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We study algorithms to analyze a particular class of Markov population processes that is often used in epidemiology. More specifically, Markov binomial chains are the model that arises from stochastic time-discretizations of classical compartmental models. In this work we formalize this class of Markov population processes and focus on the problem of computing the expected time to termination in a given such model. Our theoretical contributions include proving that Markov binomial chains whose flow of individuals through compartments is acyclic almost surely terminate. We give a PSPACE algorithm for the problem of approximating the time to termination and a direct algorithm for the exact problem in the Blum-Shub-Smale model of computation. Finally, we provide a natural encoding of Markov binomial chains into a common input language for probabilistic model checkers. We implemented the latter encoding and present some initial empirical results showcasing what formal methods can do for practicing epidemilogists.

In medical research, individual-level patient data provide invaluable information, but the patients' right to confidentiality remains of utmost priority. This poses a huge challenge when estimating statistical models such as linear mixed models, which is an extension of linear regression models that can account for potential heterogeneity whenever data come from different data providers. Federated learning algorithms tackle this hurdle by estimating parameters without retrieving individual-level data. Instead, iterative communication of parameter estimate updates between the data providers and analyst is required. In this paper, we propose an alternative framework to federated learning algorithms for fitting linear mixed models. Specifically, our approach only requires the mean, covariance, and sample size of multiple covariates from different data providers once. Using the principle of statistical sufficiency within the framework of likelihood as theoretical support, this proposed framework achieves estimates identical to those derived from actual individual-level data. We demonstrate this approach through real data on 15 068 patient records from 70 clinics at the Children's Hospital of Pennsylvania (CHOP). Assuming that each clinic only shares summary statistics once, we model the COVID-19 PCR test cycle threshold as a function of patient information. Simplicity, communication efficiency, and wider scope of implementation in any statistical software distinguish our approach from existing strategies in the literature.

Kriging is an established methodology for predicting spatial data in geostatistics. Current kriging techniques can handle linear dependencies on spatially referenced covariates. Although splines have shown promise in capturing nonlinear dependencies of covariates, their combination with kriging, especially in handling count data, remains underexplored. This paper proposes a novel Bayesian approach to the low-rank representation of geoadditive models, which integrates splines and kriging to account for both spatial correlations and nonlinear dependencies of covariates. The proposed method accommodates Gaussian and count data inherent in many geospatial datasets. Additionally, Laplace approximations to selected posterior distributions enhances computational efficiency, resulting in faster computation times compared to Markov chain Monte Carlo techniques commonly used for Bayesian inference. Method performance is assessed through a simulation study, demonstrating the effectiveness of the proposed approach. The methodology is applied to the analysis of heavy metal concentrations in the Meuse river and vulnerability to the coronavirus disease 2019 (COVID-19) in Belgium. Through this work, we provide a new flexible and computationally efficient framework for analyzing spatial data.

Random effect models for time-to-event data, also known as frailty models, provide a conceptually appealing way of quantifying association between survival times and of representing heterogeneities resulting from factors which may be difficult or impossible to measure. In the literature, the random effect is usually assumed to have a continuous distribution. However, in some areas of application, discrete frailty distributions may be more appropriate. The present paper is about the implementation and interpretation of the Addams family of discrete frailty distributions. We propose methods of estimation for this family of densities in the context of shared frailty models for the hazard rates for case I interval-censored data. Our optimization framework allows for stratification of random effect distributions by covariates. We highlight interpretational advantages of the Addams family of discrete frailty distributions and the K-point distribution as compared to other frailty distributions. A unique feature of the Addams family and the K-point distribution is that the support of the frailty distribution depends on its parameters. This feature is best exploited by imposing a model on the distributional parameters, resulting in a model with non-homogeneous covariate effects that can be analysed using standard measures such as the hazard ratio. Our methods are illustrated with applications to multivariate case I interval-censored infection data.

