When intuition fails: on fixed and uncertain mixture weights for mixture priors - Simon Wandel, Novartis Pharma AG 
Mixture priors have gained much interest and proven useful in practical applications. For example, they can be used to approximate any given prior distribution (e.g. Dallal and Hall 1983, Diaconis and Ylvisaker 1984), to robustify priors (Schmidli et al, 2014), to represent expert opinions (Moatti et al, 2013; Dallow et al, 2018) or scenarios (Gajewski and Mayo 2006), to support variable selection (Malsiner-Walli & Wagner, 2011) and to identify subgroups or subpopulations (Berry & Berry, 2004). 
While the weights of the mixture components need be specified beforehand, these are updated following mixture calculus once data have been observed. Typically, fixed weights are used. Intuitively, however, one would think that uncertainty about the weights would be better reflected using uncertain weights. For example, for a single two-component mixture prior one could use uncertain weights such as w ~ Beta(a, b) instead of fixed weights (w, 1-w). On the other hand the situation is more complex for multiple mixture priors where weights (w1; 1- w1), (w2;1- w2) are required, one could imagine uncertain weights of another form: wi ~ Beta(a,b).
We will shed light on why intuition fails here, i.e. why the use of uncertain weights is not necessary for single mixture priors. For multiple mixtures priors, the situation is more complex, which leads also to some challenges in interpretation of priors that use uncertain weights. The cases of single and multiple mixture priors will be illustrated with two examples using a historical data prior and a problem in variable selection. 

Application of Bayesian Meta-Analytic Priors Across Disease Settings - Kristine Broglio and Fredrik Öhrn, AstraZeneca
Dapagliflozin has been evaluated in several large confirmatory randomized trials in patients with chronic diseases, including Type II diabetes, heart failure, and chronic kidney disease. In each of these studies, dapagliflozin was shown to have protective benefits for the heart and kidneys. DARE-19 was a randomized clinical trial evaluating whether treatment with dapagliflozin would be effective in patients hospitalized with COVID-19. DARE-19 had dual primary endpoints to assess the prevention of organ dysfunction and improvement in clinical status. Neither primary endpoint achieved the required level of statistical significance in the confirmatory analysis.  The primary organ dysfunction endpoint in DARE-19 included components of respiratory, cardiac, and renal function and consistent with previous trials, a large benefit was observed for the renal function endpoint.  Under the hypothesis that the mechanism responsible for a protective effect on the kidneys in patients with chronic diseases is the same as that for patients hospitalized with an acute illness, we used Bayesian methods to synthesize the available data.  We evaluate both renal endpoints and all-cause mortality.  We demonstrate the use of Bayesian meta-analytic predictive priors constructed from the chronic illness studies to include as an informative prior distribution in the estimation of the treatment effect in the acute illness setting.  We explore how the a priori level of belief in the applicability of the chronic disease data affects inference in the acute setting.   

Assessing efficacy in important subgroups in confirmatory trials – an example using Bayesian dynamic borrowing - Oliver Keene, KeeneONStatistics Ltd. 
Analysis by key subgroups is an important aspect of assessing the results of confirmatory trials.  When there is evidence of an overall effect of treatment, there are questions about whether there is evidence of efficacy in important subgroups, for example those defined by disease severity, sex, age, race and region. Analysis is typically performed using separate analysis of the specific subgroup but this ignores relevant information from the complementary subgroup. Bayesian dynamic borrowing uses an informative prior based on analysis of the complementary subgroup and a weak prior distribution centred on a mean of zero to construct a robust mixture prior. This combination of priors allows for dynamic borrowing of prior information; the analysis learns how much of the complementary subgroup prior information to borrow based on the consistency between the subgroup of interest and the complementary subgroup. A tipping point analysis can be carried out to identify how much prior weight needs to be placed on the complementary subgroup component of the robust mixture prior to establish efficacy in the subgroup of interest. An attractive feature of the tipping point analysis is that it enables the evidence from the source subgroup, the evidence from the target subgroup, and the combined evidence to be displayed alongside each other. This method is illustrated with an example trial in severe asthma where efficacy in the adolescent subgroup was assessed using a mixture prior combining an informative prior from the adult data in the same trial with a non-informative prior. 

Dynamic Borrowing of Predicted Historical Controls - Andrea Callegaro, GSK Vaccines 
In clinical drug development, the use of methods for dynamic borrowing of historical information to support statistical inference from a current study is becoming increasingly accepted. These methods enable the integration of evidence in a formal and transparent way. Dynamic borrowing models are flexible, in the sense that they borrow information to a degree that depends on the extent of discrepancy (drift) between historical and current data. In this work, we consider the adjustment for covariates where historical controls are standardized using predictions from prognostic models. In particular, we illustrate the approach with a retrospective analysis of a Phase 3 Vaccine study where historical controls are predicted using a (published) Correlate of Risk model.