Bayesian hierarchical spatiotemporal models for prediction of (under)reporting rates and cases: COVID-19 infection among the older people in the United States during the 2020-2022 pandemic

The gap between the reported and actual COVID-19 infection cases has been an issue of concern. Here, we present Bayesian hierarchical spatiotemporal disease mapping models for state-level predictions of COVID-19 infection risks and (under)reporting rates among people aged 65 and above during the first two years of the pandemic in the United States. With prior elicitation based on recent prevalence studies, the study suggests that the median state-level reporting rate of COVID-19 infection was 90% (interquartile range: [78%, 96%]). Our study uncovers spatiotemporal variations and dynamics in state-level infection risks and (under)reporting rates, suggesting time-varying associations between higher population density, higher percentage of minorities, and higher percentage of vaccination and increased risks of COVID-19 infection, as well as an association between more easily accessible tests and higher reporting rates. With sensitivity analyses, we highlight the impact and importance of incorporating covariates information and objective prior references for evaluating the issue of underreporting.

A Bayesian nonparametric approach to correct for underreporting in count data

We propose a nonparametric compound Poisson model for underreported count data that introduces a latent clustering structure for the reporting probabilities. The latter are estimated with the model's parameters based on experts' opinion and exploiting a proxy for the reporting process. The proposed model is used to estimate the prevalence of chronic kidney disease in Apulia, Italy, based on a unique statistical database covering information on m = 258 municipalities obtained by integrating multisource register information. Accurate prevalence estimates are needed for monitoring, surveillance, and management purposes; yet, counts are deemed to be considerably underreported, especially in some areas of Apulia, one of the most deprived and heterogeneous regions in Italy. Our results agree with previous findings and highlight interesting geographical patterns of the disease. We compare our model to existing approaches in the literature using simulated as well as real data on early neonatal mortality risk in Brazil, described in previous research: the proposed approach proves to be accurate and particularly suitable when partial information about data quality is available.

Estimating the real burden of gestational syphilis in Brazil, 2007-2018: a Bayesian modeling study

Background

Although several studies have estimated gestational syphilis (GS) incidence in several countries, underreporting correction is rarely considered. This study aimed to estimate the level of under-registration and correct the GS incidence rates in the 557 Brazilian microregions.

Methods

Brazilian GS notifications between 2007 and 2018 were obtained from the SINAN-Syphilis system. A cluster analysis was performed to group microregions according to the quality of GS notification. A Bayesian hierarchical Poisson regression model was applied to estimate the reporting probabilities among the clusters and to correct the associated incidence rates.

Findings

We estimate that 45,196 (90%-HPD: 13,299; 79,310) GS cases were underreported in Brazil from 2007 to 2018, representing a coverage of 87.12% (90%-HPD: 79.40%; 95.83%) of registered cases, where HPD stands for the Bayesian highest posterior density credible interval. Underreporting levels differ across the country, with microregions in North and Northeast regions presenting the highest percentage of missed cases. After underreporting correction, Brazil's estimated GS incidence rate increased from 8.74 to 10.02 per 1000 live births in the same period.

Interpretation

Our findings highlight disparities in the registration level and incidence rate of GS in Brazil, reflecting regional heterogeneity in the quality of syphilis surveillance, access to prenatal care, and childbirth assistance services. This study provides robust evidence to enhance national surveillance systems, guide specific policies for GS detection disease control, and potentially mitigate the harmful consequences of mother-to-child transmission. The methodology might be applied in other regions to correct disease underreporting.

Funding

National Council for Scientific and Technological Development; The Bill Melinda Gates Foundation and Wellcome Trust.

Efficiently exploring for human robot interaction: partially observable Poisson processes

Consider a mobile robot exploring an office building with the aim of observing as much human activity as possible over several days. It must learn where and when people are to be found, count the observed activities, and revisit popular places at the right time. In this paper we present a series of Bayesian estimators for the levels of human activity that improve on simple counting. We then show how these estimators can be used to drive efficient exploration for human activities. The estimators arise from modelling the human activity counts as a partially observable Poisson process (POPP). This paper presents novel extensions to POPP for the following cases: (i) the robot’s sensors are correlated, (ii) the robot’s sensor model, itself built from data, is also unreliable, (iii) both are combined. It also combines the resulting Bayesian estimators with a simple, but effective solution to the exploration-exploitation trade-off faced by the robot in a real deployment. A series of 15 day robot deployments show how our approach boosts the number of human activities observed by 70% relative to a baseline and produces more accurate estimates of the level of human activity in each place and time.

