An Efficient Approach to Nowcasting the Time-varying Reproduction Number.

Estimating the instantaneous reproduction number () in near real time is crucial for monitoring and responding to epidemic outbreaks on a daily basis. However, such estimates often suffer from bias due to reporting delays inherent in surveillance systems. We propose a fast and flexible Bayesian methodology to overcome this challenge by estimating while taking into account reporting delays. Furthermore, the method naturally takes into account the uncertainty associated with the nowcasting of cases to get a valid uncertainty estimation of the nowcasted reproduction number. We evaluate the proposed methodology through a simulation study and apply it to COVID-19 incidence data in Belgium.

The combined effect of systemic antibiotics and proton pump inhibitors on Clostridioides difficile infection and recurrence.

BACKGROUND: Antibiotics and proton pump inhibitors (PPI) are recognized risk factors for acquisition and recurrence of Clostridioides difficile infection (CDI), yet combined effects remain unclear. OBJECTIVES: To assess the short- and long-term effects of antibiotics and PPIs on CDI risk and recurrence. METHODS: Population-based study including all 43 152 patients diagnosed with CDI in Sweden (2006-2019), and 355 172 matched population controls without CDI. The impact of antibiotics and PPIs on CDI risk and recurrence was explored for recent (0-30 days) and preceding (31-180 days) use prior to their first CDI diagnosis, using multivariable conditional logistic regression presented as odds ratios (ORs) and 95% confidence interval, adjusted for demographics, comorbidities and other drugs. RESULTS: Compared to controls, the combined effect of recent PPIs and antibiotics [ORAB+PPI = 17.51 (17.48-17.53)] on CDI risk was stronger than the individual effects [ORAB = 15.37 (14.83-15.93); ORPPI = 2.65 (2.54-2.76)]. Results were less pronounced for exposure during the preceding months. Dose-response analyses showed increasing exposure correlated with CDI risk [recent use: ORAB = 6.32 (6.15-6.49); ORPPI = 1.65 (1.62-1.68) per prescription increase].Compared to individuals without recurrence (rCDI), recent [ORAB = 1.30 (1.23-1.38)] and preceding [ORAB = 1.23 (1.16-1.31); ORPPI = 1.12 (1.03-1.21)] use also affected the risk of recurrence yet without significant interaction between both. Recent macrolides/lincosamides/streptogramins; other antibacterials including nitroimidazole derivates; non-penicillin beta lactams and quinolones showed the strongest association with CDI risk and recurrence, particularly for recent use. PPI use, both recent and preceding, further increased the CDI risk associated with almost all antibiotic classes. CONCLUSION: Recent and less recent use of PPIs and systemic antibiotics was associated with an increased risk of CDI, particularly in combination.

Cohort-based smoothing methods for age-specific contact rates.

The use of social contact rates is widespread in infectious disease modeling since it has been shown that they are key driving forces of important epidemiological parameters. Quantification of contact patterns is crucial to parameterize dynamic transmission models and to provide insights on the (basic) reproduction number. Information on social interactions can be obtained from population-based contact surveys, such as the European Commission project POLYMOD. Estimation of age-specific contact rates from these studies is often done using a piecewise constant approach or bivariate smoothing techniques. For the latter, typically, smoothness is introduced in the dimensions of the respondent's and contact's age (i.e., the rows and columns of the social contact matrix). We propose a smoothing constrained approach-taking into account the reciprocal nature of contacts-introducing smoothness over the diagonal (including all subdiagonals) of the social contact matrix. This modeling approach is justified assuming that when people age their contact behavior changes smoothly. We call this smoothing from a cohort perspective. Two approaches that allow for smoothing over social contact matrix diagonals are proposed, namely (i) reordering of the diagonal components of the contact matrix and (ii) reordering of the penalty matrix ensuring smoothness over the contact matrix diagonals. Parameter estimation is done in the likelihood framework by using constrained penalized iterative reweighted least squares. A simulation study underlines the benefits of cohort-based smoothing. Finally, the proposed methods are illustrated on the Belgian POLYMOD data of 2006. Code to reproduce the results of the article can be downloaded on this GitHub repository https://github.com/oswaldogressani/Cohort_smoothing.

