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The 4C Deterioration model was developed and validated on data collected in UK hospitals until August 26, 2020, but has not yet been validated in the presence of SARS-CoV-2 variants and novel treatment regimens that have emerged subsequently. In this first validation study of the 4C Deterioration model on patients admitted between August 27, 2020 and April 16, 2021 we found, despite a slightly overestimation of risk, that the discrimination (area under the curve 0.75, 95% CI 0.71-0.78) and calibration of the model remained consistent with the development study, strengthening the evidence for adopting this model into clinical practice.

Background: There is no consensus on the optimal method for the assessment of frailty. We compared the prognostic utility of two approaches (modified Frailty Index [mFI], Clinical Frailty Scale [CFS]) in older adults (≥65 years) hospitalised with COVID-19 versus age. Methods: We used a test and validation cohort that enrolled participants hospitalised with COVID-19 between 27 February and 30 June 2020. Multivariable mixed-effects logistic modelling was undertaken, with 28-day mortality as the primary outcome. Nested models were compared between a base model, age and frailty assessments using likelihood ratio testing (LRT) and an area under the receiver operating curves (AUROC). Results: The primary cohort enrolled 998 participants from 13 centres. The median age was 80 (range:65–101), 453 (45%) were female, and 377 (37.8%) died within 28 days. The sample was replicated in a validation cohort of two additional centres (n = 672) with similar characteristics. In the primary cohort, both mFI and CFS were associated with mortality in the base models. There was improved precision when fitting CFS to the base model +mFI (LRT = 25.87, p < 0.001); however, there was no improvement when fitting mFI to the base model +CFS (LRT = 1.99, p = 0.16). AUROC suggested increased discrimination when fitting CFS compared to age (p = 0.02) and age +mFI (p = 0.03). In contrast, the mFI offered no improved discrimination in any comparison (p > 0.05). Similar findings were seen in the validation cohort. Conclusions: These observations suggest the CFS has superior prognostic value to mFI in predicting mortality following COVID-19. Our data do not support the use of the mFI as a tool to aid clinical decision-making and prognosis.

We present "interoperability" as a guiding framework for statistical modelling to assist policy makers asking multiple questions using diverse datasets in the face of an evolving pandemic response. Interoperability provides an important set of principles for future pandemic preparedness, through the joint design and deployment of adaptable systems of statistical models for disease surveillance using probabilistic reasoning. We illustrate this through case studies for inferring spatial-temporal coronavirus disease 2019 (COVID-19) prevalence and reproduction numbers in England., Comment: 26 pages, 10 figures, for associated mpeg file Movie 1 please see https://www.dropbox.com/s/kn9y1v6zvivfla1/Interoperability_of_models_Movie_1.mp4?dl=0

When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the prior for this quantity can be implicit, and its prior density must be estimated. We show that error in this density estimate makes the two-stage Markov chain Monte Carlo sampler employed by Markov melding unstable and unreliable. We propose a robust two-stage algorithm that estimates the required prior marginal self-density ratios using weighted samples, dramatically improving accuracy in the tails of the distribution. The stabilised version of the algorithm is pragmatic and provides reliable inference. We demonstrate our approach using an evidence synthesis for inferring HIV prevalence, and an evidence synthesis of A/H1N1 influenza., Comment: 16 pages, 5 figures, 1 table. Major revisions, with substantial changes to Section 3

A challenge for practitioners of Bayesian inference is specifying a model that incorporates multiple relevant, heterogeneous data sets. It may be easier to instead specify distinct submodels for each source of data, then join the submodels together. We consider chains of submodels, where submodels directly relate to their neighbours via common quantities which may be parameters or deterministic functions thereof. We propose chained Markov melding, an extension of Markov melding, a generic method to combine chains of submodels into a joint model. One challenge we address is appropriately capturing the prior dependence between common quantities within a submodel, whilst also reconciling differences in priors for the same common quantity between two adjacent submodels. Estimating the posterior of the resulting overall joint model is also challenging, so we describe a sampler that uses the chain structure to incorporate information contained in the submodels in multiple stages, possibly in parallel. We demonstrate our methodology using two examples. The first example considers an ecological integrated population model, where multiple data sets are required to accurately estimate population immigration and reproduction rates. We also consider a joint longitudinal and time-to-event model with uncertain, submodel-derived event times. Chained Markov melding is a conceptually appealing approach to integrating submodels in these settings., 37 pages, 14 figures. Revisions to text

