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 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.

Cluster pattern analysis of environmental stressors and quantifying their impact on all-cause mortality in Belgium.

Environmental stress represents an important burden on health and leads to a considerable number of diseases, hospitalisations, and excess mortality. Our study encompasses a representative sample size drawn from the Belgian population in 2016 (n = 11.26 million, with a focus on n = 11.15 million individuals). The analysis is conducted at the geographical level of statistical sectors, comprising a total of n = 19,794 sectors, with a subset of n = 18,681 sectors considered in the investigation. We integrated multiple parameters at the finest spatial level and constructed three categories of environmental stress through clustering: air pollution, noise stress and stress related to specific land-use types. We observed identifiable patterns in the spatial distribution of stressors within each cluster category. We assessed the relationship between age-standardized all-cause mortality rates (ASMR) and environmental stressors. Our research found that especially very high air pollution values in areas where traffic is the dominant local component of air pollution (ASMR + 14,8%, 95% CI: 10,4 - 19,4%) and presence of industrial land (ASMR + 14,7%, 95% CI: 9,4 - 20,2%) in the neighbourhood are associated with an increased ASMR. Cumulative exposure to multiple sources of unfavourable environmental stress (simultaneously high air pollution, high noise, presence of industrial land or proximity of primary/secondary roads and lack of green space) is associated with an increase in ASMR (ASMR + 26,9%, 95% CI: 17,1 - 36,5%).

Trends in socioeconomic inequalities in cause-specific premature mortality in Belgium, 1998-2019.

BACKGROUND: Higher levels of socioeconomic deprivation have been consistently associated with increased risk of premature mortality, but a detailed analysis by causes of death is lacking in Belgium. We aim to investigate the association between area deprivation and all-cause and cause-specific premature mortality in Belgium over the period 1998-2019. METHODS: We used the 2001 and 2011 Belgian Indices of Multiple Deprivation to assign statistical sectors, the smallest geographical units in the country, into deprivation deciles. All-cause and cause-specific premature mortality rates, population attributable fraction, and potential years of life lost due to inequality were estimated by period, sex, and deprivation deciles. RESULTS: Men and women living in the most deprived areas were 1.96 and 1.78 times more likely to die prematurely compared to those living in the least deprived areas over the period under study (1998-2019). About 28% of all premature deaths could be attributed to socioeconomic inequality and about 30% of potential years of life lost would be averted if the whole population of Belgium faced the premature mortality rates of the least deprived areas. CONCLUSION: Premature mortality rates have declined over time, but inequality has increased due to a faster pace of decrease in the least deprived areas compared to the most deprived areas. As the causes of death related to poor lifestyle choices contribute the most to the inequality gap, more effective, country-level interventions should be put in place to target segments of the population living in the most deprived areas as they are facing disproportionately high risks of dying.

The impact of quality-adjusted life years on evaluating COVID-19 mitigation strategies: lessons from age-specific vaccination roll-out and variants of concern in Belgium (2020-2022).

BACKGROUND: When formulating and evaluating COVID-19 vaccination strategies, an emphasis has been placed on preventing severe disease that overburdens healthcare systems and leads to mortality. However, more conventional outcomes such as quality-adjusted life years (QALYs) and inequality indicators are warranted as additional information for policymakers. METHODS: We adopted a mathematical transmission model to describe the infectious disease dynamics of SARS-COV-2, including disease mortality and morbidity, and to evaluate (non)pharmaceutical interventions. Therefore, we considered temporal immunity levels, together with the distinct transmissibility of variants of concern (VOCs) and their corresponding vaccine effectiveness. We included both general and age-specific characteristics related to SARS-CoV-2 vaccination. Our scenario study is informed by data from Belgium, focusing on the period from August 2021 until February 2022, when vaccination for children aged 5-11 years was initially not yet licensed and first booster doses were administered to adults. More specifically, we investigated the potential impact of an earlier vaccination programme for children and increased or reduced historical adult booster dose uptake. RESULTS: Through simulations, we demonstrate that increasing vaccine uptake in children aged 5-11 years in August-September 2021 could have led to reduced disease incidence and ICU occupancy, which was an essential indicator for implementing non-pharmaceutical interventions and maintaining healthcare system functionality. However, an enhanced booster dose regimen for adults from November 2021 onward could have resulted in more substantial cumulative QALY gains, particularly through the prevention of elevated levels of infection and disease incidence associated with the emergence of Omicron VOC. In both scenarios, the need for non-pharmaceutical interventions could have decreased, potentially boosting economic activity and mental well-being. CONCLUSIONS: When calculating the impact of measures to mitigate disease spread in terms of life years lost due to COVID-19 mortality, we highlight the impact of COVID-19 on the health-related quality of life of survivors. Our study underscores that disease-related morbidity could constitute a significant part of the overall health burden. Our quantitative findings depend on the specific setup of the interventions under review, which is open to debate or should be contextualised within future situations.

