A joint penalized spline smoothing model for the number of positive and negative COVID-19 tests.

One of the key tools to understand and reduce the spread of the SARS-CoV-2 virus is testing. The total number of tests, the number of positive tests, the number of negative tests, and the positivity rate are interconnected indicators and vary with time. To better understand the relationship between these indicators, against the background of an evolving pandemic, the association between the number of positive tests and the number of negative tests is studied using a joint modeling approach. All countries in the European Union, Switzerland, the United Kingdom, and Norway are included in the analysis. We propose a joint penalized spline model in which the penalized spline is reparameterized as a linear mixed model. The model allows for flexible trajectories by smoothing the country-specific deviations from the overall penalized spline and accounts for heteroscedasticity by allowing the autocorrelation parameters and residual variances to vary among countries. The association between the number of positive tests and the number of negative tests is derived from the joint distribution for the random intercepts and slopes. The correlation between the random intercepts and the correlation between the random slopes were both positive. This suggests that, when countries increase their testing capacity, both the number of positive tests and negative tests will increase. A significant correlation was found between the random intercepts, but the correlation between the random slopes was not significant due to a wide credible interval.

The influence of resolution on the predictive power of spatial heterogeneity measures as biomarkers of liver fibrosis.

Spatial heterogeneity of cells in liver biopsies can be used as biomarker for disease severity of patients. This heterogeneity can be quantified by non-parametric statistics of point pattern data, which make use of an aggregation of the point locations. The method and scale of aggregation are usually chosen ad hoc, despite values of the aforementioned statistics being heavily dependent on them. Moreover, in the context of measuring heterogeneity, increasing spatial resolution will not endlessly provide more accuracy. The question then becomes how changes in resolution influence heterogeneity indicators, and subsequently how they influence their predictive abilities. In this paper, cell level data of liver biopsy tissue taken from chronic Hepatitis B patients is used to analyze this issue. Firstly, Morisita-Horn indices, Shannon indices and Getis-Ord statistics were evaluated as heterogeneity indicators of different types of cells, using multiple resolutions. Secondly, the effect of resolution on the predictive performance of the indices in an ordinal regression model was investigated, as well as their importance in the model. A simulation study was subsequently performed to validate the aforementioned methods. In general, for specific heterogeneity indicators, a downward trend in predictive performance could be observed. While for local measures of heterogeneity a smaller grid-size is outperforming, global measures have a better performance with medium-sized grids. In addition, the use of both local and global measures of heterogeneity is recommended to improve the predictive performance.

A Comparison of Items and Constructs of Standardized Health-Related Quality of Life and Mental Well-Being Measures.

OBJECTIVES: This study aimed to explore the internal constructs of the concepts being measured by EQ-5D-5L (a health-related quality of life measure that can produce preference-based utility values) and the 12-item General Health Questionnaire (GHQ-12, a mental well-being measure) and to understand to what extent the items of EQ-5D-5L and GHQ-12 associate with each other. METHODS: We used data from 12 701 respondents participating in a Belgian survey in 2022. Correlation coefficients between GHQ-12 and EQ-5D-5L were calculated at both the aggregate and item levels. Multidimensional scaling, exploratory factor analysis, and regression models were performed to investigate the underlying constructs that are associated with the items. RESULTS: Despite a moderate correlation (0.39) between the EQ-5D-5L and GHQ-12 total scores, only a trivial or weak correlation (<0.3) was observed between the first 4 EQ-5D-5L items and any GHQ-12 item. Multidimensional scaling and exploratory factor analysis showed the first 4 EQ-5D-5L dimensions were clustered together with EuroQol visual analog scale and positively phrased GHQ-12 items were close to each other, whereas EQ-anxiety/depression and negatively phrased GHQ-12 items were grouped with overall life satisfaction. In the regression models, not all GHQ-12 items had a significant coefficient to predict EQ-5D-5L responses. CONCLUSIONS: To the best of our knowledge, we present the first comparison of items and underlying constructs of GHQ-12 and EQ-5D-5L. The results showed that GHQ-12 can only partially predict the responses of EQ-5D-5L and the 2 instruments measure different constructs. Researchers should carefully consider conceptual legitimacy while applying the mapping technique and consider sensitivity analyses for the mapping estimates.

