  The process of approving and assessing new drugs is often quite complicated,
mainly due to the fact that multiple criteria need to be considered. A standard
way to proceed is with benefit risk analysis, often under the Bayesian paradigm
to account for uncertainty and combine data with expert judgement, which is
operationalised via multi-criteria decision analysis (MCDA) scores. The
procedure is based on a suitable model to accommodate key features of the data,
which are typically of mixed type and potentially depended, with factor models
providing a standard choice. The contribution of this paper is threefold:
first, we extend the family of existing structured factor models. Second, we
provide a framework for choosing between them, which combines fit and
out-of-sample predictive performance. Third, we present a sequential estimation
framework that can offer multiple benefits: (i) it allows us to efficiently
re-estimate MCDA scores of different drugs each time new data become available,
thus getting an idea on potential fluctuations in differences between them,
(ii) it can provide information on potential early stopping in cases of evident
conclusions, thus reducing unnecessary further exposure to undesirable
treatments; (iii) it can potentially allow to assign treatment groups
dynamically based on research objectives. A drawback of sequential estimation
is the increased computational time, but this can be mitigated by efficient
sequential Monte Carlo schemes which we tailor in this paper to the context of
Bayesian benefit risk analysis. The developed methodology is illustrated on
real data on Type II diabetes patients who were administered Metformin (MET),
Rosiglitazone (RSG) and a combination of the two (AVM).