Introduction: We describe the clinical features and inpatient trajectories of older adults hospitalized with COVID-19 and explore relationships with frailty. Methods: This retrospective observational study included older adults admitted as an emergency to a University Hospital who were diagnosed with COVID-19. Patient characteristics and hospital outcomes, primarily inpatient death or death within 14 days of discharge, were described for the whole cohort and by frailty status. Associations with mortality were further evaluated using Cox Proportional Hazards Regression (Hazard Ratio (HR), 95% Confidence Interval). Results: 214 patients (94 women) were included of whom 142 (66.4%) were frail with a median Clinical Frailty Scale (CFS) score of 6. Frail compared to nonfrail patients were more likely to present with atypical symptoms including new or worsening confusion (45.1% vs. 20.8%, p &lt, 0.001) and were more likely to die (66% vs. 16%, p = 0.001). Older age, being male, presenting with high illness acuity and high frailty were independent predictors of death and a dose–response association between frailty and mortality was observed (CFS 1–4: reference, CFS 5–6: HR 1.78, 95% CI 0.90, 3.53, CFS 7–8: HR 2.57, 95% CI 1.26, 5.24). Conclusions: Clinicians should have a low threshold for testing for COVID-19 in older and frail patients during periods of community viral transmission, and diagnosis should prompt early advanced care planning.

Background: While numerous point-of-admission disease severity models for COVID-19 have been proposed, disease stratification that accounts for changes in a patient’s condition while in hospital is urgently needed to facilitate patient management and resource allocation. Methods: We developed a prognostic model for 48-hour in-hospital mortality using 473 consecutive patients with COVID-19 presenting to a UK hospital between March 1 and September 12, 2020; and temporally validated using data on 405 patients presenting between September 13, 2020 and January 3, 2021.The primary outcome was all-cause in-hospital mortality. We additionally considered the competing risks of discharge from hospital and transfer to a tertiary Intensive Care Unit for extracorporeal membrane oxygenation. We adopted a landmarking approach to dynamic prediction that accounts for competing risks and informative missingness, and selected predictors using penalised regression. The model estimates, at any point during a hospital visit, the probability of in-hospital mortality during the next 48 hours. Results: Our final model includes age, Clinical Frailty Scale score, heart rate, respiratory rate, SpO2/FiO2 ratio, white cell count, presence of acidosis (pH < 7.35) and Interleukin-6. Internal validation achieved an AUROC of 0.90 (95% CI 0.87–0.93) and temporal validation gave an AUROC of 0.91 (95% CI 0.88-0.95). Interpretation: Our model uniquely incorporates both static risk factors (e.g. age) and evolving clinical and laboratory data, to provide a dynamic risk prediction model that adapts to both sudden and gradual changes in an individual patient’s clinical condition. External validation outside the study hospital will be required before adoption. Funding: NIHR Cambridge Biomedical Research Centre, UKRI Medical Research Council Declaration of Interest: None to declare. Ethical Approval: The study was approved by a UK Health Research Authority ethics committee (20/WM/0125). Patient consent was waived because the de-identified data presented here were collected during routine clinical practice; there was no requirement for informed consent.