Key risk factors associated with fractal dimension based geographical clustering of COVID-19 data in the Flemish and Brussels region, Belgium.

Introduction: COVID-19 remains a major concern globally. Therefore, it is important to evaluate COVID-19's rapidly changing trends. The fractal dimension has been proposed as a viable method to characterize COVID-19 curves since epidemic data is often subject to considerable heterogeneity. In this study, we aim to investigate the association between various socio-demographic factors and the complexity of the COVID-19 curve as quantified through its fractal dimension. Methods: We collected population indicators data (ethnic composition, socioeconomic status, number of inhabitants, population density, the older adult population proportion, vaccination rate, satisfaction, and trust in the government) at the level of the statistical sector in Belgium. We compared these data with fractal dimension indicators of COVID-19 incidence between 1 January - 31 December 2021 using canonical correlation analysis. Results: Our results showed that these population indicators have a significant association with COVID-19 incidences, with the highest explanatory and predictive power coming from the number of inhabitants, population density, and ethnic composition. Conclusion: It is important to monitor these population indicators during a pandemic, especially when dealing with targeted interventions for a specific population.

Assessing trends in population size of three unmarked species: A comparison of a multi-species N-mixture model and random encounter models.

Estimation of changes in abundances and densities is essential for the research, management, and conservation of animal populations. Recently, technological advances have facilitated the surveillance of animal populations through the adoption of passive sensors, such as camera traps (CT). Several methods, including the random encounter model (REM), have been developed for estimating densities of unmarked populations but require additional information. Hierarchical abundance models, such as the N-mixture model (NMM), can estimate abundances without performing additional fieldwork but do not explicitly estimate the area effectively sampled. This obscures the interpretation of its densities and requires its users to focus on relative measures of abundance instead. Hence, the main objective of our study is to evaluate if REM and NMM yield consistent results qualitatively. Therefore, we compare relative trends: (i) between species, (ii) between years and (iii) across years obtained from annual density/abundance estimates of three species (fox, wild boar and red deer) in central Spain monitored by a camera trapping network for five consecutive winter periods. We reveal that NMM and REM provided density estimates in the same order of magnitude for wild boar, but not for foxes and red deer. Assuming a Poisson detection process in the NMM was important to control for inflation of abundance estimates for frequently detected species. Both methods consistently ranked density/abundance across species (between species trend), but did not always agree on relative ranks of yearly estimates within a single population (between years trend), nor on its linear population trends across years (across years trend). Our results suggest that relative trends are generally consistent when the range of variability is large, but can become inconsistent when the range of variability is smaller.

Measures of spatial heterogeneity in the liver tissue micro-environment as predictive factors for fibrosis score.

The organization and interaction between hepatocytes and other hepatic non-parenchymal cells plays a pivotal role in maintaining normal liver function and structure. Although spatial heterogeneity within the tumor micro-environment has been proven to be a fundamental feature in cancer progression, the role of liver tissue topology and micro-environmental factors in the context of liver damage in chronic infection has not been widely studied yet. We obtained images from 110 core needle biopsies from a cohort of chronic hepatitis B patients with different fibrosis stages according to METAVIR score. The tissue sections were immunofluorescently stained and imaged to determine the locations of CD45 positive immune cells and HBsAg-negative and HBsAg-positive hepatocytes within the tissue. We applied several descriptive techniques adopted from ecology, including Getis-Ord, the Shannon Index and the Morisita-Horn Index, to quantify the extent to which immune cells and different types of liver cells co-localize in the tissue biopsies. Additionally, we modeled the spatial distribution of the different cell types using a joint log-Gaussian Cox process and proposed several features to quantify spatial heterogeneity. We then related these measures to the patient fibrosis stage by using a linear discriminant analysis approach. Our analysis revealed that the co-localization of HBsAg-negative hepatocytes with immune cells and the co-localization of HBsAg-positive hepatocytes with immune cells are equally important factors for explaining the METAVIR score in chronic hepatitis B patients. Moreover, we found that if we allow for an error of 1 on the METAVIR score, we are able to reach an accuracy of around 80%. With this study we demonstrate how methods adopted from ecology and applied to the liver tissue micro-environment can be used to quantify heterogeneity and how these approaches can be valuable in biomarker analyses for liver topology.