Approximate functional dependencies (AFDs) are functional dependencies (FDs) that "almost" hold in a relation. While various measures have been proposed to quantify the level to which an FD holds approximately, they are difficult to compare and it is unclear which measure is preferable when one needs to discover FDs in real-world data, i.e., data that only approximately satisfies the FD. In response, this paper formally and qualitatively compares AFD measures. We obtain a formal comparison through a novel presentation of measures in terms of Shannon and logical entropy. Qualitatively, we perform a sensitivity analysis w.r.t. structural properties of input relations and quantitatively study the effectiveness of AFD measures for ranking AFDs on real world data. Based on this analysis, we give clear recommendations for the AFD measures to use in practice., Comment: 40th IEEE International Conference on Data Engineering (ICDE 2024)

This rejoinder responds to discussions by of Caimo, Niezink, and Schweinberger and Fritz of ''A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks'' by Krivitsky, Coletti, and Hens, all published in the Journal of the American Statistical Association in 2023., Comment: 10 pages, 3 figures, 3 tables

Individual-based epidemiological models support the study of fine-grained preventive measures, such as tailored vaccine allocation policies, in silico. As individual-based models are computationally intensive, it is pivotal to identify optimal strategies within a reasonable computational budget. Moreover, due to the high societal impact associated with the implementation of preventive strategies, uncertainty regarding decisions should be communicated to policy makers, which is naturally embedded in a Bayesian approach. We present a novel technique for evaluating vaccine allocation strategies using a multi-armed bandit framework in combination with a Bayesian anytime $m$-top exploration algorithm. $m$-top exploration allows the algorithm to learn $m$ policies for which it expects the highest utility, enabling experts to inspect this small set of alternative strategies, along with their quantified uncertainty. The anytime component provides policy advisors with flexibility regarding the computation time and the desired confidence, which is important as it is difficult to make this trade-off beforehand. We consider the Belgian COVID-19 epidemic using the individual-based model STRIDE, where we learn a set of vaccination policies that minimize the number of infections and hospitalisations. Through experiments we show that our method can efficiently identify the $m$-top policies, which is validated in a scenario where the ground truth is available. Finally, we explore how vaccination policies can best be organised under different contact reduction schemes. Through these experiments, we show that the top policies follow a clear trend regarding the prioritised age groups and assigned vaccine type, which provides insights for future vaccination campaigns.

Infectious disease outbreaks can have a disruptive impact on public health and societal processes. As decision making in the context of epidemic mitigation is hard, reinforcement learning provides a methodology to automatically learn prevention strategies in combination with complex epidemic models. Current research focuses on optimizing policies w.r.t. a single objective, such as the pathogen's attack rate. However, as the mitigation of epidemics involves distinct, and possibly conflicting criteria (i.a., prevalence, mortality, morbidity, cost), a multi-objective approach is warranted to learn balanced policies. To lift this decision-making process to real-world epidemic models, we apply deep multi-objective reinforcement learning and build upon a state-of-the-art algorithm, Pareto Conditioned Networks (PCN), to learn a set of solutions that approximates the Pareto front of the decision problem. We consider the first wave of the Belgian COVID-19 epidemic, which was mitigated by a lockdown, and study different deconfinement strategies, aiming to minimize both COVID-19 cases (i.e., infections and hospitalizations) and the societal burden that is induced by the applied mitigation measures. We contribute a multi-objective Markov decision process that encapsulates the stochastic compartment model that was used to inform policy makers during the COVID-19 epidemic. As these social mitigation measures are implemented in a continuous action space that modulates the contact matrix of the age-structured epidemic model, we extend PCN to this setting. We evaluate the solution returned by PCN, and observe that it correctly learns to reduce the social burden whenever the hospitalization rates are sufficiently low. In this work, we thus show that multi-objective reinforcement learning is attainable in complex epidemiological models and provides essential insights to balance complex mitigation policies.

The last two decades have seen considerable progress in foundational aspects of statistical network analysis, but the path from theory to application is not straightforward. Two large, heterogeneous samples of small networks of within-household contacts in Belgium were collected using two different but complementary sampling designs: one smaller but with all contacts in each household observed, the other larger and more representative but recording contacts of only one person per household. We wish to combine their strengths to learn the social forces that shape household contact formation and facilitate simulation for prediction of disease spread, while generalising to the population of households in the region. To accomplish this, we describe a flexible framework for specifying multi-network models in the exponential family class and identify the requirements for inference and prediction under this framework to be consistent, identifiable, and generalisable, even when data are incomplete; explore how these requirements may be violated in practice; and develop a suite of quantitative and graphical diagnostics for detecting violations and suggesting improvements to candidate models. We report on the effects of network size, geography, and household roles on household contact patterns (activity, heterogeneity in activity, and triadic closure)., Comment: 101 pages (3 front matter, 26 body, 72 appendix), 35 figures (4 body, 31 appendix), 66 tables (1 body, 61 appendix)

