Negative Binomial Parameter Research Articles

Investigating factors affecting rural crash frequency at marginal areas around cities in Iran: a random parameter modeling approach

ABSTRACT A significant portion of rural crashes in Iran occur in the marginal areas around cities. Exclusive crash frequency models should be developed to identify the factors affecting the occurrence of crashes in these areas. In this study, the rural crash data of highways leading to the city of Isfahan were employed to develop a negative binomial (NB) model as a constant-parameter model, along with random effects negative binomial (RENB) and random parameters negative binomial (RPNB) models as the models based on the random parameter approach. The modeling results indicated the superiority of the RPNB model over the two other models. According to the findings of this study, the traffic volume of roads and the proportion of local and non-local vehicles, the proportion of longitudinal distance-limit violation, the way of controlling access points, and the access to rest areas affected the crash frequency in the marginal areas around cities.

Unobserved heterogeneity in ramp crashes due to alignment, interchange geometry and truck volume: Insights from a random parameter model

This paper presents a negative binomial random parameter model with heterogeneity in means and variance to capture the effect of heterogeneous effect of ramp type, alignment, truck volume and interchange geometry and on freeway ramp crash frequency. Two years (2018–2019) of crash data on freeway ramps in Washington State were analyzed. Model estimation results show ramp type (directional, semi-directional and loop), alignment, and traffic characteristics significantly impact ramp crash frequency. The northwest loop ramp indicator has a random parameter. The minimum horizontal curve radius and the total number of vertical curves on the ramp appear to be statistically significant sources of heterogeneity in the mean of this parameter. Heterogeneity in the mean of the random effect is influenced by single truck percentage and the low AADT indicator (<=1,340 vehicles per day).Heterogeneity in the variance of the northwest loop ramp random parameter appears to be associated with the southwest loop ramp indicator indicating unobserved effects due to same-side loop geometries.Directional ramp indicators (on- and off-ramps) and interactions involving speed limit, AADT and horizontal curve radius are statistically significant (as fixed parameters) in their impact on ramp crash frequency.Total centerline mile footprint of all ramps at the interchange is a continuous fixed parameter effect. Ramp-specific lengths (longer than 0.335 miles) also appear to be statistically significant. The findings in this study suggest that ramp and interchange design need to account for a holistic integration of spatial footprint, type of ramp and alignment factors, in addition to traffic flow variables.

Over-dispersed Trypanosoma cruzi parasite load in sylvatic and domestic mammals and humans from northeastern Argentina

BackgroundThe distribution of parasite load across hosts may modify the transmission dynamics of infectious diseases. Chagas disease is caused by a multi-host protozoan, Trypanosoma cruzi, but the association between host parasitemia and infectiousness to the vector has not been studied in sylvatic mammalian hosts. We quantified T. cruzi parasite load in sylvatic mammals, modeled the association of the parasite load with infectiousness to the vector and compared these results with previous ones for local domestic hosts.MethodsThe bloodstream parasite load in each of 28 naturally infected sylvatic mammals from six species captured in northern Argentina was assessed by quantitative PCR, and its association with infectiousness to the triatomine Triatoma infestans was evaluated, as determined by natural or artificial xenodiagnosis. These results were compared with our previous results for 88 humans, 70 dogs and 13 cats, and the degree of parasite over-dispersion was quantified and non-linear models fitted to data on host infectiousness and bloodstream parasite load.ResultsThe parasite loads of Didelphis albiventris (white-eared opossum) and Dasypus novemcinctus (nine-banded armadillo) were directly and significantly associated with infectiousness of the host and were up to 190-fold higher than those in domestic hosts. Parasite load was aggregated across host species, as measured by the negative binomial parameter, k, and found to be substantially higher in white-eared opossums, cats, dogs and nine-banded armadillos (range: k = 0.3–0.5) than in humans (k = 5.1). The distribution of bloodstream parasite load closely followed the “80–20 rule” in every host species examined. However, the 20% of human hosts, domestic mammals or sylvatic mammals exhibiting the highest parasite load accounted for 49, 25 and 33% of the infected triatomines, respectively.ConclusionsOur results support the use of bloodstream parasite load as a proxy of reservoir host competence and individual transmissibility. The over-dispersed distribution of T. cruzi bloodstream load implies the existence of a fraction of highly infectious hosts that could be targeted to improve vector-borne transmission control efforts toward interruption transmission. Combined strategies that decrease the parasitemia and/or host–vector contact with these hosts would disproportionally contribute to T. cruzi transmission control.Graphical

Marginal modeling in community randomized trials with rare events: Utilization of the negative binomial regression model.

