters of which are chosen at the design stage to lead to desirable operating characteristics. We describe a flexible, yet computationally intensive, nested Monte Carlo algorithm for estimating operating characteristics. The method is used to revisit the design of an external pilot trial of a complex intervention designed to increase the physical activity of care home residents.