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.

Inferring age-specific differences in susceptibility to and infectiousness upon SARS-CoV-2 infection based on Belgian social contact data.

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.

A linear mixed model to estimate COVID-19-induced excess mortality.

The Corona Virus Disease (COVID-19) pandemic has increased mortality in countries worldwide. To evaluate the impact of the pandemic on mortality, the use of excess mortality rather than reported COVID-19 deaths has been suggested. Excess mortality, however, requires estimation of mortality under nonpandemic conditions. Although many methods exist to forecast mortality, they are either complex to apply, require many sources of information, ignore serial correlation, and/or are influenced by historical excess mortality. We propose a linear mixed model that is easy to apply, requires only historical mortality data, allows for serial correlation, and down-weighs the influence of historical excess mortality. Appropriateness of the linear mixed model is evaluated with fit statistics and forecasting accuracy measures for Belgium and the Netherlands. Unlike the commonly used 5-year weekly average, the linear mixed model is forecasting the year-specific mortality, and as a result improves the estimation of excess mortality for Belgium and the Netherlands.

How contact patterns during the COVID-19 pandemic are related to pre-pandemic contact patterns and mobility trends.

BACKGROUND: Non-pharmaceutical interventions (NPIs) were adopted in Belgium in order to decrease social interactions between people and as such decrease viral transmission of SARS-CoV-2. With the aim to better evaluate the impact of NPIs on the evolution of the pandemic, an estimation of social contact patterns during the pandemic is needed when social contact patterns are not available yet in real time. METHODS: In this paper we use a model-based approach allowing for time varying effects to evaluate whether mobility and pre-pandemic social contact patterns can be used to predict the social contact patterns observed during the COVID-19 pandemic between November 11, 2020 and July 4, 2022. RESULTS: We found that location-specific pre-pandemic social contact patterns are good indicators for estimating social contact patterns during the pandemic. However, the relationship between both changes with time. Considering a proxy for mobility, namely the change in the number of visitors to transit stations, in interaction with pre-pandemic contacts does not explain the time-varying nature of this relationship well. CONCLUSION: In a situation where data from social contact surveys conducted during the pandemic are not yet available, the use of a linear combination of pre-pandemic social contact patterns could prove valuable. However, translating the NPIs at a given time into appropriate coefficients remains the main challenge of such an approach. In this respect, the assumption that the time variation of the coefficients can somehow be related to aggregated mobility data seems unacceptable during our study period for estimating the number of contacts at a given time.

The impact of national and international travel on spatio-temporal transmission of SARS-CoV-2 in Belgium in 2021.

BACKGROUND: The Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has rapidly spread over the world and caused tremendous impacts on global health. Understanding the mechanism responsible for the spread of this pathogen and the impact of specific factors, such as human mobility, will help authorities to tailor interventions for future SARS-CoV-2 waves or newly emerging airborne infections. In this study, we aim to analyze the spatio-temporal transmission of SARS-CoV-2 in Belgium at municipality level between January and December 2021 and explore the effect of different levels of human travel on disease incidence through the use of counterfactual scenarios. METHODS: We applied the endemic-epidemic modelling framework, in which the disease incidence decomposes into endemic, autoregressive and neighbourhood components. The spatial dependencies among areas are adjusted based on actual connectivity through mobile network data. We also took into account other important factors such as international mobility, vaccination coverage, population size and the stringency of restriction measures. RESULTS: The results demonstrate the aggravating effect of international travel on the incidence, and simulated counterfactual scenarios further stress the alleviating impact of a reduction in national and international travel on epidemic growth. It is also clear that local transmission contributed the most during 2021, and municipalities with a larger population tended to attract a higher number of cases from neighboring areas. CONCLUSIONS: Although transmission between municipalities was observed, local transmission was dominant. We highlight the positive association between the mobility data and the infection spread over time. Our study provides insight to assist health authorities in decision-making, particularly when the disease is airborne and therefore likely influenced by human movement.