This work is motivated by the HEALing Communities Study, which is a post-test only cluster randomized trial in which communities are randomized to two different trial arms. The primary interest is in reducing opioid overdose fatalities, which will be collected as a count outcome at the community level. Communities range in size from thousands to over one million residents, and fatalities are expected to be rare. Traditional marginal modeling approaches in the cluster randomized trial literature include the use of generalized estimating equations with an exchangeable correlation structure when utilizing subject-level data, or analogously quasi-likelihood based on an over-dispersed binomial variance when utilizing community-level data. These approaches account for and estimate the intra-cluster correlation coefficient, which should be provided in the results from a cluster randomized trial. Alternatively, the coefficient of variation or R coefficient could be reported. In this article, we show that negative binomial regression can also be utilized when communities are large and events are rare. The objectives of this article are (1) to show that the negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model and to explain why the estimates may differ; (2) to derive formulas relating the negative binomial overdispersion parameter k with the intra-cluster correlation coefficient, coefficient of variation, and R coefficient; and (3) analyze pre-intervention data from the HEALing Communities Study to demonstrate and contrast models and to show how to report the intra-cluster correlation coefficient, coefficient of variation, and R coefficient when utilizing negative binomial regression. Negative binomial and over-dispersed binomial regression modeling are contrasted in terms of model setup, regression parameter estimation, and formulation of the overdispersion parameter. Three specific models are used to illustrate concepts and address the third objective. The negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model, although estimates may differ. Practical differences arise in regard to how overdispersion, and hence the intra-cluster correlation coefficient is modeled. The negative binomial overdispersion parameter is approximately equal to the ratio of the intra-cluster correlation coefficient and marginal probability, the square of the coefficient of variation, and the R coefficient minus 1. As a result, estimates corresponding to all four of these different types of overdispersion parameterizations can be reported when utilizing negative binomial regression. Negative binomial regression provides a valid, practical, alternative approach to the analysis of count data, and corresponding reporting of overdispersion parameters, from community randomized trials in which communities are large and events are rare.

Energy dependence of the multiplicity moments at the LHC

In this work, from the experimental data we evaluate the first C-moments of the multiplicity distributions recently measured in proton-proton collisions at the LHC and compare them with the predictions of two models: the Kharzeev-Levin model and the Bialas-Praszalowicz model. We divide the data into three sets according to their phase space coverage: I: $p_T > 100 $ MeV and $|\eta|< 0.5$; II: $p_T > 100 $ MeV and $|\eta|< 2.4$ and II: $p_T > 500 $ MeV and $|\eta|< 2.4$. The mean multiplicity grows with the energy according to a power law and the power is different for each set. The $C_n$ moments grow continuously with the energy, slowly in set I and faster in the other sets. Except for KL in set II, both models reproduce the main features of the data. The negative binomial parameter $k$ decreases continuously with the energy and there is no sign of change in this behavior.

鹞落坪国家级自然保护区草本植物多样性及空间分布

鹞落坪国家级自然保护区草本植物多样性及空间分布

Inferring SARS-CoV-2 RNA shedding into wastewater relative to the time of infection.

Since the start of the coronavirus disease-2019 (COVID-19) pandemic, there has been interest in using wastewater monitoring as an approach for disease surveillance. A significant uncertainty that would improve the interpretation of wastewater monitoring data is the intensity and timing with which individuals shed RNA from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) into wastewater. By combining wastewater and case surveillance data sets from a university campus during a period of heightened surveillance, we inferred that individual shedding of RNA into wastewater peaks on average 6 days (50% uncertainty interval (UI): 6-7; 95% UI: 4-8) following infection, and that wastewater measurements are highly overdispersed [negative binomial dispersion parameter, k = 0.39 (95% credible interval: 0.32-0.48)]. This limits the utility of wastewater surveillance as a leading indicator of secular trends in SARS-CoV-2 transmission during an epidemic, and implies that it could be most useful as an early warning of rising transmission in areas where transmission is low or clinical testing is delayed or of limited capacity.

