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It is of scientific interest to identify essential biomarkers in biological processes underlying diseases to facilitate precision medicine. Factor analysis (FA) has long been used to address this goal: by assuming latent biological pathways drive the activity of measurable biomarkers, a biomarker is more influential if its absolute factor loading is larger. Although correlation between biomarkers has been properly handled under this framework, correlation between latent pathways are often overlooked, as one classical assumption in FA is the independence between factors. However, this assumption may not be realistic in the context of pathways, as existing biological knowledge suggests that pathways interact with one another rather than functioning independently. Motivated by sparsely and irregularly collected longitudinal measurements of metabolites in a COVID-19 study of large sample size, we propose a dynamic factor analysis model that can account for the potential cross-correlations between pathways, through a multi-output Gaussian processes (MOGP) prior on the factor trajectories. To mitigate against overfitting caused by sparsity of longitudinal measurements, we introduce a roughness penalty upon MOGP hyperparameters and allow for non-zero mean functions. To estimate these hyperparameters, we develop a stochastic expectation maximization (StEM) algorithm that scales well to the large sample size. In our simulation studies, StEM leads across all sample sizes considered to a more accurate and stable estimate of the MOGP hyperparameters than a comparator algorithm used in previous research. Application to the motivating example identifies a kynurenine pathway that affects the clinical severity of patients with COVID-19. In particular, a novel biomarker taurine is discovered, which has been receiving increased attention clinically, yet its role was overlooked in a previous analysis.

The increasing availability of high-dimensional, longitudinal measures of gene expression can facilitate understanding of biological mechanisms, as required for precision medicine. Biological knowledge suggests that it may be best to describe complex diseases at the level of underlying pathways, which may interact with one another. We propose a Bayesian approach that allows for characterising such correlation among different pathways through Dependent Gaussian Processes (DGP) and mapping the observed high-dimensional gene expression trajectories into unobserved low-dimensional pathway expression trajectories via Bayesian Sparse Factor Analysis. Our proposal is the first attempt to relax the classical assumption of independent factors for longitudinal data and has demonstrated a superior performance in recovering the shape of pathway expression trajectories, revealing the relationships between genes and pathways, and predicting gene expressions (closer point estimates and narrower predictive intervals), as demonstrated through simulations and real data analysis. To fit the model, we propose a Monte Carlo Expectation Maximization (MCEM) scheme that can be implemented conveniently by combining a standard Markov Chain Monte Carlo sampler and an R package GPFDA (Konzen and others, 2021), which returns the maximum likelihood estimates of DGP hyperparameters. The modular structure of MCEM makes it generalizable to other complex models involving the DGP model component. Our R package DGP4LCF that implements the proposed approach is available on CRAN.

Precision medicine is an emerging field that takes into account individual heterogeneity to inform better clinical practice. In clinical trials, the evaluation of treatment effect heterogeneity is an important component, and recently, many statistical methods have been proposed for stratifying patients into different subgroups based on such heterogeneity. However, the majority of existing methods developed for this purpose focus on the case with a dichotomous treatment and are not directly applicable to multi-arm trials. In this paper, we consider the problem of patient stratification in multi-arm trial settings and propose a two-stage procedure within the Bayesian nonparametric framework. Specifically, we first use Bayesian additive regression trees (BART) to predict potential outcomes (treatment responses) under different treatment options for each patient, and then we leverage Bayesian profile regression to cluster patients into subgroups according to their baseline characteristics and predicted potential outcomes. We further embed a variable selection procedure into our proposed framework to identify the patient characteristics that actively "drive" the clustering structure. We conduct simulation studies to examine the performance of our proposed method and demonstrate the method by applying it to a UK-based multi-arm blood donation trial, wherein our method uncovers five clinically meaningful donor subgroups.

Personalized medicine has gained much popularity recently as a way of providing better healthcare by tailoring treatments to suit individuals. Our research, motivated by the UK INTERVAL blood donation trial, focuses on estimating the optimal individualized treatment rule (ITR) in the ordinal treatment-arms setting. Restrictions on minimum lengths between whole blood donations exist to safeguard donor health and quality of blood received. However, the evidence-base for these limits is lacking. Moreover, in England, the blood service is interested in making blood donation both safe and sustainable by integrating multi-marker data from INTERVAL and developing personalized donation strategies. As the three inter-donation interval options in INTERVAL have clear orderings, we propose a sequential re-estimation learning method that effectively incorporates "treatment" orderings when identifying optimal ITRs. Furthermore, we incorporate variable selection into our method for both linear and nonlinear decision rules to handle situations with (noise) covariates irrelevant for decision-making. Simulations demonstrate its superior performance over existing methods that assume multiple nominal treatments by achieving smaller misclassification rates and larger value functions. Application to a much-in-demand donor subgroup shows that the estimated optimal ITR achieves both the highest utilities and largest proportions of donors assigned to the safest inter-donation interval option in INTERVAL.

