Peter G. Challenor

Background: Predicting respiratory trajectory and prognosis of high-risk preterm infants could better support targeted interventions and parental counselling. Current models are static, limiting their utility. They provide single day predictions at 36 weeks postmenstrual age, bounded by fixed timepoints, without incorporating clinical trajectory. We aimed to develop and validate a dynamic model for predicting respiratory state trajectory and demonstrate utility in predicting successful extubation and postnatal corticosteroids use. Methods: A dynamic model based on a Markov chain modelling framework was developed and validated in a retrospective population-based National Neonatal Research Database cohort before external validation in a prospective PRemature Infant Outcome Risk cohort. Both cohorts consist of infants born <32 weeks’ gestation in participating units in England and Wales from 2010-2022 (n=93,342) and 2023-2024 (n=1,420), respectively. Fourteen static once only and six daily predictors were used. Missing data was addressed using mean and model-based imputation, respectively. The dynamic model predicted daily respiratory states (no support, supplemental oxygen only, non-invasive or invasive ventilation) or death. Discrimination (area under the receiver operating characteristic curve (AUROC)), calibration, and utility performance were assessed. Findings: The developed online dynamic model (https://premoutcome.shinyapps.io/Respiratory/) showed strong discrimination (AUROCs 0·82–0·84), calibration and utility performance, demonstrating superior net benefit across probabilities of 30%-80%, in predicting bronchopulmonary dysplasia or death during external validation. The dynamic model had excellent performance in predicting non-invasive/invasive ventilation or death within the next 7 or 14 days (AUROCs 0·89-0·96). Infants with predicted risk of poorer respiratory outcomes were more likely to remain intubated and receive postnatal dexamethasone (p<0·001). Interpretation: The dynamic model demonstrated strong performance in predicting the complex task of daily respiratory trajectory and clinical utility in predicting likelihood of extubation timing. Further external validation and impact analysis are needed to establish personalised prediction utility.

Complex computer codes or models can often be run in a hierarchy of different levels of complexity ranging from the very basic to the sophisticated. The top levels in this hierarchy are typically expensive to run, which limits the number of possible runs. To make use of simulations over all levels, and crucially improve predictions at the top level, we use multilevel Gaussian process emulators (GPs). The accuracy of the GP greatly depends on the design of the training points. In this paper, we present a multilevel adaptive sampling algorithm to sequentially increase the set of design points to optimally improve the fit of the GP. The normalized squared expected leave-one-out cross-validation error (ES-LOO) is calculated at all unobserved locations, and a new design point is chosen using expected improvement combined with a repulsion function to find the maximum ES-LOO. We use ES-LOO to obtain a model-free measure of prediction error at each level. This criterion is calculated for each model level weighted by an associated cost for the code at that level. Hence, at each iteration, our algorithm optimises for both the new point location and the model level. The algorithm is extended to batch selection as well as single point selection, where batches can be designed for single levels or optimally across all levels. We apply the new multilevel ES-LOO algorithm to a range of examples, and make comparisons to existing design methods. This includes comparisons with single-shot methods as well as more recent sequential design algorithms. A toolbox containing relevant code can be found at: github.com/EXA-UQ/EXAUQ-Toolbox .

Weather files are fundamental for building performance applications such as estimating energy demand or predicting the risk of thermal discomfort. Often such weather files are based on specific locations with limited guidance to which file to use which can lead to non-representative climate conditions for a specific building and potentially under or over engineering of systems. Recently, a new approach to generating representative weather files for building performance using climate zones has been proposed. This work presents a comparative analysis of the two approaches. Results from examining the external climate and an example building simulation reveal substantial differences: heating degree days vary by up to 931° days, cooling degree days by up to 500° days, heating energy demand differs by as much as 60%, and overheating exposure in the bedroom exceeds 26°C for up to 45 h more. Overall, we find significant variations in heating and cooling loads can be expected if unrepresentative climate data is used highlighting the importance of selecting appropriate weather data for building performance simulation. The use of zone-based files provides a more nuanced understanding of climate conditions, improving the reliability of building performance assessments and compliance with overheating standards. Practical application: Weather files are fundamental for building performance analysis and supporting design decisions including the prediction of the risk of thermal discomfort. There is a need for these weather files to be kept up to date following the continual warming of the environment to ensure that the performance analysis represents external conditions and ensuring the analysis is fit for purpose. A significant limitation of the current approach is the uncertainty of which weather file should be used for any given location particularly in locations such as the UK. This work provides a framework for the development of climate-zones and representative weather files suitable for supporting the benchmarking of building performance across the climate zone removing ambiguity within the industry for the appropriate selection of weather data.

