Marc Aerts

Introduction: A new Bayesian framework for dose-response modelling and benchmark dose determination is introduced, following guidelines from the World Health Organization and the European Food Safety Authority. It incorporates model averaging across a family of candidate models and defines prior distributions at the level of response distributions, dose-response median models, and model parameters. In addition to providing a fully probabilistic inferential framework, the Bayesian paradigm offers some methodological advantages over frequentist approaches. Methods: The proposed framework employs regularising default priors that are adaptive to study design and biologically plausible constraints. Informative priors can also be incorporated. The performance was evaluated against frequentist model averaging across four case studies using both real and simulated datasets. Results: In simulations based on the Bisphenol A study, only 3% of BMD estimates obtained using frequentist inference met the EFSA accuracy criterion (BMDU/BMDL < 50), compared with 83% obtained using Bayesian inference. Other analyses showed that design-adaptive and biology-respecting regularising priors improved estimation relative to frequentist hard constraints. In a small-sample case study with poorly informative experimental design, frequentist quantile bootstrap confidence intervals for the BMD were highly sensitive to the number of bootstrap replicates, whereas Bayesian MCMC-based inference remained stable and reliable. A final case study demonstrated that constructing an informative overarching BMD prior from multiple historical studies improved estimation performance. Discussion: The case studies illustrate improved estimation and the ability to incorporate historical information. These findings support the use of Bayesian methods as a powerful alternative for regulatory toxicology and risk assessment applications.

Longitudinal data are frequently encountered in medical research, where participants are followed throughout time. Additional structure and hence complexity occurs when there is pairing between the participants (e.g. matched case-control studies) or within the participants (e.g. analysis of participants’ both eyes). Various modelling approaches, identified through a systematic review, are discussed, including (un)paired [ ]-tests, multivariate analysis of variance, difference scores, linear mixed models (LMMs), and new or more recent statistical methods. Next, highlighting the importance of selecting appropriate models based on the data’s characteristics, the methods are applied to both a real-life case study in ophthalmology and a simulated case-control study. Key findings include the superiority of the conditional LMM and multilevel models in handling paired longitudinal data in terms of precision. Moreover, the article underscores the impact of accounting for intra-pair correlations and missing data mechanisms. Focus will be on discussing the advantages and disadvantages of the approaches, rather than on the mathematical or computational details.

Monitoring and investigating temporal trends in antimicrobial data is a high priority for human and animal health authorities. Timely detection of temporal changes in antimicrobial resistance (AMR) can rely not only on monitoring and analyzing the proportion of resistant isolates based on the use of a clinical or epidemiological cut-off value, but also on more subtle changes and trends in the full distribution of minimum inhibitory concentration (MIC) values. The nature of the MIC distribution is categorical and ordinal (discrete). In this contribution, we developed a particular family of multicategory logit models for estimating and modelling MIC distributions over time. It allows the detection of a multitude of temporal trends in the full discrete distribution, without any assumption on the underlying continuous distribution for the MIC values. The experimental ranges of the serial dilution experiments may vary across laboratories and over time. The proposed categorical model allows to estimate the MIC distribution over the maximal range of the observed experiments, and allows the observed ranges to vary across labs and over time. The use and performance of the model is illustrated with two datasets on AMR in Salmonella.

The European Commission requested scientific and technical assistance in the preparation of a EU‐wide baseline survey protocol for a European Union (EU) coordinated monitoring programme on the prevalence of methicillin‐resistant Staphylococcus Aureus (MRSA) in pigs. The objective of the survey is to estimate the MRSA prevalence in batches of fattening pigs at slaughter at both European and national levels, with a 95% level of confidence and a level of precision of 10% considering an expected prevalence of 50%. The survey protocol defines the target population, the sample size for the survey, sample collection requirements, the analytical methods (for isolation, identification, phenotypic susceptibility testing and further genotypic testing of MRSA isolates), the data reporting requirements and the plan of analysis. The samples are to be analysed according to the laboratory protocols available on the European Union Reference Laboratory (EURL‐AR) website. Generalised linear models will be used to estimate proportion (with 95% confidence intervals) of batches of slaughter pigs tested positive to MRSA. The necessary data to be reported by the EU Member States to support this baseline survey are presented in three data models. The results of the survey should be reported using the EFSA data collection framework.

When estimating a benchmark dose (BMD) from chemical toxicity experiments, model averaging is recommended by the National Institute for Occupational Safety and Health, World Health Organization and European Food Safety Authority. Though numerous studies exist for model average BMD estimation using dichotomous responses, fewer studies investigate it for BMD estimation using continuous response. In this setting, model averaging a BMD poses additional problems as the assumed distribution is essential to many BMD definitions, and distributional uncertainty is underestimated when one error distribution is chosen a priori. As model averaging combines full models, there is no reason one cannot include multiple error distributions. Consequently, we define a continuous model averaging approach over distributional models and show that it is superior to single distribution model averaging. To show the superiority of the approach, we apply the method to simulated and experimental response data.

A major outbreak of the Ebola virus occurred in 2014 in Sierra Leone. We investigate the spatial heterogeneity of the outbreak among districts in Sierra Leone. The stochastic discrete-time susceptible-exposed-infectious-removed (SEIR) model is used, allowing for probabilistic movements from one compartment to another. Our model accounts for heterogeneity among districts by making use of a hierarchical approach. The transmission rates are considered time-varying. It is investigated whether or not incubation period, infectious period and transmission rates are different among districts. Estimation is done using the Bayesian formalism. The posterior estimates of the effective reproductive number were substantially different across the districts, with pronounced variability in districts with few cases of Ebola. The posterior estimates of the reproductive number at the district level varied between below 1.0 and 4.5, whereas at nationwide level it varied between below 1.0 and 2.5. The posterior estimate of the effective reproductive number reached a value below 1.0 around December. In some districts, the effective reproductive number pointed out for the persistence of the outbreak or for a likely resurgence of new cases of Ebola virus disease (EVD). The posterior estimates have shown to be highly sensitive to prior elicitation, mainly the incubation period and infectious period.

Censoring due to a limit of detection or limit of quantification happens quite often in many medical studies. Conventional approaches to deal with censoring when analyzing these data include, for example, the substitution method and the complete case (CC) analysis. More recently, maximum likelihood estimation (MLE) has been increasingly used. While the CC analysis and the substitution method usually lead to biased estimates, the MLE approach appears to perform well in many situations. This article proposes an MLE approach to estimate the association between two measurements in the presence of censoring in one or both quantities. The central idea is to use a copula function to join the marginal distributions of the two measurements. In various simulation studies, we show that our approach outperforms existing conventional methods (CC and substitution analyses). In addition, rank‐based measures of global association such as Kendall's tau or Spearman's rho can be studied, hence, attention is not only confined to Pearson's product‐moment correlation coefficient capturing solely linear association. We have shown in our simulations that our approach is robust to misspecification of the copula function or marginal distributions given a small association. Furthermore, we propose a straightforward MLE method to fit a (multiple) linear regression model in the presence of censoring in a covariate or both the covariate and the response. Given the marginal distribution of the censored covariate, our method outperforms conventional approaches. We also compare and discuss the performance of our method with multiple imputation and missing indicator model approaches.