A Cluster-based Method to Quantify Individual Heterogeneity in Tuberculosis Transmission.

Recent evidence suggests transmission of Mycobacterium tuberculosis (Mtb) may be characterized by extreme individual heterogeneity in secondary cases (i.e., few cases account for the majority of transmission). Such heterogeneity implies outbreaks are rarer but more extensive and has profound implications in infectious disease control. However, discrete person-to-person transmission events in tuberculosis (TB) are often unobserved, precluding our ability to directly quantify individual heterogeneity in TB epidemiology. We used a modified negative binomial branching process model to quantify the extent of individual heterogeneity using only observed transmission cluster size distribution data (i.e., the simple sum of all cases in a transmission chain) without knowledge of individual-level transmission events. The negative binomial parameter k quantifies the extent of individual heterogeneity (generally, indicates extensive heterogeneity, and as transmission becomes more homogenous). We validated the robustness of the inference procedure considering common limitations affecting cluster size data. Finally, we demonstrate the epidemiologic utility of this method by applying it to aggregate US molecular surveillance data from the US Centers for Disease Control and Prevention. The cluster-based method reliably inferred k using TB transmission cluster data despite a high degree of bias introduced into the model. We found that the TB transmission in the United States was characterized by a high propensity for extensive outbreaks (; 95% confidence interval = 0.09, 0.10). The proposed method can accurately quantify critical parameters that govern TB transmission using simple, more easily obtainable cluster data to improve our understanding of TB epidemiology.

The distribution pattern and ecological restoration technology of aquatic plants in a eutrophic water landscape belt

Abstract Taking the eutrophic Taige canal and Caoqiao River in the upper reaches of North Taihu Lake as the experimental objects, 12 monitoring points were set up and data were recorded. The distribution pattern of aquatic plants in the water landscape belt was studied by variance/mean ratio, aggregation intensity index, negative binomial parameter, Cassie index and α–diversity index. Based on the principle of aquatic plants repairing eutrophic water, a suitable water environment was selected. The effect of ecological restoration was studied by photometry. The results showed that: the main aquatic plant communities in this area evolved from submerged to floating leaf and emergent plants, which shows that the vertical distribution pattern of the aquatic plant communities was greatly affected by hydrology; the distribution pattern of aquatic plant diversity showed a good single curve in the vertical direction and a single curve in the horizontal direction; the results of ecological restoration showed that the average removal rates of total nitrogen (TN) and total phosphorus (TP) by mixing the three plants were 86.76% and 93.89%, respectively. Among them, the best combination for TN removal was water hyacinth (Eichhornia crassipes) + lytchus (Lythrum salicaria) + calamus (Acorus calamus), and the best combination for TP removal was water hyacinth + lytchus + hibiscus (Nelumbonucifera).

Does the micro land snail, Kaliella barrakporensis (Mollusca: Gastropoda), exhibit plant preference and aggregation? A spatial scale analysis

The spatial scale occurrence of the micro land snail Kaliella barrakporensis (L. Pfeiffer, 1852) in the host plants was assessed in selected sites of West Bengal, India. In course of a survey, the collection of K. barrakporensis from randomly selected plants was accomplished for the purpose of highlighting – (a) distribution in host plants, (b) variation in abundance in different height and (c) the dispersion pattern. Although the snails were observed in seven different plants, the presence was more prominent in the lemon plant (Citrus limon), with an average of about 24 individuals / 100 leaves. The logit based principal component regression indicated significant differences in the choice of the host plants with abundance in C. limon followed by Hibiscus rosa sinensis and Nyctanthes arbor-tristis, which was further substantiated through ANOVA (F(1),6, 69 = 10.918; P &lt; 0.001). The heterogeneity in the distribution of K. barrakporensis at different heights of the plant C. limon was also observed with maximum abundance at about 90cm height with least number of snails at the ground level (F(1)6,139 = 3.797;P &lt; 0.0001). On the basis of the variance to mean ratio (s2/m = 1.847±0.161SE), negative binomial aggregation parameter k (1.034± 0.33 SE) and Lloyd mean crowding (ṁ) (1.083 ± 0.16SE) the dispersion of the snail appeared to comply with the clumped distribution in host plants. Apparently, the micro land snail K. barrakporensis exhibited clumped distribution in selected plant species that serve as the preferred resource and complies with the arboreal adaptation. However, further studies should be initiated on the resource preferences of the micro snail K. barrakporensis, to support conservation initiative and spread beyond native habitats.

