In statistical modeling of computer experiments, prior information is sometimes available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all inputs. We develop a Bayesian approach to Gaussian process modeling capable of incorporating monotonicity information for computer model emulation. Markov chain Monte Carlo methods are used to sample from the posterior distribution of the process given the simulator output and monotonicity information. The performance of the proposed approach in terms of predictive accuracy and uncertainty quantification is demonstrated in a number of simulated examples as well as a real queuing system application.

BackgroundEnrollment of participants to control arms in clinical trials can be challenging. This is particularly an issue in oncology trials where the standard-of-care is shifting rapidly and several promising experimental treatments are undergoing phase III testing. Novel methods for utilizing external control data may mitigate these challenges, but applied examples are sparse. Here, we therefore illustrate how Bayesian dynamic borrowing of external individual patient level control data from similar clinical trials can often reduce randomization to the control intervention without substantially trading-off precision. We further explore which types of scenarios yield viable trade-offs, and which do not.Patients and methodsWe obtained individual patient data on patients being treated with second-line therapy for non-small cell lung cancer from Project Data Sphere with minimal in/exclusion criteria restrictions, and applied Bayesian hierarchical models with uninformative priors to generate illustrative synthetic control groups.ResultsFour phase III clinical trials were identified and utilized in our analysis. Even when studies which are knowingly incongruent with one another are selected to generate a synthetic control, the nature of this methodology minimizes improper borrowing from historical data. The use of a small concurrent control group within a trial greatly reduces penalized selection, and our results demonstrate the ability to reduce allocation to the control group by up to 80% with a minimal increase in uncertainty when closely matched historical data is available.ConclusionDynamic borrowing using Bayesian hierarchical models with uninformative priors represents a novel approach to utilizing external controls for comparative estimates using single arm evidence.

a b s t r a c tConstraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behavior on the model, transformation of constraints into features on the parameter space may not be possible. Incorporation of constraints into the model often leads to truncations in the parameter space and multimodality which in turn cause difficulties in posterior sampling. A variant of the Sequential Monte Carlo algorithm is proposed by defining a sequence of densities through the imposition of the constraint. Particles generated from an unconstrained or mildly constrained distribution are filtered and moved through sampling and resampling steps to obtain a sample from the fully constrained target distribution. General and model specific forms of constraints enforcing strategies are defined. The Sequentially Constrained Monte Carlo algorithm is demonstrated on constraints defined by monotonicity of a function, densities constrained to low dimensional manifolds, adherence to a mechanistic differential equation model, and Approximate Bayesian Computation.Crown

Although all outcomes were associated with favorable point estimates, our trial did not demonstrate important effects of unconditional cash grants on health outcomes of HIV-positive patients receiving treatment.