Pneumococcal vaccination coverage and adherence to recommended dosing schedules in adults: a repeated cross-sectional study of the INTEGO morbidity registry.

BACKGROUND: Since 2014, Belgium's Superior Health Council has recommended pneumococcal vaccination for adults aged 19-85 years at increased risk for pneumococcal diseases with a specific vaccine administration sequence and timing. Currently, Belgium has no publicly funded adult pneumococcal vaccination program. This study investigated the seasonal pneumococcal vaccination trends, evolution of vaccination coverage and adherence to the 2014 recommendations. METHODS: INTEGO is a general practice morbidity registry in Flanders (Belgium) that represents 102 general practice centres and comprised over 300.000 patients in 2021. A repeated cross-sectional study was performed for the period between 2017 and 2021. Using adjusted odds ratios computed via multiple logistic regression, the association between an individual's characteristics (gender, age, comorbidities, influenza vaccination status and socioeconomic status) and schedule-adherent pneumococcal vaccination status was assessed. RESULTS: Pneumococcal vaccination coincided with seasonal flu vaccination. The vaccination coverage in the population at risk decreased from 21% in 2017 to 18.2% in 2018 and then started to increase to 23.6% in 2021. Coverage in 2021 was highest for high-risk adults (33.8%) followed by 50- to 85-year-olds with comorbidities (25.5%) and healthy 65- to 85-year-olds (18.7%). In 2021, 56.3% of the high-risk adults, 74.6% of the 50+ with comorbidities persons, and 74% of the 65+ healthy persons had an adherent vaccination schedule. Persons with a lower socioeconomic status had an adjusted odds ratio of 0.92 (95% Confidence Interval (CI) 0.87-0.97) for primary vaccination, 0.67 (95% CI 0.60-0.75) for adherence to the recommended second vaccination if the 13-valent pneumococcal conjugate vaccine was administered first and 0.86 (95% CI 0.76-0.97) if the 23-valent pneumococcal polysaccharide vaccine was administered first. CONCLUSION: Pneumococcal vaccine coverage is slowly increasing in Flanders, displaying seasonal peaks in sync with influenza vaccination campaigns. However, with less than one-fourth of the target population vaccinated, less than 60% high-risk and approximately 74% of 50 + with comorbidities and 65+ healthy persons with an adherent schedule, there is still much room for improvement. Furthermore, adults with poor socioeconomic status had lower odds of primary vaccination and schedule adherence, demonstrating the need for a publicly funded program in Belgium to ensure equitable access.

A multivariate spatio-temporal model for the incidence of imported COVID-19 cases and COVID-19 deaths in Cuba.

To monitor the COVID-19 epidemic in Cuba, data on several epidemiological indicators have been collected on a daily basis for each municipality. Studying the spatio-temporal dynamics in these indicators, and how they behave similarly, can help us better understand how COVID-19 spread across Cuba. Therefore, spatio-temporal models can be used to analyze these indicators. Univariate spatio-temporal models have been thoroughly studied, but when interest lies in studying the association between multiple outcomes, a joint model that allows for association between the spatial and temporal patterns is necessary. The purpose of our study was to develop a multivariate spatio-temporal model to study the association between the weekly number of COVID-19 deaths and the weekly number of imported COVID-19 cases in Cuba during 2021. To allow for correlation between the spatial patterns, a multivariate conditional autoregressive prior (MCAR) was used. Correlation between the temporal patterns was taken into account by using two approaches; either a multivariate random walk prior was used or a multivariate conditional autoregressive prior (MCAR) was used. All models were fitted within a Bayesian framework.