An approximate Bayesian approach for estimation of the instantaneous reproduction number under misreported epidemic data.

In epidemic models, the effective reproduction number is of central importance to assess the transmission dynamics of an infectious disease and to orient health intervention strategies. Publicly shared data during an outbreak often suffers from two sources of misreporting (underreporting and delay in reporting) that should not be overlooked when estimating epidemiological parameters. The main statistical challenge in models that intrinsically account for a misreporting process lies in the joint estimation of the time-varying reproduction number and the delay/underreporting parameters. Existing Bayesian approaches typically rely on Markov chain Monte Carlo algorithms that are extremely costly from a computational perspective. We propose a much faster alternative based on Laplacian-P-splines (LPS) that combines Bayesian penalized B-splines for flexible and smooth estimation of the instantaneous reproduction number and Laplace approximations to selected posterior distributions for fast computation. Assuming a known generation interval distribution, the incidence at a given calendar time is governed by the epidemic renewal equation and the delay structure is specified through a composite link framework. Laplace approximations to the conditional posterior of the spline vector are obtained from analytical versions of the gradient and Hessian of the log-likelihood, implying a drastic speed-up in the computation of posterior estimates. Furthermore, the proposed LPS approach can be used to obtain point estimates and approximate credible intervals for the delay and reporting probabilities. Simulation of epidemics with different combinations for the underreporting rate and delay structure (one-day, two-day, and weekend delays) show that the proposed LPS methodology delivers fast and accurate estimates outperforming existing methods that do not take into account underreporting and delay patterns. Finally, LPS is illustrated in two real case studies of epidemic outbreaks.

EpiLPS: A fast and flexible Bayesian tool for estimation of the time-varying reproduction number.

In infectious disease epidemiology, the instantaneous reproduction number [Formula: see text] is a time-varying parameter defined as the average number of secondary infections generated by an infected individual at time t. It is therefore a crucial epidemiological statistic that assists public health decision makers in the management of an epidemic. We present a new Bayesian tool (EpiLPS) for robust estimation of the time-varying reproduction number. The proposed methodology smooths the epidemic curve and allows to obtain (approximate) point estimates and credible intervals of [Formula: see text] by employing the renewal equation, using Bayesian P-splines coupled with Laplace approximations of the conditional posterior of the spline vector. Two alternative approaches for inference are presented: (1) an approach based on a maximum a posteriori argument for the model hyperparameters, delivering estimates of [Formula: see text] in only a few seconds; and (2) an approach based on a Markov chain Monte Carlo (MCMC) scheme with underlying Langevin dynamics for efficient sampling of the posterior target distribution. Case counts per unit of time are assumed to follow a negative binomial distribution to account for potential overdispersion in the data that would not be captured by a classic Poisson model. Furthermore, after smoothing the epidemic curve, a "plug-in'' estimate of the reproduction number can be obtained from the renewal equation yielding a closed form expression of [Formula: see text] as a function of the spline parameters. The approach is extremely fast and free of arbitrary smoothing assumptions. EpiLPS is applied on data of SARS-CoV-1 in Hong-Kong (2003), influenza A H1N1 (2009) in the USA and on the SARS-CoV-2 pandemic (2020-2021) for Belgium, Portugal, Denmark and France.

Laplacian-P-splines for Bayesian inference in the mixture cure model.

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. Furthermore, extra efforts have to be invested in diagnostic checks to monitor the reliability of the generated posterior samples. A sampling-free strategy for fast and flexible Bayesian inference in the mixture cure model is suggested in this article 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 posterior 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 spline specification yields smooth estimates of survival curves and functions of latent variables together with their associated credible interval are estimated in seconds. A fully stochastic algorithm based on a Metropolis-Langevin-within-Gibbs sampler is also suggested as an alternative to the proposed Laplacian-P-splines mixture cure (LPSMC) methodology. The statistical performance and computational efficiency of LPSMC is assessed in a simulation study. Results show that LPSMC is an appealing alternative to MCMC for approximate Bayesian inference in standard mixture cure models. Finally, the novel LPSMC approach is illustrated on three applications involving real survival data.