Background: Trends in hospitalised case-fatality risk (HFR), risk of intensive care unit (ICU) admission and lengths of stay for patients hospitalised for COVID-19 in England over the pre-vaccination era are unknown. Methods: Data on hospital and ICU admissions with COVID-19 at 31 NHS trusts in England were collected by Public Health England's Severe Acute Respiratory Infections surveillance system and linked to death information. We applied parametric multi-state mixture models, accounting for censored outcomes and regressing risks and times between events on month of admission, geography, and baseline characteristics. Findings: 20,785 adults were admitted with COVID-19 in 2020. Between March and June/July/August estimated HFR reduced from 31.9% (95% confidence interval 30.3-33.5%) to 10.9% (9.4-12.7%), then rose steadily from 21.6% (18.4-25.5%) in September to 25.7% (23.0-29.2%) in December, with steeper increases among older patients, those with multi-morbidity and outside London/South of England. ICU admission risk reduced from 13.9% (12.8-15.2%) in March to 6.2% (5.3-7.1%) in May, rising to a high of 14.2% (11.1-17.2%) in September. Median length of stay in non-critical care increased during 2020, from 6.6 to 12.3 days for those dying, and from 6.1 to 9.3 days for those discharged. Interpretation: Initial improvements in patient outcomes, corresponding to developments in clinical practice, were not sustained throughout 2020, with HFR in December approaching the levels seen at the start of the pandemic, whilst median hospital stays have lengthened. The role of increased transmission, new variants, case-mix and hospital pressures in increasing COVID-19 severity requires urgent further investigation., Comment: 45 pages, 12 figures

The case-cohort study design bypasses resource constraints by collecting certain expensive covariates for only a small subset of the full cohort. Weighted Cox regression is the most widely used approach for analysing case-cohort data within the Cox model, but is inefficient. Alternative approaches based on multiple imputation and nonparametric maximum likelihood suffer from incompatibility and computational issues respectively. We introduce a novel Bayesian framework for case-cohort Cox regression that avoids the aforementioned problems. Users can include auxiliary variables to help predict the unmeasured expensive covariates with a prediction model of their choice, while the models for the nuisance parameters are nonparametrically specified and integrated out. Posterior sampling can be carried out using procedures based on the pseudo-marginal MCMC algorithm. The method scales effectively to large, complex datasets, as demonstrated in our application: investigating the associations between saturated fatty acids and type 2 diabetes using the EPIC-Norfolk study. As part of our analysis, we also develop a new approach for handling compositional data in the Cox model, leading to more reliable and interpretable results compared to previous studies. The performance of our method is illustrated with extensive simulations. The code used to produce the results in this paper can be found at https://github.com/andrewyiu/bayes_cc ., Comment: 29 pages, 3 figures, 2 tables

We present the findings of "The Alzheimer's Disease Prediction Of Longitudinal Evolution" (TADPOLE) Challenge, which compared the performance of 92 algorithms from 33 international teams at predicting the future trajectory of 219 individuals at risk of Alzheimer's disease. Challenge participants were required to make a prediction, for each month of a 5-year future time period, of three key outcomes: clinical diagnosis, Alzheimer's Disease Assessment Scale Cognitive Subdomain (ADAS-Cog13), and total volume of the ventricles. The methods used by challenge participants included multivariate linear regression, machine learning methods such as support vector machines and deep neural networks, as well as disease progression models. No single submission was best at predicting all three outcomes. For clinical diagnosis and ventricle volume prediction, the best algorithms strongly outperform simple baselines in predictive ability. However, for ADAS-Cog13 no single submitted prediction method was significantly better than random guesswork. Two ensemble methods based on taking the mean and median over all predictions, obtained top scores on almost all tasks. Better than average performance at diagnosis prediction was generally associated with the additional inclusion of features from cerebrospinal fluid (CSF) samples and diffusion tensor imaging (DTI). On the other hand, better performance at ventricle volume prediction was associated with inclusion of summary statistics, such as the slope or maxima/minima of biomarkers. TADPOLE's unique results suggest that current prediction algorithms provide sufficient accuracy to exploit biomarkers related to clinical diagnosis and ventricle volume, for cohort refinement in clinical trials for Alzheimer's disease. However, results call into question the usage of cognitive test scores for patient selection and as a primary endpoint in clinical trials., Comment: Presents final results of the TADPOLE competition. 60 pages, 7 tables, 14 figures