Background: A comprehensive description of the clinical characteristics, inpatient trajectory and relationship with frailty of older inpatients admitted with COVID-19 is essential in the management of older adults during the COVID-19 pandemic. The aim of this study was to describe the clinical features and inpatient trajectory of older inpatients with confirmed COVID -19.Methods: This was a retrospective observational study of hospitalised older adults. Subjects include unscheduled medical admissions of older inpatients to a University Hospital with laboratory and clinically confirmed COVID-19. The primary outcome was death during the inpatient stay or within 14 days of discharge after a maximum follow up time of 45 days. The characteristics of the cohort were described in detail as a whole and by frailty status.Results: 214 patients were included in this study with a mean length of stay of 11 days (Range 6 to 18 days), of whom 140 (65.4%) patients were discharged and 74 (34.6%) patients died in hospital. 142 (66.4%) patients were frail with median Clinical Frailty Scale (CFS) score of 6. Frail patients were more likely to present with atypical symptoms including new or worsening confusion compared to non-frail patients (20.8% vs 45.1%, pConclusions: Older adult inpatients with COVID-19 infection are likely to present with atypical symptoms, experience delirium and have a high mortality, especially if they are also living with frailty. Clinicians should have a low threshold for testing for COVID-19 in older and frail patients presenting to hospital as an emergency during periods when there is community transmission of COVID-19 and, when diagnosed, this should prompt early advanced care planning with the patient and family.

Delirium incidence in intensive care unit (ICU) patients is high and associated with poor outcome. Identification of high-risk patients may facilitate its prevention.To develop and validate a model based on data available at ICU admission to predict delirium development during a patient's complete ICU stay and to determine the predictive value of this model in relation to the time of delirium development.Prospective cohort study in 13 ICUs from seven countries. Multiple logistic regression analysis was used to develop the early prediction (E-PRE-DELIRIC) model on data of the first two-thirds and validated on data of the last one-third of the patients from every participating ICU.In total, 2914 patients were included. Delirium incidence was 23.6%. The E-PRE-DELIRIC model consists of nine predictors assessed at ICU admission: age, history of cognitive impairment, history of alcohol abuse, blood urea nitrogen, admission category, urgent admission, mean arterial blood pressure, use of corticosteroids, and respiratory failure. The area under the receiver operating characteristic curve (AUROC) was 0.76 [95% confidence interval (CI) 0.73-0.77] in the development dataset and 0.75 (95% CI 0.71-0.79) in the validation dataset. The model was well calibrated. AUROC increased from 0.70 (95% CI 0.67-0.74), for delirium that developed2 days, to 0.81 (95% CI 0.78-0.84), for delirium that developed6 days.Patients' delirium risk for the complete ICU length of stay can be predicted at admission using the E-PRE-DELIRIC model, allowing early preventive interventions aimed to reduce incidence and severity of ICU delirium.

Analysing multiple evidence sources is often feasible only via a modular approach, with separate submodels specified for smaller components of the available evidence. Here we introduce a generic framework that enables fully Bayesian analysis in this setting. We propose a generic method for forming a suitable joint model when joining submodels, and a convenient computational algorithm for fitting this joint model in stages, rather than as a single, monolithic model. The approach also enables splitting of large joint models into smaller submodels, allowing inference for the original joint model to be conducted via our multi-stage algorithm. We motivate and demonstrate our approach through two examples: joining components of an evidence synthesis of A/H1N1 influenza, and splitting a large ecology model.

MultiBUGS (https://www.multibugs.org) is a new version of the general-purpose Bayesian modelling software BUGS that implements a generic algorithm for parallelising Markov chain Monte Carlo (MCMC) algorithms to speed up posterior inference of Bayesian models. The algorithm parallelises evaluation of the product-form likelihoods formed when a parameter has many children in the directed acyclic graph (DAG) representation; and parallelises sampling of conditionally-independent sets of parameters. A heuristic algorithm is used to decide which approach to use for each parameter and to apportion computation across computational cores. This enables MultiBUGS to automatically parallelise the broad range of statistical models that can be fitted using BUGS-language software, making the dramatic speed-ups of modern multi-core computing accessible to applied statisticians, without requiring any experience of parallel programming. We demonstrate the use of MultiBUGS on simulated data designed to mimic a hierarchical e-health linked-data study of methadone prescriptions including 425,112 observations and 20,426 random effects. Posterior inference for the e-health model takes several hours in existing software, but MultiBUGS can perform inference in only 28 minutes using 48 computational cores., 20 pages, 4 figures

