Abstract
In the era of precision medicine, novel designs are developed to deal with flexible clinical trials that incorporate many treatment strategies for multiple diseases in one trial setting. This situation often leads to small sample sizes in disease‐treatment combinations and has fostered the discussion about the benefits of borrowing of external or historical information for decision‐making in these trials. Several methods have been proposed that dynamically discount the amount of information borrowed from historical data based on the conformity between historical and current data. Specifically, Bayesian methods have been recommended and numerous investigations have been performed to characterize the properties of the various borrowing mechanisms with respect to the gain to be expected in the trials. However, there is common understanding that the risk of type I error inflation exists when information is borrowed and many simulation studies are carried out to quantify this effect. To add transparency to the debate, we show that if prior information is conditioned upon and a uniformly most powerful test exists, strict control of type I error implies that no power gain is possible under any mechanism of incorporation of prior information, including dynamic borrowing. The basis of the argument is to consider the test decision function as a function of the current data even when external information is included. We exemplify this finding in the case of a pediatric arm appended to an adult trial and dichotomous outcome for various methods of dynamic borrowing from adult information to the pediatric arm. In conclusion, if use of relevant external data is desired, the requirement of strict type I error control has to be replaced by more appropriate metrics.
Highlights
Borrowing of information from an external data source to inform inference in a current trial is gaining popularity in situations where only small samples are available for practical or ethical reasons
To add transparency to the debate, we show that if prior information is conditioned upon and a uniformly most powerful test exists, strict control of type I error implies that no power gain is possible under any mechanism of incorporation of prior information, including dynamic borrowing
For scenarios in which a uniformly most powerful (UMP)- or UMP-unbiased test exists, we have shown in general that borrowing from external information cannot improve power while controlling type I error, even when borrowing is adapted to prior-data conflict
Summary
Borrowing of information from an external data source to inform inference in a current trial is gaining popularity in situations where only small samples are available for practical or ethical reasons. The rationale for using such dynamic borrowing mechanisms is often given by the desire to take into account external information only when it improves inference It seems to be hidden knowledge in the Bayesian community that no power gain is possible when type I error needs to be controlled, which has been stated before by, for example, Psioda and Ibrahim (2018): “If one wishes to control the type I error rate in the traditional frequentist sense, all prior information must be disregarded in the analysis.”.
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