Social contact patterns during the COVID-19 pandemic in 21 European countries - evidence from a two-year study.

BACKGROUND: Most countries have enacted some restrictions to reduce social contacts to slow down disease transmission during the COVID-19 pandemic. For nearly two years, individuals likely also adopted new behaviours to avoid pathogen exposure based on personal circumstances. We aimed to understand the way in which different factors affect social contacts - a critical step to improving future pandemic responses. METHODS: The analysis was based on repeated cross-sectional contact survey data collected in a standardized international study from 21 European countries between March 2020 and March 2022. We calculated the mean daily contacts reported using a clustered bootstrap by country and by settings (at home, at work, or in other settings). Where data were available, contact rates during the study period were compared with rates recorded prior to the pandemic. We fitted censored individual-level generalized additive mixed models to examine the effects of various factors on the number of social contacts. RESULTS: The survey recorded 463,336 observations from 96,456 participants. In all countries where comparison data were available, contact rates over the previous two years were substantially lower than those seen prior to the pandemic (approximately from over 10 to < 5), predominantly due to fewer contacts outside the home. Government restrictions imposed immediate effect on contacts, and these effects lingered after the restrictions were lifted. Across countries, the relationships between national policy, individual perceptions, or personal circumstances determining contacts varied. CONCLUSIONS: Our study, coordinated at the regional level, provides important insights into the understanding of the factors associated with social contacts to support future infectious disease outbreak responses.

A practical illustration of spatial smoothing methods for disconnected regions with INLA: spatial survey on overweight and obesity in Malaysia.

BACKGROUND: National prevalence could mask subnational heterogeneity in disease occurrence, and disease mapping is an important tool to illustrate the spatial pattern of disease. However, there is limited information on techniques for the specification of conditional autoregressive models in disease mapping involving disconnected regions. This study explores available techniques for producing district-level prevalence estimates for disconnected regions, using as an example childhood overweight in Malaysia, which consists of the Peninsular and Borneo regions separated by the South China Sea. We used data from Malaysia National Health and Morbidity Survey conducted in 2015. We adopted Bayesian hierarchical modelling using the integrated nested Laplace approximation (INLA) program in R-software to model the spatial distribution of overweight among 6301 children aged 5-17 years across 144 districts located in two disconnected regions. We illustrate different types of spatial models for prevalence mapping across disconnected regions, taking into account the survey design and adjusting for district-level demographic and socioeconomic covariates. RESULTS: The spatial model with split random effects and a common intercept has the lowest Deviance and Watanabe Information Criteria. There was evidence of a spatial pattern in the prevalence of childhood overweight across districts. An increasing trend in smoothed prevalence of overweight was observed when moving from the east to the west of the Peninsular and Borneo regions. The proportion of Bumiputera ethnicity in the district had a significant negative association with childhood overweight: the higher the proportion of Bumiputera ethnicity in the district, the lower the prevalence of childhood overweight. CONCLUSION: This study illustrates different available techniques for mapping prevalence across districts in disconnected regions using survey data. These techniques can be utilized to produce reliable subnational estimates for any areas that comprise of disconnected regions. Through the example, we learned that the best-fit model was the one that considered the separate variations of the individual regions. We discovered that the occurrence of childhood overweight in Malaysia followed a spatial pattern with an east-west gradient trend, and we identified districts with high prevalence of overweight. This information could help policy makers in making informed decisions for targeted public health interventions in high-risk areas.

Spatio-temporal dynamic of the COVID-19 epidemic and the impact of imported cases in Rwanda.

INTRODUCTION: Africa was threatened by the coronavirus disease 2019 (COVID-19) due to the limited health care infrastructure. Rwanda has consistently used non-pharmaceutical strategies, such as lockdown, curfew, and enforcement of prevention measures to control the spread of COVID-19. Despite the mitigation measures taken, the country has faced a series of outbreaks in 2020 and 2021. In this paper, we investigate the nature of epidemic phenomena in Rwanda and the impact of imported cases on the spread of COVID-19 using endemic-epidemic spatio-temporal models. Our study provides a framework for understanding the dynamics of the epidemic in Rwanda and monitoring its phenomena to inform public health decision-makers for timely and targeted interventions. RESULTS: The findings provide insights into the effects of lockdown and imported infections in Rwanda's COVID-19 outbreaks. The findings showed that imported infections are dominated by locally transmitted cases. The high incidence was predominant in urban areas and at the borders of Rwanda with its neighboring countries. The inter-district spread of COVID-19 was very limited due to mitigation measures taken in Rwanda. CONCLUSION: The study recommends using evidence-based decisions in the management of epidemics and integrating statistical models in the analytics component of the health information system.

