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In patients with atrial fibrillation, local activation time (LAT) maps are routinely used for characterizing patient pathophysiology. The gradient of LAT maps can be used to calculate conduction velocity (CV), which directly relates to material conductivity and may provide an important measure of atrial substrate properties. Including uncertainty in CV calculations would help with interpreting the reliability of these measurements. Here, we build upon a recent insight into reduced-rank Gaussian processes (GPs) to perform probabilistic interpolation of uncertain LAT directly on human atrial manifolds. Our Gaussian process manifold interpolation (GPMI) method accounts for the topology of the atrium, and allows for calculation of statistics for predicted CV. We demonstrate our method on two clinical cases, and perform validation against a simulated ground truth. CV uncertainty depends on data density, wave propagation direction and CV magnitude. GPMI is suitable for probabilistic interpolation of other uncertain quantities on non-Euclidean manifolds.\ud \ud This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.

Background: Pairwise and network meta-analyses using fixed effect and random effects models are commonly applied to synthesise evidence from randomised controlled trials. The models differ in their assumptions and the interpretation of the results. The model choice depends on the objective of the analysis and knowledge of the included studies. Fixed effect models are often used because there are too few studies with which to estimate the between-study standard deviation from the data alone. Objectives: The aim is to propose a framework for eliciting an informative prior distribution for the between-study standard deviation in a Bayesian random effects meta-analysis model to genuinely represent heterogeneity when data are sparse. Methods: We developed an elicitation method using external information such as empirical evidence and experts' beliefs on the 'range' of treatment effects in order to infer the prior distribution for the between-study standard deviation. We also developed the method to be implemented in R. Results: The three-stage elicitation approach allows uncertainty to be represented by a genuine prior distribution to avoid making misleading inferences. It is flexible to what judgments an expert can provide, and is applicable to all types of outcome measure for which a treatment effect can be constructed on an additive scale. Conclusions: The choice between using a fixed effect or random effects meta-analysis model depends on the inferences required and not on the number of available studies. Our elicitation framework captures external evidence about heterogeneity and overcomes the often implausible assumption that studies are estimating the same treatment effect, thereby improving the quality of inferences in decision making.

History matching is a model (pre-)calibration method that has been applied to computer models from a wide range of scientific disciplines. In this work we apply history matching to an individual-based epidemiological model of HIV that has 96 input and 50 output parameters, a model of much larger scale than others that have been calibrated before using this or similar methods. Apart from demonstrating that history matching can analyze models of this complexity, a central contribution of this work is that the history match is carried out using linear regression, a statistical tool that is elementary and easier to implement than the Gaussian process--based emulators that have previously been used. Furthermore, we address a practical difficulty with history matching, namely, the sampling of tiny, nonimplausible spaces, by introducing a sampling algorithm adjusted to the specific needs of this method. The effectiveness and simplicity of the history matching method presented here shows that it is a useful tool for the calibration of computationally expensive, high dimensional, individual-based models.\ud \ud \ud Read More: http://epubs.siam.org/doi/abs/10.1137/16M1093008

We calibrate a stochastic computer simulation model of ‘moderate’ computational expense. The simulator is an imperfect representation of reality, and we recognise this discrepancy to ensure a reliable calibration. The calibration model combines a Gaussian process emulator of the likelihood surface with importance sampling. Changing the discrepancy specification changes only the importance weights, which lets us investigate sensitivity to different discrepancy specifications at little computational cost. We present a case study of a natural history model that has been used to characterise UK bowel cancer incidence. Data sets and computer code are provided as supplementary material.

A “law-driven” or “mechanistic” computer model is a representation of judgments about the functional relationship between one set of quantities (the model inputs) and another set of target quantities (the model outputs). We recognize that we can rarely define with certainty a “true” model for a particular problem. Building an “incorrect” model will result in an uncertain prediction error, which we denote “structural uncertainty.” Structural uncertainty can be quantified within a Bayesian framework via the specification of a series of internal discrepancy terms, each representing at a subfunction level within the model the difference between the subfunction output and the true value of the intermediate parameter implied by the subfunction. By using value of information analysis we can then determine the expected value of learning the discrepancy terms, which we loosely interpret as an upper bound on the “expected value of model improvement.” We illustrate the method using a case study model drawn from the health economics literature.

We consider the use of the assurance method in clinical trial planning. In the assurance method, which is an alternative to a power calculation, we calculate the probability of a clinical trial resulting in a successful outcome, via eliciting a prior probability distribution about the relevant treatment effect. This is typically a hybrid Bayesian-frequentist procedure, in that it is usually assumed that the trial data will be analysed using a frequentist hypothesis test, so that the prior distribution is only used to calculate the probability of observing the desired outcome in the frequentist test. We argue that assessing the probability of a successful clinical trial is a useful part of the trial planning process. We develop assurance methods to accommodate survival outcome measures, assuming both parametric and nonparametric models. We also develop prior elicitation procedures for each survival model so that the assurance calculations can be performed more easily and reliably. We have made free software available for implementing our methods.