Duchenne Muscular Dystrophy is a progressive neuromuscular disorder characterized by the gradual weakening and deterioration of muscles, leading to loss of ambulation in affected individuals. This decline in mobility can be effectively assessed using the North Star Ambulatory Assessment (NSAA) scores, along with measures such as the 10-m walk time and the time taken to rise from the floor. We propose a dynamic linear model to predict the trajectories of these clinical outcomes, with a primary focus on NSAA scores. Our model aims to assist clinicians in forecasting the progression of the disease, thereby enabling more informed and personalized treatment plans for their patients. We also evaluate the effectiveness of our models in generating synthetic NSAA score datasets. We assess the performance of our modelling approach and compare the results with those of a previous study. We show that the most robust model demonstrates narrower prediction intervals and improved quantile coverage, indicating superior predictive accuracy and reliability. This article is part of the theme issue ‘Uncertainty quantification for healthcare and biological systems (Part 2)’.

Complex numerical models are increasingly being used in healthcare and epidemiology. To represent the complex features, modellers often make the decision to include stochastic behaviour where repeated runs of the model with identical inputs produce different outputs. When computational constraints limit the number of model runs and replications, heteroscedastic Gaussian processes can be used as a fast surrogate, allowing for efficient emulation of varying noise levels across the input space. The accuracy of any emulator is greatly dependent on the design of the training data, where sequential design algorithms increase the number of design points iteratively based on predefined criteria. For stochastic models, the design problem is more challenging due to the possibility of replicates at design points. This article develops a new sequential design method for stochastic models which scales well in high-dimensional input spaces. We build upon an existing method for deterministic models using an expected squared leave-one-out error criterion that balances exploration and replication. We compare our approach with existing sequential design methods as well as applying it to an agent-based model and a COVID-19 model. Results demonstrate that the proposed method performs well in noisy environments, offering a scalable alternative to existing methods. This article is part of the theme issue ‘Uncertainty quantification for healthcare and biological systems (Part 2)’.

A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is a function that describes the evolution of the system from an initial condition to a subsequent value at the next time step. This yields a probabilistic distribution over the entire flow map function, with each draw offering an approximation to the flow map. The model output time series is then predicted (under the Markov assumption) by drawing a sample from the emulated flow map (i.e., its posterior distribution) and using it to iterate from the initial condition ahead in time. Repeating this procedure with multiple such draws creates a distribution over the time series. The mean and variance of this distribution at a specific time point serve as the model output prediction and the associated uncertainty, respectively. However, drawing a GP posterior sample that represents the underlying function across its entire domain is computationally infeasible, given the infinite-dimensional nature of this object. To overcome this limitation, one can generate such a sample in an approximate manner using random Fourier features (RFF). RFF is an efficient technique for approximating the kernel and generating GP samples, offering both computational efficiency and theoretical guarantees. The proposed method is applied to emulate several dynamic nonlinear simulators including the well-known Lorenz and van der Pol models. The results suggest that our approach has a promising predictive performance and the associated uncertainty can capture the dynamics of the system appropriately.

Predicting the trajectory of rare degenerative diseases can be extremely beneficial, especially when these predictions are personalised to be relevant for a specific patient. These predictions can help inform and advise patients, families, and clinicians about the next stages of treatment and care. Obtaining such predictions, however, can be challenging, especially when data is limited. In particular, it is important that these predictions do not rely too heavily on general trends from the wider afflicted population while not relying exclusively on the, potentially sparse, data from the patient in question. We present a case study, wherein a modelling framework is developed for predicting a patient’s long term trajectory, using a mix of data from the patient of concern and a database of previously observed patients. This framework directly accounts for the temporal structure of a patient’s trajectory, effortlessly handles a large amount of missing data, allows for a wide range of patient progression, and offers a robust quantification of the various uncertainties. We showcase this framework to an example involving Duchenne Muscular Dystrophy, where it provides promising results.

Gaussian Process (GP) emulators are widely used to approximate complex computer model behaviour across the input space. Motivated by the problem of coupling computer models, recently progress has been made in the theory of the analysis of networks of connected GP emulators. In this paper, we combine these recent methodological advances with classical state-space models to construct a Bayesian decision support system. This approach gives a coherent probability model that produces predictions with the measure of uncertainty in terms of two first moments and enables the propagation of uncertainty from individual decision components. This methodology is used to produce a decision support tool for a UK county council considering low carbon technologies to transform its infrastructure to reach a net-zero carbon target. In particular, we demonstrate how to couple information from an energy model, a heating demand model, and gas and electricity price time-series to quantitatively assess the impact on operational costs of various policy choices and changes in the energy market.