The influence of COVID-19 risk perception and vaccination status on the number of social contacts across Europe: insights from the CoMix study.

BACKGROUND: The SARS-CoV-2 transmission dynamics have been greatly modulated by human contact behaviour. To curb the spread of the virus, global efforts focused on implementing both Non-Pharmaceutical Interventions (NPIs) and pharmaceutical interventions such as vaccination. This study was conducted to explore the influence of COVID-19 vaccination status and risk perceptions related to SARS-CoV-2 on the number of social contacts of individuals in 16 European countries. METHODS: We used data from longitudinal surveys conducted in the 16 European countries to measure social contact behaviour in the course of the pandemic. The data consisted of representative panels of participants in terms of gender, age and region of residence in each country. The surveys were conducted in several rounds between December 2020 and September 2021 and comprised of 29,292 participants providing a total of 111,103 completed surveys. We employed a multilevel generalized linear mixed effects model to explore the influence of risk perceptions and COVID-19 vaccination status on the number of social contacts of individuals. RESULTS: The results indicated that perceived severity played a significant role in social contact behaviour during the pandemic after controlling for other variables (p-value < 0.001). More specifically, participants who had low or neutral levels of perceived severity reported 1.25 (95% Confidence intervals (CI) 1.13 - 1.37) and 1.10 (95% CI 1.00 - 1.21) times more contacts compared to those who perceived COVID-19 to be a serious illness, respectively. Additionally, vaccination status was also a significant predictor of contacts (p-value < 0.001), with vaccinated individuals reporting 1.31 (95% CI 1.23 - 1.39) times higher number of contacts than the non-vaccinated. Furthermore, individual-level factors played a more substantial role in influencing contact behaviour than country-level factors. CONCLUSION: Our multi-country study yields significant insights on the importance of risk perceptions and vaccination in behavioral changes during a pandemic emergency. The apparent increase in social contact behaviour following vaccination would require urgent intervention in the event of emergence of an immune escaping variant.

Longitudinal social contact data analysis: insights from 2 years of data collection in Belgium during the COVID-19 pandemic.

BACKGROUND: During the COVID-19 pandemic, the CoMix study, a longitudinal behavioral survey, was designed to monitor social contacts and public awareness in multiple countries, including Belgium. As a longitudinal survey, it is vulnerable to participants' "survey fatigue", which may impact inferences. METHODS: A negative binomial generalized additive model for location, scale, and shape (NBI GAMLSS) was adopted to estimate the number of contacts reported between age groups and to deal with under-reporting due to fatigue within the study. The dropout process was analyzed with first-order auto-regressive logistic regression to identify factors that influence dropout. Using the so-called next generation principle, we calculated the effect of under-reporting due to fatigue on estimating the reproduction number. RESULTS: Fewer contacts were reported as people participated longer in the survey, which suggests under-reporting due to survey fatigue. Participant dropout is significantly affected by household size and age categories, but not significantly affected by the number of contacts reported in any of the two latest waves. This indicates covariate-dependent missing completely at random (MCAR) in the dropout pattern, when missing at random (MAR) is the alternative. However, we cannot rule out more complex mechanisms such as missing not at random (MNAR). Moreover, under-reporting due to fatigue is found to be consistent over time and implies a 15-30% reduction in both the number of contacts and the reproduction number ([Formula: see text]) ratio between correcting and not correcting for under-reporting. Lastly, we found that correcting for fatigue did not change the pattern of relative incidence between age groups also when considering age-specific heterogeneity in susceptibility and infectivity. CONCLUSIONS: CoMix data highlights the variability of contact patterns across age groups and time, revealing the mechanisms governing the spread/transmission of COVID-19/airborne diseases in the population. Although such longitudinal contact surveys are prone to the under-reporting due to participant fatigue and drop-out, we showed that these factors can be identified and corrected using NBI GAMLSS. This information can be used to improve the design of similar, future surveys.

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.

A spatial model to jointly analyze self-reported survey data of COVID-19 symptoms and official COVID-19 incidence data.