Non-Stationary Modeling of Microlevel Road-Curve Crash Frequency with Geographically Weighted Regression

Vehicle crashes on roads are caused by many factors. However, the influence of these factors is not necessarily homogenous across locations, which is a challenge for non-stationary modeling approaches. To address this problem, this paper adopts two types of methods allowing parameters to fluctuate among observations, that is, the random parameter approach and the geographically weighted regression (GWR) approach. With road curvature, curve length, pavement friction, and traffic volume as independent variables, vehicle crash frequencies are modeled by two non-spatial methods, including the negative binomial (NB) model and random parameter negative binomial (RPNB), as well as three spatial methods (GWR approach). These models are calibrated in microlevel using a dataset of 9415 horizontal curve segments with a total length of 1545 kilometers for a period of three years (2016–2018) over the State of Indiana. The results revealed that the GWR approach can capture spatial heterogeneity and therefore significantly outperforms the conventional non-spatial approach. Based on the Akaike Information Criterion (AICc), geographically weighted negative binomial regression (GWNBR) was proved to be a superior approach for statewide microlevel crash analysis.

The impact of community-wide, mass drug administration on aggregation of soil-transmitted helminth infection in human host populations

BackgroundSoil-transmitted helminths (STH) are intestinal parasites estimated to infect over 1.5 billion people. Current treatment programmes are aimed at morbidity control through school-based deworming programmes (targeting school-aged children, SAC) and treating women of reproductive age (WRA), as these two groups are believed to record the highest morbidity. More recently, however, the potential for interrupting transmission by treating entire communities has been receiving greater emphasis and the feasibility of such programmes are now under investigation in randomised clinical trials through the Bill & Melinda Gates Foundation funded DeWorm3 studies. Helminth parasites are known to be highly aggregated within human populations, with a small minority of individuals harbouring most worms. Empirical evidence from the TUMIKIA project in Kenya suggests that aggregation may increase significantly after anthelminthic treatment.MethodsA stochastic, age-structured, individual-based simulation model of parasite transmission is employed to better understand the factors that might induce this pattern. A simple probabilistic model based on compounded negative binomial distributions caused by age-dependencies in both treatment coverage and exposure to infection is also employed to further this understanding.ResultsBoth approaches confirm helminth aggregation is likely to increase post-mass drug administration as measured by a decrease in the value of the negative binomial aggregation parameter, k. Simple analytical models of distribution compounding describe the observed patterns well.ConclusionsThe helminth aggregation that was observed in the field was replicated with our stochastic individual-based model. Further work is required to generalise the probabilistic model to take account of the respective sensitivities of different diagnostics on the presence or absence of infection.

Heterogeneity in helminth infections: factors influencing aggregation in a simple host-parasite system.

The almost universally-occurring aggregated distributions of helminth burdens in host populations have major significance for parasite population ecology and evolutionary biology, but the mechanisms generating heterogeneity remain poorly understood. For the direct life cycle monogenean Discocotyle sagittata infecting rainbow trout, Oncorhynchus mykiss, variables potentially influencing aggregation can be analysed individually. This study was based at a fish farm where every host individual becomes infected by D. sagittata during each annual transmission period. Worm burdens were examined in one trout population maintained in isolation for 9 years, exposed to self-contained transmission. After this year-on-year recruitment, prevalence was 100% with intensities 10-2628, mean 576, worms per host. Parasite distribution, amongst hosts with the same age and environmental experience, was highly aggregated with variance to mean ratio 834 and negative binomial parameter, k, 0.64. The most heavily infected 20% of fish carried around 80% of the total adult parasite population. Aggregation develops within the first weeks post-infection; hosts typically carried intensities of successive age-specific cohorts that were consistent for that individual, such that heavily-infected individuals carried high numbers of all parasite age classes. Results suggest that host factors alone, operating post-infection, are sufficient to generate strongly overdispersed parasite distributions, rather than heterogeneity in exposure and initial invasion.

