Using publicly available data on the number of new hospitalisations we use a newly developed statistical model to produce a phase portrait to monitor the epidemic allowing for assessing whether or not intervention measures are needed to keep hospital capacity under control. The phase portrait is called a cliquets' diagram, referring to the discrete alarm phases it points to. Using this cliquets' diagram we show that intervention measures were associated with an effective mitigation of a Summer resurgence but that too little too late was done to prevent a large autumn wave in Belgium. ; European Union's Horizon 2020 research and innovation programme - project EpiPose [101003688]; European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (ERC) [682540]
COVID-19 has developed into a pandemic, hitting hard on our communities. As the pandemic continues to bring health and economic hardship, keeping mortality as low as possible will be the highest priority for individuals; hence governments must put in place measures to ameliorate the inevitable economic downturn. The course of an epidemic may be defined by a series of key factors. In the early stages of a new infectious disease outbreak, it is crucial to understand the transmission dynamics of the infection. The basic reproduction number (R(0)), which defines the mean number of secondary cases generated by one primary case when the population is largely susceptible to infection ('totally naïve'), determines the overall number of people who are likely to be infected, or, more precisely, the area under the epidemic curve. Estimation of changes in transmission over time can provide insights into the epidemiological situation and identify whether outbreak control measures are having a measurable effect. For R(0) > 1, the number infected tends to increase, and for R(0) < 1, transmission dies out. Non-pharmaceutical strategies to handle the epidemic are sketched and based on current knowledge, the current situation is sketched and scenarios for the near future discussed.
COVID-19 has developed into a pandemic, hitting hard on our communities. As the pandemic continues to bring health and economic hardship, keeping mortality as low as possible will be the highest priority for individuals; hence governments must put in place measures to ameliorate the inevitable economic downturn. The course of an epidemic may be defined by a series of key factors. In the early stages of a new infectious disease outbreak, it is crucial to understand the transmission dynamics of the infection. The basic reproduction number (R-0), which defines the mean number of secondary cases generated by one primary case when the population is largely susceptible to infection ('totally naive'), determines the overall number of people who are likely to be infected, or, more precisely, the area under the epidemic curve. Estimation of changes in transmission over time can provide insights into the epidemiological situation and identify whether outbreak control measures are having a measurable effect. For R-0 > 1, the number infected tends to increase, and for R-0 < 1, transmission dies out. Non-pharmaceutical strategies to handle the epidemic are sketched and based on current knowledge, the current situation is sketched and scenarios for the near future discussed. ; Molenberghs, G (corresponding author), Hasselt Univ, I BioStat, Martelarenpl 42, B-3500 Hasselt, Belgium; Katholieke Univ Leuven, Martelarenpl 42, B-3500 Hasselt, Belgium. geert.molenberghs@uhasselt.be
Frailty models are often used in survival analysis to model multivariate time-to-event data. In infectious disease epidemiology, frailty models have been proposed to model heterogeneity in the acquisition of infection and to accommodate association in the occurrence of multiple types of infection. Although traditional frailty models rely on the assumption of lifelong immunity after recovery, refinements have been made to account for reinfections with the same pathogen. Recently, Abrams and Hens quantified the effect of misspecifying the underlying infection process on the basic and effective reproduction number in the context of bivariate current status data on parvovirus B19 and varicella zoster virus. Furthermore, Farrington, Unkel and their co-workers introduced and applied time varying shared frailty models to paired bivariate serological data. In this paper, we consider an extension of the proposed frailty methodology by Abrams and Hens to account for age-dependence in individual heterogeneity through the use of age-dependent shared and correlated gamma frailty models. The methodology is illustrated by using two data applications. ; The authors gratefully acknowledge support by the Research Fund of Hasselt University (grantBOF11NI31) and support of the University of Antwerp Scientific Chair in Evidence-based Vaccinology sponsored in 2009–2016 by a gift from Pfizer and GlaxoSmithKline. The work of AW was supported by the German Research Council, project WI 3288/1-2. This research is part of a project that has received funding from the European Research Council under the European Union's 'Horizon 2020' research and innovation program (grant agreement 682540—TransMID). The computational resources and services used in this work were provided by the Flemish Supercomputer Center, funded by the Research Foundation—Flanders and the Flemish Government—Department Economy, Science and Innovation.