In psoriatic arthritis, it is important to understand the joint activity (represented by swelling and pain) and damage processes because both are related to severe physical disability. This paper aims to provide a comprehensive investigation in to both processes occurring over time, in particular their relationship, by specifying a joint multi-state model at the individual hand joint-level, which also accounts for many of their important features. As there are multiple hand joints, such an analysis will be based on the use of clustered multi-state models. Here we consider an observation-level random effects structure with dynamic covariates and allow for the possibility that a subpopulation of patients are at minimal risk of damage. Such an analysis is found to provide further understanding of the activity-damage relationship beyond that provided by previous analyses. Consideration is also given to the modelling of mean sojourn times and jump probabilities. In particular, a novel model parameterization which allows easily interpretable covariate effects to act on these quantities is proposed.

A prompt public health response to a new epidemic relies on the ability to monitor and predict its evolution in real time as data accumulate. The 2009 A/H1N1 outbreak in the UK revealed pandemic data as noisy, contaminated, potentially biased, and originating from multiple sources. This seriously challenges the capacity for real-time monitoring. Here we assess the feasibility of real-time inference based on such data by constructing an analytic tool combining an age-stratified SEIR transmission model with various observation models describing the data generation mechanisms. As batches of data become available, a sequential Monte Carlo (SMC) algorithm is developed to synthesise multiple imperfect data streams, iterate epidemic inferences and assess model adequacy amidst a rapidly evolving epidemic environment, substantially reducing computation time in comparison to standard MCMC, to ensure timely delivery of real-time epidemic assessments. In application to simulated data designed to mimic the 2009 A/H1N1 epidemic, SMC is shown to have additional benefits in terms of assessing predictive performance and coping with parameter non-identifiability., Comment: 30 pages, 8 figures

Knowledge of the severity of an influenza outbreak is crucial for informing and monitoring appropriate public health responses, both during and after an epidemic. However, case-fatality, case-intensive care admission and case-hospitalisation risks are difficult to measure directly. Bayesian evidence synthesis methods have previously been employed to combine fragmented, under-ascertained and biased surveillance data coherently and consistently, to estimate case-severity risks in the first two waves of the 2009 A/H1N1 influenza pandemic experienced in England. We present in detail the complex probabilistic model underlying this evidence synthesis, and extend the analysis to also estimate severity in the third wave of the pandemic strain during the 2010/2011 influenza season. We adapt the model to account for changes in the surveillance data available over the three waves. We consider two approaches: (a) a two-stage approach using posterior distributions from the model for the first two waves to inform priors for the third wave model; and (b) a one-stage approach modelling all three waves simultaneously. Both approaches result in the same key conclusions: (1) that the age-distribution of the case-severity risks is "u"-shaped, with children and older adults having the highest severity; (2) that the age-distribution of the infection attack rate changes over waves, school-age children being most affected in the first two waves and the attack rate in adults over 25 increasing from the second to third waves; and (3) that when averaged over all age groups, case-severity appears to increase over the three waves. The extent to which the final conclusion is driven by the change in age-distribution of those infected over time is subject to discussion., Comment: Published in at http://dx.doi.org/10.1214/14-AOAS775 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We develop a maximum likelihood estimating approach for time-to-event Weibull regression models with outcome-dependent sampling, where sampling of subjects is dependent on the residual fraction of the time left to developing the event of interest. Additionally, we propose a two-stage approach which proceeds by iteratively estimating, through a pseudo score, the Weibull parameters of interest (i.e., the regression parameters) conditional on the inverse probability of sampling weights; and then re-estimating these weights (given the updated Weibull parameter estimates) through the profiled full likelihood. With these two new methods, both the estimated sampling mechanism parameters and the Weibull parameters are consistently estimated under correct specification of the conditional referral distribution. Standard errors for the regression parameters are obtained directly from inverting the observed information matrix in the full likelihood specification and by either calculating bootstrap or robust standard errors for the hybrid pseudo score/profiled likelihood approach. Loss of efficiency with the latter approach is considered. Robustness of the proposed methods to misspecification of the referral mechanism and the time-to-event distribution is also briefly examined. Further, we show how to extend our methods to the family of parametric time-to-event distributions characterized by the generalized gamma distribution. The motivation for these two approaches came from data on time to cirrhosis from hepatitis C viral infection in patients referred to the Edinburgh liver clinic. We analyze these data here., Comment: Published in at http://dx.doi.org/10.1214/14-AOAS725 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)