Psychological symptoms do not discriminate between reflux phenotypes along the organic-functional refractory GERD spectrum.

OBJECTIVE: Historically, psychological processes are associated with disorders at the functional end of the gastro-oesophageal reflux disease (GERD) spectrum. However, recent research suggests that psychological symptoms are relevant across the entire GERD spectrum. We aim to investigate whether psychological symptoms are associated with reflux phenotype (True GERD, Borderline GERD, reflux hypersensitivity, functional heartburn) along the GERD spectrum in a cohort of refractory reflux patients. DESIGN: Consecutive adult patients with refractory reflux symptoms underwent standard 24-hour pH-impedance monitoring and completed questionnaires assessing demographic, clinical and psychological information. Bayesian one-way analysis of variance assessed whether psychological variables differed across reflux phenotypes. Next, we applied multinomial and ordinal logistic regressions with clinical, demographic and psychological variables set as independent variables and reflux phenotype as the outcome variable. The complementary machine-learning approach entered all demographic, clinical and psychological variables into models, with reflux phenotype set nominally and ordinally. Cross-validated model performance was used to select the best model. RESULTS: 393 participants (mean (SD) age=48.5 (14.1); 60% female) were included. The Bayesian analyses found no difference in psychological variables across reflux phenotypes. Similarly, age, gender and proton pump inhibitor use were the only significant variables in the multinomial logistic regression and body mass index was significant in both regressions. Machine-learning analyses revealed poorly performing models with high misclassification rates (67-68%) in both models. CONCLUSION: Psychological symptoms do not differ between nor predict reflux phenotype membership in refractory reflux patients. Findings suggest that psychological symptoms are relevant across the spectrum of GERD, rather than specific to functional oesophageal disorders.

Fractal dimension based geographical clustering of COVID-19 time series data.

Understanding the local dynamics of COVID-19 transmission calls for an approach that characterizes the incidence curve in a small geographical unit. Given that incidence curves exhibit considerable day-to-day variation, the fractal structure of the time series dynamics is investigated for the Flanders and Brussels Regions of Belgium. For each statistical sector, the smallest administrative geographical entity in Belgium, fractal dimensions of COVID-19 incidence rates, based on rolling time spans of 7, 14, and 21 days were estimated using four different estimators: box-count, Hall-Wood, variogram, and madogram. We found varying patterns of fractal dimensions across time and location. The fractal dimension is further summarized by its mean, variance, and autocorrelation over time. These summary statistics are then used to cluster regions with different incidence rate patterns using k-means clustering. Fractal dimension analysis of COVID-19 incidence thus offers important insight into the past, current, and arguably future evolution of an infectious disease outbreak.

The Impact of the COVID-19 Pandemic on the Registration and Care Provision of Mental Health Problems in General Practice: Registry-Based Study.