In geostatistics, both kriging and smoothing splines are commonly used to generate an interpolated map of a quantity of interest. The geoadditive model proposed by Kammann and Wand (J R Stat Soc: Ser C (Appl Stat) 52(1):1–18, 2003) represents a fusion of kriging and penalized spline additive models. Complex data issues, including non-linear covariate trends, multiple measurements at a location and clustered observations are easily handled using the geoadditive model. We propose a likelihood based estimation procedure that enables the estimation of the range (spatial decay) parameter associated with the penalized splines of the spatial component in the geoadditive model. We present how the spatial covariance structure (covariogram) can be derived from the geoadditive model. In a simulation study, we show that the underlying spatial process and prediction of the spatial map are estimated well using the proposed likelihood based estimation procedure. We present several applications of the proposed methods on real-life data examples. ; Support from a doctoral Grant of Hasselt University is acknowledged (BOF11D04 FAEC to YV). Support from the National Institutes of Health is acknowledged [award number R01CA172805 to CF]. Support from the University of Antwerp scientific chair in Evidence-Based Vaccinology, financed in 2009–2014 by a gift from Pfizer, is acknowledged [to NH]. Support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy) is gratefully acknowledged. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government – department EWI.
IntroductionConcurrent partnerships (CPs) have been suggested as a risk factor for transmitting HIV, but their impact on the epidemic depends upon how prevalent they are in populations, the average number of CPs an individual has and the length of time they overlap. However, estimates of prevalence of CPs in Southern Africa vary widely, and the duration of overlap in these relationships is poorly documented. We aim to characterize concurrency in a more accurate and complete manner, using data from three disadvantaged communities of Cape Town, South Africa.MethodsWe conducted a sexual behaviour survey (n=878) from June 2011 to February 2012 in Cape Town, using Audio Computer‐Assisted Self‐Interviewing to collect sexual relationship histories on partners in the past year. Using the beginning and end dates for the partnerships, we calculated the point prevalence, the cumulative prevalence and the incidence rate of CPs, as well as the duration of overlap for relationships begun in the previous year. Linear and binomial regression models were used to quantify race (black vs. coloured) and sex differences in the duration of overlap and relative risk of having CPs in the past year.ResultsThe overall point prevalence of CPs six months before the survey was 8.4%: 13.4% for black men, 1.9% for coloured men, 7.8% black women and 5.6% for coloured women. The median duration of overlap in CPs was 7.5 weeks. Women had less risk of CPs in the previous year than men (RR 0.43; 95% CI: 0.32–0.57) and black participants were more at risk than coloured participants (RR 1.86; 95% CI: 1.17–2.97).ConclusionsOur results indicate that in this population the prevalence of CPs is relatively high and is characterized by overlaps of long duration, implying there may be opportunities for HIV to be transmitted to concurrent partners.
The Akaike information criterion, AIC, is one of the most frequently used methods to select one or a few good, optimal regression models from a set of candidate models. In case the sample is incomplete, the naive use of this criterion on the so-called complete cases can lead to the selection of poor or inappropriate models. A similar problem occurs when a sample based on a design with unequal selection probabilities, is treated as a simple random sample. In this paper, we consider a modification of AIC, based on reweighing the sample in analogy with the weighted Horvitz-Thompson estimates. It is shown that this weighted AIC-criterion provides better model choices for both incomplete and design-based samples. The use of the weighted AIC-criterion is illustrated on data from the Belgian Health Interview Survey, which motivated this research. Simulations show its performance in a variety of settings. Copyright (c) 2006 John Wiley & Sons, Ltd. ; Financial support from the IAP research network No. P5=24 of the Belgian Government (Belgian Science Policy) is gratefully acknowledged.
In this paper, we investigate the effect of pre-smoothing on model selection. Christobal et al 6 showed the beneficial effect of pre-smoothing on estimating the parameters in a linear regression model. Here, in a regression setting, we show that smoothing the response data prior to model selection by Akaike's information criterion can lead to an improved selection procedure. The bootstrap is used to control the magnitude of the random error structure in the smoothed data. The effect of pre-smoothing on model selection is shown in simulations. The method is illustrated in a variety of settings, including the selection of the best fractional polynomial in a generalized linear model. ; We also gratefully acknowledge the support from the IAP research network nr P5/24 of the Belgian Government (Belgian Science Policy). The research of Niel Hens has been financially supported by the Fund of Scientific Research (FWO, Research Grant # G039304) of Flanders, Belgium.
