Existing statutes in the United States and Europe require manufacturers to demonstrate evidence of effectiveness through the conduct of adequate and well-controlled studies to obtain marketing approval of a therapeutic product. What constitutes adequate and well-controlled studies is usually interpreted as randomized controlled trials (RCTs). However, these trials are sometimes unfeasible because of their size, duration, cost, patient preference, or in some cases, ethical concerns. For example, RCTs may not be fully powered in rare diseases or in infections caused by multidrug resistant pathogens because of the low number of enrollable patients. In this case, data available from external controls (including historical controls and observational studies or data registries) can complement information provided by RCT. Propensity score matching methods can be used to select or "borrow" additional patients from the external controls, for maintaining a one-to-one randomization between the treatment arm and active control, by matching the new treatment and control units based on a set of measured covariates, ie, model-based pairing of treatment and control units that are similar in terms of their observable pretreatment characteristics. To this end, 2 matching schemes based on propensity scores are explored and applied to a real clinical data example with the objective of using historical or external observations to augment data in a trial where the randomization is disproportionate or asymmetric.

We study sequential Bayesian inference in continuous-time stochastic kinetic models with latent factors. Assuming continuous observation of all the reactions, our focus is on joint inference of the unknown reaction rates and the dynamic latent states, modeled as a hidden Markov factor. Using insights from nonlinear filtering of jump Markov processes we develop a novel sequential Monte Carlo algorithm for this purpose. Our approach applies the ideas of particle learning to minimize particle degeneracy and exploit the analytical jump Markov structure. A motivating application of our methods is modeling of seasonal infectious disease outbreaks represented through a compartmental epidemic model. We demonstrate inference in such models with several numerical illustrations and also discuss predictive analysis of epidemic countermeasures using sequential Bayes estimates.

Drug developers are required to demonstrate substantial evidence of effectiveness through the conduct of adequate and well-controlled (A&WC) studies to obtain marketing approval of their medicine. What constitutes A&WC is interpreted as the conduct of randomized controlled trials (RCTs). However, these trials are sometimes unfeasible because of their size, duration, and cost. One way to reduce sample size is to leverage information on the control through a prior. One consideration when forming data-driven prior is the consistency of the external and the current data. It is essential to make this process less susceptible to choosing information that only helps improve the chances toward making an effectiveness claim. For this purpose, propensity score methods are employed for two reasons: (1) it gives the probability of a patient to be in the trial, and (2) it minimizes selection bias by pairing together treatment and control within the trial and control subjects in the external data that are similar in terms of their pretreatment characteristics. Two matching schemes based on propensity scores, estimated through generalized boosted methods, are applied to a real example with the objective of using external data to perform Bayesian augmented control in a trial where the allocation is disproportionate. The simulation results show that the data augmentation process prevents prior and data conflict and improves the precision of the estimator of the average treatment effect.

As the availability of real‐world data sources (eg, EHRs, claims data, registries) and historical data has rapidly surged in recent years, there is an increasing interest and need from investigators and health authorities to leverage all available information to reduce patient burden and accelerate both drug development and regulatory decision making. Bayesian meta‐analytic approaches are a popular historical borrowing method that has been developed to leverage such data using robust hierarchical models. The model structure accounts for various degrees of between‐trial heterogeneity, resulting in adaptively discounting the external information in the case of data conflict. In this article, we propose to integrate the propensity score method and Bayesian meta‐analytic‐predictive (MAP) prior to leverage external real‐world and historical data. The propensity score methodology is applied to select a subset of patients from external data that are similar to those in the current study with regards to key baseline covariates and to stratify the selected patients together with those in the current study into more homogeneous strata. The MAP prior approach is used to obtain stratum‐specific MAP prior and derive the overall propensity score integrated meta‐analytic predictive (PS‐MAP) prior. Additionally, we allow for tuning the prior effective sample size for the proposed PS‐MAP prior, which quantifies the amount of information borrowed from external data. We evaluate the performance of the proposed PS‐MAP prior by comparing it to the existing propensity score‐integrated power prior approach in a simulation study and illustrate its implementation with an example of a single‐arm phase II trial.

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