Several important aspects related to SARS-CoV-2 transmission are not well known due to a lack of appropriate data. However, mathematical and computational tools can be used to extract part of this information from the available data, like some hidden age-related characteristics. In this paper, we present a method to investigate age-specific differences in transmission parameters related to susceptibility to and infectiousness upon contracting SARS-CoV-2 infection. More specifically, we use panel-based social contact data from diary-based surveys conducted in Belgium combined with the next generation principle to infer the relative incidence and we compare this to real-life incidence data. Comparing these two allows for the estimation of age-specific transmission parameters. Our analysis implies the susceptibility in children to be around half of the susceptibility in adults, and even lower for very young children (preschooler). However, the probability of adults and the elderly to contract the infection is decreasing throughout the vaccination campaign, thereby modifying the picture over time., Comment: Revised version, 17 pages, supplementary material 15 pages

The mixture cure model for analyzing survival data is characterized by the assumption that the population under study is divided into a group of subjects who will experience the event of interest over some finite time horizon and another group of cured subjects who will never experience the event irrespective of the duration of follow-up. When using the Bayesian paradigm for inference in survival models with a cure fraction, it is common practice to rely on Markov chain Monte Carlo (MCMC) methods to sample from posterior distributions. Although computationally feasible, the iterative nature of MCMC often implies long sampling times to explore the target space with chains that may suffer from slow convergence and poor mixing. An alternative strategy for fast and flexible sampling-free Bayesian inference in the mixture cure model is suggested in this paper by combining Laplace approximations and penalized B-splines. A logistic regression model is assumed for the cure proportion and a Cox proportional hazards model with a P-spline approximated baseline hazard is used to specify the conditional survival function of susceptible subjects. Laplace approximations to the conditional latent vector are based on analytical formulas for the gradient and Hessian of the log-likelihood, resulting in a substantial speed-up in approximating posterior distributions. The statistical performance and computational efficiency of the proposed Laplacian-P-splines mixture cure (LPSMC) model is assessed in a simulation study. Results show that LPSMC is an appealing alternative to classic MCMC for approximate Bayesian inference in standard mixture cure models. Finally, the novel LPSMC approach is illustrated on three applications involving real survival data., Comment: 36 pages, 7 figures, 7 tables

Epidemics of infectious diseases are an important threat to public health and global economies. Yet, the development of prevention strategies remains a challenging process, as epidemics are non-linear and complex processes. For this reason, we investigate a deep reinforcement learning approach to automatically learn prevention strategies in the context of pandemic influenza. Firstly, we construct a new epidemiological meta-population model, with 379 patches (one for each administrative district in Great Britain), that adequately captures the infection process of pandemic influenza. Our model balances complexity and computational efficiency such that the use of reinforcement learning techniques becomes attainable. Secondly, we set up a ground truth such that we can evaluate the performance of the 'Proximal Policy Optimization' algorithm to learn in a single district of this epidemiological model. Finally, we consider a large-scale problem, by conducting an experiment where we aim to learn a joint policy to control the districts in a community of 11 tightly coupled districts, for which no ground truth can be established. This experiment shows that deep reinforcement learning can be used to learn mitigation policies in complex epidemiological models with a large state space. Moreover, through this experiment, we demonstrate that there can be an advantage to consider collaboration between districts when designing prevention strategies.

In observational surveys, post-stratification is used to reduce bias resulting from differences between the survey population and the population under investigation. However, this can lead to inflated post-stratification weights and, therefore, appropriate methods are required to obtain less variable estimates. Proposed methods include collapsing post-strata, trimming post-stratification weights, generalized regression estimators (GREG) and weight smoothing models, the latter defined by random-effects models that induce shrinkage across post-stratum means. Here, we first describe the weight-smoothing model for prevalence estimation from binary survey outcomes in observational surveys. Second, we propose an extension of this method for trend estimation. And, third, a method is provided such that the GREG can be used for prevalence and trend estimation for observational surveys. Variance estimates of all methods are described. A simulation study is performed to compare the proposed methods with other established methods. The performance of the nonparametric GREG is consistent over all simulation conditions and therefore serves as a valuable solution for prevalence and trend estimation from observational surveys. The method is applied to the estimation of the prevalence and incidence trend of influenza-like illness using the 2010/2011 Great Influenza Survey in Flanders, Belgium., Comment: Published at http://dx.doi.org/10.1214/15-AOAS874 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)