BACKGROUND: The impact of the COVID-19 pandemic on mental health in general practice remains uncertain. Several studies showed an increase in terms of mental health problems during the pandemic. In Belgium, especially during the first waves of the pandemic, access to general practice was limited. Specifically, it is unclear how this impacted not only the registration of mental health problems itself but also the care for patients with an existing mental health problem. OBJECTIVE: This study aimed to know the impact of the COVID-19 pandemic on (1) the incidence of newly registered mental health problems and (2) the provision of care for patients with mental health problems in general practice, both using a pre-COVID-19 baseline. METHODS: The prepandemic volume of provided care (care provision) for patients with mental health problems was compared to that from 2020-2021 by using INTEGO, a Belgian general practice morbidity registry. Care provision was defined as the total number of new registrations in a patient's electronic medical record. Regression models evaluated the association of demographic factors and care provision in patients with mental health problems, both before and during the pandemic. RESULTS: During the COVID-19 pandemic as compared to before the COVID-19 pandemic, the incidence of registered mental health problems showed a fluctuating course, with a sharp drop in registrations during the first wave. Registrations for depression and anxiety increased, whereas the incidence of registered eating disorders, substance abuse, and personality problems decreased. During the 5 COVID-19 waves, the overall incidence of registered mental health problems dropped during the wave and rose again when measures were relaxed. A relative rise of 8.7% and 40% in volume of provided care, specifically for patients with mental health problems, was seen during the first and second years of the COVID-19 pandemic, respectively. Care provision for patients with mental health problems was higher in older patients, male patients, patients living in center cities (centrumsteden), patients with lower socioeconomic status (SES), native Belgian patients, and patients with acute rather than chronic mental health problems. Compared to prepandemic care provision, a reduction of 10% was observed in people with a low SES. CONCLUSIONS: This study showed (1) a relative overall increase in the registrations of mental health problems in general practice and (2) an increase in care provision for patients with mental health problems in the first 2 years of the COVID-19 pandemic. Low SES remained a determining factor for more care provision, but care provision dropped significantly in people with mental health problems with a low SES. Our findings suggest that the pandemic in Belgium was also largely a "syndemic," affecting different layers of the population disproportionately.

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.

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.

The doubling effect of COVID-19 cases on key health indicators.

From the beginning of the COVID-19 pandemic, researchers advised policy makers to make informed decisions towards the adoption of mitigating interventions. Key easy-to-interpret metrics applied over time can measure the public health impact of epidemic outbreaks. We propose a novel method which quantifies the effect of hospitalizations or mortality when the number of COVID-19 cases doubles. Two analyses are used, a country-by-country analysis and a multi-country approach which considers all countries simultaneously. The new measure is applied to several European countries, where the presence of different variants, vaccination rates and intervention measures taken over time leads to a different risk. Based on our results, the vaccination campaign has a clear effect for all countries analyzed, reducing the risk over time. However, the constant emergence of new variants combined with distinct intervention measures impacts differently the risk per country.

Change in COVID19 outbreak pattern following vaccination in long-term care facilities in Flanders, Belgium.

INTRODUCTION: Long term care facilities for elderly (LTCFs) in Europe encountered a high disease burden at the start of the COVID-19 pandemic. Therefore, these facilities were the first to receive COVID-19 vaccines in many European countries. A limited COVID-19 vaccine supply early 2021 resulted in a majority of residents and healthcare workers (HCWs) in LTCFs being vaccinated compared to a minority in the general population. This study exploits this imbalance to assess the efficiency of COVID-19 vaccination in containing outbreaks in LTCFs. METHODS: Exploratory statistics were performed using data from a COVID-19 surveillance system covering all 842 LTCFs in Flanders (the northern region of Belgium). The number and size of COVID-19 outbreaks in LTCFs were compared (1) before and after introducing vaccines and (2) with the status of the pandemic in the general population. Based on individual data from 15 LTCFs, the infection rate and symptoms of vaccinated and unvaccinated residents and HCWs were compared during a COVID-19 outbreak. RESULTS: 95.8% of the residents and 90.9% of the HCWs in Flemish LTCFs were vaccinated before May 30, 2021. Before vaccine introduction, residents in LTCFs were 10 times more likely to test positive for COVID-19 than the general population of Flanders. This ratio reversed after vaccination. Furthermore, after vaccination fewer and shorter outbreaks were observed involving fewer residents. During these outbreaks, vaccinated and unvaccinated residents were equally likely to test positive, but positive vaccinated residents were less likely to develop severe symptoms. In contrast, unvaccinated HCWs were more likely to test positive. CONCLUSION: In the first half of 2021, two-dose vaccination was highly efficient in preventing and containing outbreaks in LTCFs, reducing COVID-19 hospitalizations and deaths. The high likelihood of unvaccinated HCWs to be involved in COVID-19 outbreaks in vaccinated LTCFs emphasizes the importance of vaccinating HCWs.

The impact of the Covid-19 pandemic on the incidence of diseases and the provision of primary care: A registry-based study.