This work presents a joint spatial modeling framework to improve estimation of the spatial distribution of the latent COVID-19 incidence in Belgium, based on test-confirmed COVID-19 cases and crowd-sourced symptoms data as reported in a large-scale online survey. Correction is envisioned for stochastic dependence between the survey's response rate and spatial COVID-19 incidence, commonly known as preferential sampling, but not found significant. Results show that an online survey can provide valuable auxiliary data to optimize spatial COVID-19 incidence estimation based on confirmed cases in situations with limited testing capacity. Furthermore, it is shown that an online survey on COVID-19 symptoms with a sufficiently large sample size per spatial entity is capable of pinpointing the same locations that appear as test-confirmed clusters, approximately 1 week earlier. We conclude that a large-scale online study provides an inexpensive and flexible method to collect timely information of an epidemic during its early phase, which can be used by policy makers in an early phase of an epidemic and in conjunction with other monitoring systems.

On realized serial and generation intervals given control measures: The COVID-19 pandemic case.

The SARS-CoV-2 pathogen is currently spreading worldwide and its propensity for presymptomatic and asymptomatic transmission makes it difficult to control. The control measures adopted in several countries aim at isolating individuals once diagnosed, limiting their social interactions and consequently their transmission probability. These interventions, which have a strong impact on the disease dynamics, can affect the inference of the epidemiological quantities. We first present a theoretical explanation of the effect caused by non-pharmaceutical intervention measures on the mean serial and generation intervals. Then, in a simulation study, we vary the assumed efficacy of control measures and quantify the effect on the mean and variance of realized generation and serial intervals. The simulation results show that the realized serial and generation intervals both depend on control measures and their values contract according to the efficacy of the intervention strategies. Interestingly, the mean serial interval differs from the mean generation interval. The deviation between these two values depends on two factors. First, the number of undiagnosed infectious individuals. Second, the relationship between infectiousness, symptom onset and timing of isolation. Similarly, the standard deviations of realized serial and generation intervals do not coincide, with the former shorter than the latter on average. The findings of this study are directly relevant to estimates performed for the current COVID-19 pandemic. In particular, the effective reproduction number is often inferred using both daily incidence data and the generation interval. Failing to account for either contraction or mis-specification by using the serial interval could lead to biased estimates of the effective reproduction number. Consequently, this might affect the choices made by decision makers when deciding which control measures to apply based on the value of the quantity thereof.

Modelling longitudinal binary outcomes with outcome dependent observation times: an application to a malaria cohort study.

BACKGROUND : In spite of the global reduction of 21% in malaria incidence between 2010 and 2015, the disease still threatens many lives of children and pregnant mothers in African countries. A correct assessment and evaluation of the impact of malaria control strategies still remains quintessential in order to eliminate the disease and its burden. Malaria follow-up studies typically involve routine visits at pre-scheduled time points and/or clinical visits whenever individuals experience malaria-like symptoms. In the latter case, infection triggers outcome assessment, thereby leading to outcome-dependent sampling (ODS). Commonly used methods to analyze such longitudinal data ignore ODS and potentially lead to biased estimates of malaria-specific transmission parameters, hence, inducing an incorrect assessment and evaluation of malaria control strategies. METHODS : In this paper, a new method is proposed to handle ODS by use of a joint model for the longitudinal binary outcome measured at routine visits and the clinical event times. The methodology is applied to malaria parasitaemia data from a cohort of [Formula: see text] Ugandan children aged 0.5-10 years from 3 regions (Walukuba-300 children, Kihihi-355 children and Nagongera-333 children) with varying transmission intensities (entomological inoculation rate equal to 2.8, 32 and 310 infectious bites per unit year, respectively) collected between 2011-2014. RESULTS : The results indicate that malaria parasite prevalence and force of infection (FOI) increase with age in the region of high malaria intensity with highest FOI in age group 5-10 years. For the region of medium intensity, the prevalence slightly increases with age and the FOI for the routine process is highest in age group 5-10 years, yet for the clinical infections, the FOI gradually decreases with increasing age. For the region with low intensity, both the prevalence and FOI peak at the age of 1 year after which the former remains constant with age yet the latter suddenly decreases with age for the clinically observed infections. CONCLUSION : Malaria parasite prevalence and FOI increase with age in the region of high malaria intensity. In all study sites, both the prevalence and FOI are highest among previously asymptomatic children and lowest among their symptomatic counterparts. Using a simulation study inspired by the malaria data at hand, the proposed methodology shows to have the smallest bias, especially when consecutive positive malaria parasitaemia presence results within a time period of 35 days were considered to be due to the same infection.

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.