Practical help for specifying the target difference in sample size calculations for RCTs: the DELTA2 five-stage study, including a workshop
Authors: Cook Jonathan A , Julious Steven A , Sones William , Hampson Lisa V , Hewitt Catherine , Berlin Jesse A , Ashby Deborah , Emsley Richard , Fergusson Dean A , Walters Stephen J , Wilson Edward CF , MacLennan Graeme , Stallard Nigel , Rothwell Joanne C , Bland Martin , Brown Louise , Ramsay Craig R , Cook Andrew , Armstrong David , Altman Douglas , Vale Luke D 
Published: October 2019

Background
The randomised controlled trial is widely considered to be the gold standard study for comparing the effectiveness of health interventions. Central to its design is a calculation of the number of participants needed (the sample size) for the trial. The sample size is typically calculated by specifying the magnitude of the difference in the primary outcome between the intervention effects for the population of interest. This difference is called the ‘target difference’ and should be appropriate for the principal estimand of interest and determined by the primary aim of the study. The target difference between treatments should be considered realistic and/or important by one or more key stakeholder groups.

Objective
The objective of the report is to provide practical help on the choice of target difference used in the sample size calculation for a randomised controlled trial for researchers and funder representatives.

Methods
The Difference ELicitation in TriAls2 (DELTA2) recommendations and advice were developed through a five-stage process, which included two literature reviews of existing funder guidance and recent methodological literature; a Delphi process to engage with a wider group of stakeholders; a 2-day workshop; and finalising the core document.

Results
Advice is provided for definitive trials (Phase III/IV studies). Methods for choosing the target difference are reviewed. To aid those new to the topic, and to encourage better practice, 10 recommendations are made regarding choosing the target difference and undertaking a sample size calculation. Recommended reporting items for trial proposal, protocols and results papers under the conventional approach are also provided. Case studies reflecting different trial designs and covering different conditions are provided. Alternative trial designs and methods for choosing the sample size are also briefly considered.

Conclusions
Choosing an appropriate sample size is crucial if a study is to inform clinical practice. The number of patients recruited into the trial needs to be sufficient to answer the objectives; however, the number should not be higher than necessary to avoid unnecessary burden on patients and wasting precious resources. The choice of the target difference is a key part of this process under the conventional approach to sample size calculations. This document provides advice and recommendations to improve practice and reporting regarding this aspect of trial design. Future work could extend the work to address other less common approaches to the sample size calculations, particularly in terms of appropriate reporting items.

Funding
Funded by the Medical Research Council (MRC) UK and the National Institute for Health Research as part of the MRC–National Institute for Health Research Methodology Research programme.