We consider situations, which are common in medical statistics, where we have a number of sets of response data, from different individuals, say, potentially under different conditions. A parametric model is defined for each set of data, giving rise to a set of random effects. Our goal here is to efficiently explore a range of possible 'population' models for the random effects, to select the most appropriate model. The range of possible models is potentially vast, because the random effects may depend on observed covariates, and there may be multiple credible ways of partitioning their variability. Here, we consider pharmacokinetic (PK) data on insulin aspart, a fast acting insulin analogue used in the treatment of diabetes. PK models are typically nonlinear (in their parameters), often complex and sometimes only available as a set of differential equations, with no closed-form solution. Fitting such a model for just a single individual can be a challenging task. Fitting a joint model for all individuals can be even harder, even without the complication of an overarching model selection objective. We describe a two-stage approach that decouples the population model for the random effects from the PK model applied to the response data but nevertheless fits the full, joint, hierarchical model, accounting fully for uncertainty. This allows us to repeatedly reuse results from a single analysis of the response data to explore various population models for the random effects. This greatly expedites not only model exploration but also cross-validation for the purposes of model criticism. © 2015 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

OBJECTIVE A recent randomized trial compared prandial insulin aspart (IAsp) with human insulin in type 1 diabetic pregnancy. The aim of this exploratory analysis was to investigate the incidence of severe hypoglycemia during pregnancy and compare women enrolled preconception with women enrolled during early pregnancy. RESEARCH DESIGN AND METHODS IAsp administered immediately before each meal was compared with human insulin administered 30 min before each meal in 99 subjects (44 to IAsp and 55 to human insulin) randomly assigned preconception and in 223 subjects (113 for IAsp and 110 for human insulin) randomly assigned in early pregnancy (

The advantages of Bayesian statistical approaches, such as flexibility and the ability to acknowledge uncertainty in all parameters, have made them the prevailing method for analysing the spread of infectious diseases in human or animal populations. We introduce a Bayesian approach to experimental host-pathogen systems that shares these attractive features. Since uncertainty in all parameters is acknowledged, existing information can be accounted for through prior distributions, rather than through fixing some parameter values. The non-linear dynamics, multi-factorial design, multiple measurements of responses over time and sampling error that are typical features of experimental host-pathogen systems can also be naturally incorporated. We analyse the dynamics of the free-living protozoan Paramecium caudatum and its specialist bacterial parasite Holospora undulata. Our analysis provides strong evidence for a saturable infection function, and we were able to reproduce the two waves of infection apparent in the data by separating the initial inoculum from the parasites released after the first cycle of infection. In addition, the parameter estimates from the hierarchical model can be combined to infer variations in the parasite's basic reproductive ratio across experimental groups, enabling us to make predictions about the effect of resources and host genotype on the ability of the parasite to spread. Even though the high level of variability between replicates limited the resolution of the results, this Bayesian framework has strong potential to be used more widely in experimental ecology.

Most governments try to discourage their citizens from taking extreme risks with their health and lives. Yet, for reasons not understood, many people continue to do so. We suggest a new approach to this longstanding question. First, we show that expected-utility theory predicts that 'happier' people will be less attracted to risky behaviors. Second, using BRFSS data on seatbelt use in a sample of 300,000 Americans, we document evidence strongly consistent with that prediction. Our result is demonstrated with various methodological approaches, including Bayesian model-selection and instrumental-variable estimation (based on unhappiness caused by widowhood). Third, using data on road accidents from the Add Health data set, we find strongly corroborative longitudinal evidence. These results suggest that government policy may need to address the underlying happiness of individuals rather than focus on behavioural symptoms.