Evaluating the Impact of Meningococcal Vaccines With Synthetic Controls

Invasive meningococcal disease (IMD) has a low and unpredictable incidence, presenting challenges for real-world evaluations of meningococcal vaccines. Traditionally, meningococcal vaccine impact is evaluated by predicting counterfactuals from pre-immunization IMD incidences, possibly controlling for IMD in unvaccinated age groups, but the selection of controls can influence results. We retrospectively applied a synthetic control (SC) method, previously used for pneumococcal disease, to data from 2 programs for immunization of infants against serogroups B and C IMD in England and Brazil. Time series of infectious/noninfectious diseases in infants and IMD cases in older unvaccinated age groups were used as candidate controls, automatically combined in a SC through Bayesian variable selection. SC closely predicted IMD in absence of vaccination, adjusting for nontrivial changes in IMD incidence. Vaccine impact estimates were in line with previous assessments. IMD cases in unvaccinated age groups were the most frequent SC-selected controls. Similar results were obtained when excluding IMD from control sets and using other diseases only, particularly respiratory diseases and measles. Using non-IMD controls may be important where there are herd immunity effects. SC is a robust and flexible method that addresses uncertainty introduced when equally plausible controls exhibit different post-immunization behaviors, allowing objective comparisons of IMD programs between countries.

A Bayesian Hierarchical Spatial Model to Correct for Misreporting in Count Data: Application to State-Level COVID-19 Data in the United States

The COVID-19 pandemic that began at the end of 2019 has caused hundreds of millions of infections and millions of deaths worldwide. COVID-19 posed a threat to human health and profoundly impacted the global economy and people’s lifestyles. The United States is one of the countries severely affected by the disease. Evidence shows that the spread of COVID-19 was significantly underestimated in the early stages, which prevented governments from adopting effective interventions promptly to curb the spread of the disease. This paper adopts a Bayesian hierarchical model to study the under-reporting of COVID-19 at the state level in the United States as of the end of April 2020. The model examines the effects of different covariates on the under-reporting and accurate incidence rates and considers spatial dependency. In addition to under-reporting (false negatives), we also explore the impact of over-reporting (false positives). Adjusting for misclassification requires adding additional parameters that are not directly identified by the observed data. Informative priors are required. We discuss prior elicitation and include R functions that convert expert information into the appropriate prior distribution.

Estimating underreporting of leprosy in Brazil using a Bayesian approach

BACKGROUND

Leprosy remains concentrated among the poorest communities in low-and middle-income countries and it is one of the primary infectious causes of disability. Although there have been increasing advances in leprosy surveillance worldwide, leprosy underreporting is still common and can hinder decision-making regarding the distribution of financial and health resources and thereby limit the effectiveness of interventions. In this study, we estimated the proportion of unreported cases of leprosy in Brazilian microregions.

METHODOLOGY/PRINCIPAL FINDINGS

Using data collected between 2007 to 2015 from each of the 557 Brazilian microregions, we applied a Bayesian hierarchical model that used the presence of grade 2 leprosy-related physical disabilities as a direct indicator of delayed diagnosis and a proxy for the effectiveness of local leprosy surveillance program. We also analyzed some relevant factors that influence spatial variability in the observed mean incidence rate in the Brazilian microregions, highlighting the importance of socioeconomic factors and how they affect the levels of underreporting. We corrected leprosy incidence rates for each Brazilian microregion and estimated that, on average, 33,252 (9.6%) new leprosy cases went unreported in the country between 2007 to 2015, with this proportion varying from 8.4% to 14.1% across the Brazilian States.

CONCLUSIONS/SIGNIFICANCE

The magnitude and distribution of leprosy underreporting were adequately explained by a model using Grade 2 disability as a marker for the ability of the system to detect new missing cases. The percentage of missed cases was significant, and efforts are warranted to improve leprosy case detection. Our estimates in Brazilian microregions can be used to guide effective interventions, efficient resource allocation, and target actions to mitigate transmission.

Bayesian Variable Selection for Gaussian Copula Regression Models

We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any combination of discrete and/or continuous responses and their association with a set of predictors. We utilize the parameter expansion for data augmentation strategy to construct a Markov chain Monte Carlo algorithm for the estimation of the parameters and the latent variables of the model. Based on a centered parametrization of the Gaussian latent variables, we design a fixed-dimensional proposal distribution to update jointly the latent binary vectors of important predictors and the corresponding non-zero regression coefficients. For Gaussian responses and for outcomes that can be modeled as a dependent version of a Gaussian response, this proposal leads to a Metropolis-Hastings step that allows an efficient exploration of the predictors' model space. The proposed strategy is tested on simulated data and applied to real data sets in which the responses consist of low-intensity counts, binary, ordinal and continuous variables.

A marginal moment matching approach for fitting endemic-epidemic models to underreported disease surveillance counts

Count data are often subject to underreporting, especially in infectious disease surveillance. We propose an approximate maximum likelihood method to fit count time series models from the endemic-epidemic class to underreported data. The approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class. Moreover, the form of the bias when underreporting is ignored or taken into account via multiplication factors is analyzed. Notably, we show that this leads to a downward bias in model-based estimates of the effective reproductive number. A marginal moment matching approach can also be used to account for reporting intervals which are longer than the mean serial interval of a disease. The good performance of the proposed methodology is demonstrated in simulation studies. An extension to time-varying parameters and reporting probabilities is discussed and applied in a case study on weekly rotavirus gastroenteritis counts in Berlin, Germany.