Heterogeneity in transmission parameters of hookworm infection within the baseline data from the TUMIKIA study in Kenya

BackgroundAs many countries with endemic soil-transmitted helminth (STH) burdens achieve high coverage levels of mass drug administration (MDA) to treat school-aged and pre-school-aged children, understanding the detailed effects of MDA on the epidemiology of STH infections is desirable in formulating future policies for morbidity and/or transmission control. Prevalence and mean intensity of infection are characterized by heterogeneity across a region, leading to uncertainty in the impact of MDA strategies. In this paper, we analyze this heterogeneity in terms of factors that govern the transmission dynamics of the parasite in the host population.ResultsUsing data from the TUMIKIA study in Kenya (cluster STH prevalence range at baseline: 0–63%), we estimated these parameters and their variability across 120 population clusters in the study region, using a simple parasite transmission model and Gibbs-sampling Monte Carlo Markov chain techniques. We observed great heterogeneity in R0 values, with estimates ranging from 1.23 to 3.27, while k-values (which vary inversely with the degree of parasite aggregation within the human host population) range from 0.007 to 0.29 in a positive association with increasing prevalence. The main finding of this study is the increasing trend for greater parasite aggregation as prevalence declines to low levels, reflected in the low values of the negative binomial parameter k in clusters with low hookworm prevalence. Localized climatic and socioeconomic factors are investigated as potential drivers of these observed epidemiological patterns.ConclusionsOur results show that lower prevalence is associated with higher degrees of aggregation and hence prevalence alone is not a good indicator of transmission intensity. As a consequence, approaches to MDA and monitoring and evaluation of community infection status may need to be adapted as transmission elimination is aimed for by targeted treatment approaches.

Distribution of Bemisia tabaci within soybean plants and on individual leaflets

AbstractTo control whiteflies on soybean crops in an effective and economically viable way, it is necessary to quantify the occurrence and density of Bemisia tabaci (Gennadius) (Hemiptera: Aleyrodidae) on the leaflets. Estimating the number of B. tabaci cm‐2 on leaflets is difficult, because its distribution pattern on the various parts of the plant canopy and on the leaflet surface is unknown. The aim of this study was to evaluate the distribution of B. tabaci nymphs on soybean plants and leaflets, under greenhouse and field conditions. One hundred soybean plants infested with all nymph stages were randomly selected in a greenhouse, and 25 in a field. Of each plant, a trifoliate leaf of the middle third of the plant’s height was selected and its central leaflet was collected (greenhouse experiment), or a trifoliate leaf of each third layer (upper, middle, and lower), of which the left, central, and right leaflets were collected (field experiment). The collected leaflets were divided into 32 sections (1 cm2 per section), arranged in an array of eight rows and four columns to count whitefly nymphs. The Morisita index (Iδ), the negative binomial parameter k, and the dispersion index (I) were calculated for each leaflet, using the number of nymphs as variable. The highest population densities of whitefly nymphs were found in the middle third of the soybean plants. In leaflets from the middle third, the nymphs concentrated in the middle and bottom parts of the leaflets, whereas in the upper and lower thirds of the plant, they were randomly distributed on the leaflets.

