### Abstract

In designing a randomised controlled trial, it has been argued that trialists should consider existing evidence about the likely intervention effect. One approach is to form a prior distribution for the intervention effect based on a meta-analysis of previous studies, and then power the trial on its ability to affect the posterior distribution in a Bayesian analysis. Alternatively, methods have been proposed to calculate the power of the trial to influence the ‘pooled’ estimate in an updated meta-analysis. These two approaches can give very different results if the existing evidence is heterogeneous, summarised using a random effects meta-analysis.

We argue that the random effects mean will rarely represent the trialist’s target parameter, and so it will rarely be appropriate to power a trial based on its impact upon the random effects mean. Furthermore, the random effects mean will not generally provide an appropriate prior distribution. More appropriate alternatives include the predictive distribution and shrinkage estimate for the most similar study. Consideration of the impact of the trial on the entire random effects distribution might sometimes be appropriate.

We describe how beliefs about likely sources of heterogeneity have implications for how the previous evidence should be used, and can have a profound impact on the expected power of the new trial. We conclude that likely causes of heterogeneity among existing studies need careful consideration. In the absence of explanations for heterogeneity, we suggest using the predictive distribution from the meta-analysis as the basis for a prior distribution for the intervention effect.

We argue that the random effects mean will rarely represent the trialist’s target parameter, and so it will rarely be appropriate to power a trial based on its impact upon the random effects mean. Furthermore, the random effects mean will not generally provide an appropriate prior distribution. More appropriate alternatives include the predictive distribution and shrinkage estimate for the most similar study. Consideration of the impact of the trial on the entire random effects distribution might sometimes be appropriate.

We describe how beliefs about likely sources of heterogeneity have implications for how the previous evidence should be used, and can have a profound impact on the expected power of the new trial. We conclude that likely causes of heterogeneity among existing studies need careful consideration. In the absence of explanations for heterogeneity, we suggest using the predictive distribution from the meta-analysis as the basis for a prior distribution for the intervention effect.

Original language | English |
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Number of pages | 15 |

Journal | Statistics in Medicine |

Early online date | 6 Sep 2018 |

DOIs | |

Publication status | E-pub ahead of print - 6 Sep 2018 |

### Keywords

- Bayesian analysis
- expected power calculations
- heterogeneity
- prior distributions
- sample size calculations