INTRODUCTION: The Covid-19 pandemic had a tremendous impact on healthcare but uncertainty remains about the extent to which primary care provision was affected. Therefore, this paper aims to assess the impact on primary care provision and the evolution of the incidence of disease during the first year of the Covid-19 pandemic in Flanders (Belgium). METHODS: Care provision was defined as the number of new entries added to a patient's medical history. Pre-pandemic care provision (February 1, 2018-January 31, 2020) was compared with care provision during the pandemic (February 1, 2020-January 31, 2021). A large morbidity registry (Intego) was used. Regression models compared the effect of demographic characteristics on care provision and on acute and chronic diagnoses incidence both prior and during the pandemic. RESULTS: During the first year of the Covid-19 pandemic, overall care provision increased with 9.1% (95%CI 8.5%;9.6%). There was an increase in acute diagnoses of 5.1% (95%CI 4.2%;6.0%) and a decrease in the selected chronic diagnoses of 12.8% (95% CI 7.0%;18.4%). Obesity was an exception with an overall incidence increase. The pandemic led to strong fluctuations in care provision that were not the same for all types of care and all demographic groups in Flanders. Relative to other groups in the population, the pandemic caused a reduction in care provision for children aged 0-17 year and patients from a lower socio-economic situation. CONCLUSION: This paper strengthened the claim that Covid-19 should be considered as a syndemic instead of a pandemic. During the first Covid-19 year, overall care provision and the incidence of acute diagnoses increased, whereas chronic diseases' incidence decreased, except for obesity diagnoses which increased. More granular, care provision and chronic diseases' incidence decreased during the lockdowns, especially for people with a lower socio-economic status. After the lockdowns they both returned to baseline.

The COVID-19 wave in Belgium during the Fall of 2020 and its association with higher education.

Soon after SARS-CoV-2 emerged in late 2019, Belgium was confronted with a first COVID-19 wave in March-April 2020. SARS-CoV-2 circulation declined in the summer months (late May to early July 2020). Following a successfully trumped late July-August peak, COVID-19 incidence fell slightly, to then enter two successive phases of rapid incline: in the first half of September, and then again in October 2020. The first of these coincided with the peak period of returning summer travelers; the second one coincided with the start of higher education's academic year. The largest observed COVID-19 incidence occurred in the period 16-31 October, particularly in the Walloon Region, the southern, French-speaking part of Belgium. We examine the potential association of the higher education population with spatio-temporal spread of COVID-19, using Bayesian spatial Poisson models for confirmed test cases, accounting for socio-demographic heterogeneity in the population. We find a significant association between the number of COVID-19 cases in the age groups 18-29 years and 30-39 years and the size of the higher education student population at the municipality level. These results can be useful towards COVID-19 mitigation strategies, particularly in areas where virus transmission from higher education students into the broader community could exacerbate morbidity and mortality of COVID-19 among populations with prevalent underlying conditions associated with more severe outcomes following infection.

Disease mapping method comparing the spatial distribution of a disease with a control disease.

Small-area methods are being used in spatial epidemiology to understand the effect of location on health and detect areas where the risk of a disease is significantly elevated. Disease mapping models relate the observed number of cases to an expected number of cases per area. Expected numbers are often calculated by internal standardization, which requires both accurate population numbers and disease rates per gender and/or age group. However, confidentiality issues or the absence of high-quality information about the characteristics of a population-at-risk can hamper those calculations. Based on methods in point process analysis for situations without accurate population data, we propose the use of a case-control approach in the context of lattice data, in which an unrelated, spatially unstructured disease is used as a control disease. We correct for the uncertainty in the estimation of the expected values, which arises by using the control-disease's observed number of cases as a representation of a fraction of the total population. We apply our methods to a Belgian study of mesothelioma risk, where pancreatic cancer serves as the control disease. The analysis results are in close agreement with those coming from traditional disease mapping models based on internally standardized expected counts. The simulation study results confirm our findings for different spatial structures. We show that the proposed method can adequately address the problem of inaccurate or unavailable population data in disease mapping analysis.