Evaluation of contributory factors’ effects on bicycle-car crash risk at signalized intersections

Bicycle-car accidents at signalized intersections account for a considerable part of bicycle accidents. Factors that have effects on the bicycle-car crash risk at signalized intersections are not well understood. Especially, the safety effects of bicycle facilities are controversial at intersections. This paper aims to identify factors that have significant effects on bicycle-car crash risk at signalized intersections and their effect directions.The negative binomial regression model is used to model associations between the frequency of bicycle-car accidents at signalized intersections and the contributory factors, based on 6-year accident history at 140 signalized intersections in Berlin, Germany. The considered factors include the traffic volume, geometric data, and bicycle-specific and car-specific infrastructures. The factor effect coefficients are estimated by the maximum likelihood approach. The estimated coefficient of the negative binomial dispersion parameter is significant at the level of 0.001. Three factors are identified to have significant effects on the crash risk. The traffic volume of cars across intersections has negative effects on the cycling safety. Regarding bicycle facilities, the number of bicycle lanes on intersection approaches has positive safety effects, whereas the intersections with more bicycle paths is subject to a higher crash risk, though intersection modifications are applied for bicycle paths. The results support the choice of the negative binomial regression over the Poisson regression in this study. The estimated effects provide implications for the cycling safety improvement at signalized intersections.

Association Between Muscle Strength and Modeling Estimates of Muscle Tissue Heterogeneity in Young and Old Adults.

Assessing aging muscle through estimates of muscle heterogeneity may overcome some of the limitations of grayscale analyses. The objectives of this study included determining statistical model parameters that characterize muscle echogenicity and are associated with strength in younger and older participants. Thirty-three community-dwelling participants were assigned to younger and older groups. Quantitative B-mode ultrasound scanning of the rectus femoris and isometric grip strength testing were completed. Shape or dispersion parameters from negative binomial distribution, Nakagami, gamma, and gamma mixture models were fitted to the grayscale histograms. The mean ages ± SDs of the younger and older groups were 24.0 ± 2.3 and 65.1 ± 6.5 years, respectively. Statistical model shape and dispersion parameters for the grayscale histograms significantly differed between the younger and older participants (P = .002-.006). Among all of the statistical models considered, the gamma mixture model showed the best fit with the grayscale histograms (χ2 goodness of fit = 62), whereas the Nakagami distribution displayed the poorest fit (χ2 goodness of fit = 2595). Grayscale values were significantly associated with peak grip strength force in younger adult participants (R2 = 0.36; P < .008). However, the negative binomial dispersion parameter k (adjusted R2 = 0.70; P < .001) and gamma shape parameter α (adjusted R2 = 0.68; P < .01) showed the highest associations with peak grip strength force in older adult participants. The negative binomial dispersion parameter k and the gamma shape parameter α have clinical relevance for the assessment of age-related muscle changes. Statistical models of muscle heterogeneity may characterize the association between muscle tissue composition estimates and strength better than grayscale measures in samples of community-dwelling older adults.

Estimates of caribou herd size using post-calving surveys in the Northwest Territories and Nunavut, Canada: A meta-analysis

Post-calving surveys to estimate herd size of barren-ground caribou (Rangifer tarandus groenlandicus, R. t. granti, and R. t. caribou) have been used for caribou herds in Alaska, Yukon, Northwest Territories, Nunavut, and Québec/Labrador. The main field procedure uses relocation of collared caribou to locate aggregated groups of hundreds or thousands of caribou during times of high insect harassment that usually occur in July. These groups are then pho­tographed to obtain a count of the caribou in the aggregated groups. Often some caribou are missed, and the count of caribou may be a negatively biased estimate of total herd size, unless a high proportion of the herd is found and photographed. To address this, some previous studies have used the Lincoln-Petersen estimator, which estimates the proportion of the herd counted based on the percentage of available collared caribou found during the survey. However, this estimator assumes equal probabilities of all groups of caribou being found, regardless of group size and the numbers of collared caribou in the group. These assumptions may not be valid, as larger groups are more likely to be found than smaller groups, particularly if there are several collared caribou present. This may lead to estimates that are biased low, along with an estimate of variance that may also be biased low. A two phase estimator developed by Rivest et al., in 1998 became available in R statistical software in 2012. We analyzed 20 data sets from post-calving surveys in the NWT and NU carried out between 2000 and 2015 using the Rivest estimator to explore working characteristics of this estimator. We compared the Rivest estimates with Lincoln-Petersen estimates and total counts on each survey. We considered factors that influence precision of the Rivest estimator with a focus on sampling factors such as the proportion of collars found, the number of collars available, and natural factors such as the degree of aggregation of caribou in each survey (as indexed by the negative binomial dispersion parameter). In general, the Rivest estimator displayed acceptable preci­sion when high proportions of caribou groups with collars were detected and counted, collar numbers were sufficient, and aggregation was adequate. Notable exceptions occurred in years of lower aggregation which resulted in many small groups with 0 or few collared caribou, and in these cases herd estimates had large variances and low precision. Estimates from the Rivest estimator, Lincoln-Petersen estimator, and total counts converged when sampling effort was high, collar numbers relative to herd size were high, and caribou were well aggregated in a limited number of groups. In other cases, estimates of the Rivest estimator were generally higher than Lincoln-Petersen estimates, presumably due to negative bias with the Lincoln-Petersen estimator. We provide a set of working recommendations to optimize field sampling to ensure reliable estimates of herd size using post-calving methods.