Frailty models are often used to study the individual heterogeneity in multivariate survival analysis. Whereas the shared frailty model is widely applied, the correlated frailty model has gained attention because it elevates the restriction Of unobserved factors to act similar within clusters. Estimating frailty models is not straightforward due to various types of censoring. In this paper, we Study the behavior of the bivariate-correlated gamma frailty model for type I interval-censored data, better known as Current status data. We show that applying a shared rather than a correlated frailty model to cross-sectionally collected serological data on hepatitis A and B leads to biased estimates for the baseline hazard and variance parameters. Copyright (c) 2009 John Wiley & Sons, Ltd. ; We thank the associate editor and both reviewers for their comments leading to an improved presentation of the paper. We thank Philippe Beutels for making the data available to us and Tom Cattaert for the insightful discussions on the matter. This work has been funded by 'SIMID', a strategic basic research project funded by the institute for the Promotion of Innovation by Science and Technology in Flanders (IWT), project number 060081 and by the IAP research network nr P6/03 of the Belgian Government (Belgian Science Policy). This work has benefitted from discussion held in POLYMOD, a European Commission project funded within the Sixth Framework Programme, contract number: SSP22-CT-2004-502084. Andreas Wienke was supported by the German Research Council, project number WI 3288/1-1.
Frailty models have a prominent place in survival analysis to model univariate and multivariate time-to-event data, often complicated by the presence of different types of censoring. In recent years, frailty modeling gained popularity in infectious disease epidemiology to quantify unobserved heterogeneity using Type I interval-censored serological data or current status data. In a multivariate setting, frailty models prove useful to assess the association between infection times related to multiple distinct infections acquired by the same individual. In addition to dependence among individual infection times, overdispersion can arise when the observed variability in the data exceeds the one implied by the model. In this article, we discuss parametric overdispersed frailty models for time-to-event data under Type I interval-censoring, building upon the work by Molenberghs et al. (2010) and Hens et al. (2009). The proposed methodology is illustrated using bivariate serological data on hepatitis A and B from Flanders, Belgium anno 1993–1994. Furthermore, the relationship between individual heterogeneity and overdispersion at a stratum-specific level is studied through simulations. Although it is important to account for overdispersion, one should be cautious when modeling both individual heterogeneity and overdispersion based on current status data as model selection is hampered by the loss of information due to censoring. ; This work was supported by the Research Fund of Hasselt University (grant BOF11NI31 to S.A.). N.H. received support from the University of Antwerp by way of the Scientific Chair in Evidence-based Vaccinology, financed in 2009–2014 by a gift from Pfizer, Inc., New York. The authors gratefully acknowledge financial support from the IAP research Network P7/06 of the Belgian Government (Belgian Science Policy). This research is part of a project that has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement 682540 – TransMID).
This paper shows how to model seroprevalence data using change-point fractional polynomials (FPs). The inclusion of a change point in the FP framework allows to detect distortions arising from common (often untestable) assumptions made in the estimation of the age-specific prevalence and force of infection from cross-sectional data. The method is motivated using seroprevalence data on the parvovirus B19 and the varicella zoster virus in Belgium. ; We gratefully acknowledge two referees and an associate editor for provoking thoughts that have led to an improved version of the manuscript. This work was based on a serum sample collected for the European Commission's ESEN2-project. We are grateful to the Institute of Public Health, Brussels (Dr Robert Vranckx, Dr Veronik Hutse) for assistance with PVB19 testing. This work is part of the research project MSM 0021620839 that has been funded by 'SIMID', a strategic basic research project funded by the institute for the Promotion of Innovation by Science and Technology in Flanders, project number 060081, by the Fund of Scientific Research (Research Grant G039304) in Flanders, Belgium, by the IAP research network number P6/03 of the Belgian Government (Belgian Science Policy) and by the Grant Agency of Charles University, project number 252387/2007. This work benefited from discussions held in POLYMOD, a European Commission project funded within the Sixth Framework Programme, contract number: SSP22-CT-2004-502084.
