COMPREHENSIVE EVIDENCE SYNTHESIS AND TRIAL-BASED COST-EFFECTIVENESS ANALYSIS: CAN THEY BE COMFORTABLE BED FELLOWS?

Purpose: The contemporary methods for cost-effectiveness analysis (CEAs) conducted alongside randomized clinical trials (RCT) neglect the existing external evidence that resides outside of the realm of the clinical trial. We introduce the “vetted bootstrap”, a Bayesian framework for incorporation of external evidence into RCT-based CEAs.

Methods: First, the conventional bootstrap method for characterizing uncertainty in RCT-based CEAs is shown to be analogous to sampling from the posterior ‘distribution of the distribution’ of the RCT data. Such analogy can then be used to argue that external evidence imposes a prior distribution on the distribution of the data. This argument is evolved into an acceptance-rejection algorithm: the value of the statistics for which external evidence is available is calculated from the bootstrapped sample; and the likelihood of the statistics given the external evidence is used to probabilistically accept/reject that bootstrap sample (hence ‘vetting’ the bootstrap).

Results: Let X be the data of the RCT. Let θ be the statistics for which external evidence is available in the form of (multivariate) probability density function P_θ. The vetted bootstrap can be formulated as For i=1, ... , M, where M is the number of simulations:

1. Generate X_b, a bootstrap sample of X with bootstrapping performed within each arm of the trial.
2. Calculate θ’ = θ(X_b), the statistics for which external evidence is available, from this sample.
3. Calculate ω=P_θ (θ'), the likelihood of the calculated statistics given its probability distribution.
4. Accept the bootstrap sample X_b with a probability proportional to ω, otherwise ignore the sample and jump to (1).
5. Calculate costs and effectiveness outcomes from X_b

The vectors of costs and effectiveness outcomes can be interpreted as random draws from their respective posterior distribution having observed the RCT data, with the external evidence as prior information. All downstream calculations remain unchanged.  As an alternative to the vetted bootstrap, the weights ω can directly be incorporated in all downstream calculation (“weighted bootstrap”).

Conclusion: Our method, providing the ability to incorporate evidence on any aspect of intervention within a non-parametric framework is operationally simple and removes an important drawback of RCT-based CEAs. The accompanying paper will include a step-by-step demonstration of the analogy of this method with parametric Bayesian inference and an exemplary application.