Of bats and livestock: The epidemiology of rabies in Trinidad, West Indies

Vampire bat-transmitted human rabies was first recognized in Trinidad during a major outbreak during the first half of the 20th century. To date, Trinidad is the only Caribbean island with vampire bat-transmitted rabies. Herein, we summarized the epidemiological situation of rabies in Trinidad during the period 1971–2015 through the analysis of field and laboratory records. During the study period, 259 domestic and wild animal rabies cases were laboratory confirmed with an annual median of 2 animal rabies cases. Over the 45 years, five significant epizootic events occurred (in 1974, 1997–1998, 2000, 2010 and 2012–2013) over which there was a significant increasing trend for the occurrence of rabies cases. The highest number of cases (87 cases) occurred during the 1997–1998 event, and the rabies positive proportion, was highest (0.7, 95% CI 0.52-0.84) for the year 2000. Rabies risk was highest for cattle (negative binomial parameter estimate 4.84, 95% CI 3.45–6.76), although numerous rabies cases were seen in the caprine population during the study period. In light of this finding, consideration should be given to including the small ruminant population in the national rabies vaccination program. Outbreaks affected mainly the counties of St. Patrick and St. George East, with epidemic progression outwards, and these areas should be prioritized for prevention and control efforts.

Predictive accuracy of particle filtering in dynamic models supporting outbreak projections

BackgroundWhile a new generation of computational statistics algorithms and availability of data streams raises the potential for recurrently regrounding dynamic models with incoming observations, the effectiveness of such arrangements can be highly subject to specifics of the configuration (e.g., frequency of sampling and representation of behaviour change), and there has been little attempt to identify effective configurations.MethodsCombining dynamic models with particle filtering, we explored a solution focusing on creating quickly formulated models regrounded automatically and recurrently as new data becomes available. Given a latent underlying case count, we assumed that observed incident case counts followed a negative binomial distribution. In accordance with the condensation algorithm, each such observation led to updating of particle weights. We evaluated the effectiveness of various particle filtering configurations against each other and against an approach without particle filtering according to the accuracy of the model in predicting future prevalence, given data to a certain point and a norm-based discrepancy metric. We examined the effectiveness of particle filtering under varying times between observations, negative binomial dispersion parameters, and rates with which the contact rate could evolve.ResultsWe observed that more frequent observations of empirical data yielded super-linearly improved accuracy in model predictions. We further found that for the data studied here, the most favourable assumptions to make regarding the parameters associated with the negative binomial distribution and changes in contact rate were robust across observation frequency and the observation point in the outbreak.ConclusionCombining dynamic models with particle filtering can perform well in projecting future evolution of an outbreak. Most importantly, the remarkable improvements in predictive accuracy resulting from more frequent sampling suggest that investments to achieve efficient reporting mechanisms may be more than paid back by improved planning capacity. The robustness of the results on particle filter configuration in this case study suggests that it may be possible to formulate effective standard guidelines and regularized approaches for such techniques in particular epidemiological contexts. Most importantly, the work tentatively suggests potential for health decision makers to secure strong guidance when anticipating outbreak evolution for emerging infectious diseases by combining even very rough models with particle filtering method.