When estimating important measures such as the herd immunity threshold, and the corresponding efforts required to eliminate measles, it is often assumed that susceptible individuals are uniformly distributed throughout populations. However, unvaccinated individuals may be clustered in a variety of ways, including by geographic location, by age, in schools, or in households. Here, we investigate to which extent different levels of within-household clustering of susceptible individuals may impact the risk and persistence of measles outbreaks. To this end, we apply an individual-based model, Stride, to a population of 600,000 individuals, using data from Flanders, Belgium. We construct a metric to estimate the level of within-household susceptibility clustering in the population. Furthermore, we compare realistic scenarios regarding the distribution of susceptible individuals within households in terms of their impact on epidemiological measures for outbreak risk and persistence. We find that higher levels of within-household clustering of susceptible individuals increase the risk, size and persistence of measles outbreaks. Ignoring within-household clustering thus leads to underestimations of required measles elimination and outbreak mitigation efforts. ; EK, LW and PB acknowledge support of the Antwerp Study Centre for Infectious Diseases (ASCID) at the University of Antwerp, and the Research Foundation Flanders (FWO) (research project G043815N and a postdoctoral fellowship 1234620N (LW)). NH acknowledges funding received from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement 682540-TransMID). Acknowledgements EK, LW and PB acknowledge support of the Antwerp Study Centre for Infectious Diseases (ASCID) at the University of Antwerp, and the Research Foundation Flanders (FWO) (research project G043815N and a postdoctoral fellowship 1234620N (LW)). NH acknowledges funding received from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement 682540-TransMID). ; Kuylen, E (corresponding author), Univ Antwerp, Ctr Hlth Econ Res & Modelling Infect Dis CHERMID, Vaccine & Infect Dis Inst, Antwerp, Belgium ; Hasselt Univ, Data Sci Inst DSI, Hasselt, Belgium. elise.kuylen@uantwerpen.be
Background: Large measles and mumps outbreaks recently occurred throughout Europe and the United States. Aim: Our aim was to estimate and map the risk of resurgence for measles, mumps and rubella in France. Methods: We used a multi-cohort model combining seroprevalence information, vaccine coverage and social contact data. Results: The overall outbreak risk for France in 2018 was highest for mumps, remained significant for measles despite a recent measles outbreak and was low for rubella. Outbreak risks were heterogeneous between departments, as the effective reproduction numbers for 2018 ranged from 1.08 to 3.66. The seroprevalence, and therefore the risk of measles and rubella infection, differed significantly between mates and females. There was a lower seroprevalence, and therefore a higher risk, for males. Infants of less thane year would be seriously affected in a future outbreak of measles, mumps or rubella, but the highest overall caseload contribution would come from teenagers and young adults (10-25 years old). Conclusions: The high risk for teenagers and young adults is of concern in view of their vulnerability to more severe measles, mumps and rubella disease and complications. ; NH gratefully acknowledges the support from the University of Antwerp scientific chair in Evidence-Based Vaccinology, which was financed by a gift from Pfizer (2009-2017) and GlaxoSmithKline (2016). This project was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement 682540 - TransMID). GB gratefully acknowledges special research funding provided by Hasselt University (BOF14BL07). SA gratefully acknowledges support by the Research Fund of Hasselt University (Grant BOF11NI31). GB gratefully acknowledges special research funding provided by Hasselt University (BOF14BL07). SA gratefully acknowledges support by the Research Fund of Hasselt University (Grant BOF11NI31).
This chapter focuses on the deteminants of a number of immunization programme outcomes in Flanders (Belgium), such as vaccine initiation and uptake; completion of the vaccination schedule and compliance to official validity criteria. These were assessed in both infant and adolescent age groups. Three main groups of potential influencing factors are looked at: (1)individual background variables; (2)family level variables; (3)external factors such as the governmental vaccination programme and other initiatives to promote vaccination. Data on parental willingness to pay for and willingness to accept multiple concomitant injections and their determinants are discussed as well. Exploring relationships between vaccination programme outcomes and influencing factors can give important information to optimize vaccination programme performance.
