Statistical inclusion of expanded access data 181 III ♥ The types of borrowing Various types of borrowing information exist. An excellent overview is provided by Viele et al.2 Broadly speaking, there are two types of borrowing: static and dynamic. Static methods fix whether to borrow and to what degree. The easiest example of this is called pooling, and simply involves piling the two datasets together and analyzing if it were one large set. Dynamic methods borrow depending on the similarity of the historical and current datasets. A simple approach is to first investigate the datasets to assess their similarity, and only combine the datasets if they are similar. This method is known as test-then-pool. First, the means of the two groups are tested through significance testing. If there is no significant change in group means, the groups are pooled, and else, the historical data is discarded. These methods perform dynamic borrowing, aiming to synthesize more evidence when data sources are ‘comparable’ and to synthesize less (or completely exclude evidence) as data sources differ increasingly. Primarily, these methods aim to address unmeasured confounding. The less similar data sets are, the less weight is addressed to the historical data. A variety of methods are developed in this field, such as the meta-analytic predictive prior,14,15 the commensurate prior,16,17 Bayesian hierarchical models and the power-prior.7,15,18–20 Hybrid borrowing methods Recently, there have been innovations proposed by regulatory statisticians known as ‘hybrid’ methods,14,21–24 that involve a two-stage procedure: 1. Attempt to account for measured confounding, for example through propensity score methods or covariate adjustment. 2. Attenuate residual unmeasured confounding through the use of dynamic borrowing methods. This two-step procedure entails a dual safeguard by using two separate methods to measure the similarity of data sets on which subsequently the propensity and borrowing weights are based. Moreover, the analysis could be split between two independent statisticians, a principle known as an ‘outcome-free’ design25. Here, a first statistician independently models the propensity score process ignorant of the trial conduct and outcome. At trial completion, a second statistician analyzes the data using the allocation process predefined by the first statistician.
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