Centre for Statistics in Medicine
The DELTA2 project aimed to develop guidance for specifying the target difference (or effect size) in the sample size calculation for a randomised clinical trial (RCT). This guidance is aimed at researchers and funders of RCTs. It is hoped that the guidance will help improve the design of future RCTs.
Sample size and Target difference for an RCT
A key step in developing a robust RCT is calculating how many participants are needed, called the sample size.1,2 The sample size needs to be chosen so that the trial can identify a difference of a particular magnitude, if such a difference exists. Researchers need to decide what difference would be appropriate for a trial given the interventions under evaluation and the anticipated study population. This difference is called the target difference.
From a scientific and ethical standpoint, as well as a practical point of view, selecting an appropriate target difference (sometime referred to simply as the ‘effect size’) is of crucial importance. If the selected target difference is much larger than the actual difference, then the sample size may be too small to identify the actual difference. As a consequence, specifying too small a target difference could be a wasteful (and unethical) use of data and resources. If the selected target difference is much smaller than the actual difference, then the sample size used will be much larger than was needed to identify the actual difference. An undersized study may not usefully contribute to the knowledge base and could negatively affect decision making. It could also result in some participants being unnecessarily exposed to additional risk or receiving a suboptimal treatment.
Need for further Guidance
A large amount of work has focused on the statistical considerations for a sample size calculation. However, until recently the choice of the target difference, despite its key role, has received relatively little focus. Various approaches have been proposed to help determine what would be an important and/or realistic difference. A recent comprehensive systematic review by members of the DELTA2 team summarised these approaches3-4 and initial guidance has been produced for specifiying the target difference for a standard RCT design5. However, there was a need for more extensive guidance for researchers and funders that was applicable to a wider range of trial designs.
The DELTA2 project6-8 sought to address this gap in the literature. Findings from the project and related outputs are available here.
This project is funded by the Medical Research Council-National Institute for Health Research Methodology Research Programme in the UK.
- Julious S. Sample Sizes for Clinical Trials. Boca Raton, FL: Chapman and Hall/CRC Press; 2010.
- Charles P. et al. Reporting of sample size calculation in randomised controlled trials: review. BMJ 2009; 338: b1732. http://doi.org/10.1136/bmj.b1732
- Cook J. et al. Assessing methods to specify the target difference for a randomised controlled trial - DELTA (Difference ELicitation in TriAls) review. Health Technology Assessment 2014; 18: 28. http://doi.org/10.3310/hta18280
- Hislop J. et al. Methods for specifying the target difference in a randomised controlled trial: the Difference ELicitation in TriAls (DELTA) systematic review. PLOS Medicine 2014; 11(5): e1001645. http://doi.org/10.1371/journal.pmed.1001645
- Cook J. et al. Specifying the target difference in the primary outcome for a randomised controlled trial: guidance for researchers. Trials 2015; 16: 12. http://doi.org/10.1186/s13063-014-0526-8
Cook J.A. et al. Choosing the target difference ("effect size") for a randomised controlled trial - DELTA2 guidance protocol. Trials 2017; 18: 271. https://doi.org/10.1186/s13063-017-1969-5
Sones W. et al. Choosing the target difference ("effect size") for a randomised controlled trial - the development of the DELTA2 guidance. Trials 2018; 19: 542. https://doi.org/10.1186/s13063-018-2887-x
Cook J. A. et al. DELTA2 guidance on choosing the target difference and undertaking and reporting the sample size calculation for a randomised controlled trial. BMJ 2018; 363. https://doi.org/10.1136/bmj.k3750