Estimation and inference of R0 of an infectious pathogen by a removal method

The basic reproductive ratio, R0, is a central quantity in the investigation and management of infectious pathogens. The standard model for describing stochastic epidemics is the continuous time epidemic birth-and-death process. The incidence data used to fit this model tend to be collected in discrete units (days, weeks, etc.), which makes model fitting, and estimation of R0 difficult. Discrete time epidemic models better match the time scale of data collection but make simplistic assumptions about the stochastic epidemic process. By investigating the nature of the assumptions of a discrete time epidemic model, we derive a bias corrected maximum likelihood estimate of R0 based on the chain binomial model. The resulting 'removal' estimators provide estimates of R0 and the initial susceptible population size from time series of infectious case counts. We illustrate the performance of the estimators on both simulated data and real epidemics. Lastly, we discuss methods to address data collected with observation error.     

Estimation of the mixing proportion in a mixture of two normal distributions from simple, rapid measurements

A mixture of two or more normal distributions often provides an adequate model for the distribution of a population consisting of varying proportions of component subpopulations. We consider here the problem of estimating the mixing proportion in a mixture of two normal distributions, the parameters of which can be assumed known. Very large samples may be needed if reasonably precise estimates are to be obtained, thus bringing into consideration the cost or time involved in obtaining large numbers of exact measurements and computing the estimates from them. Simple estimators based on simple, rapidly obtained measurements may then be attractive alternatives provided efficiency losses are not too great. Three such estimators studied here are based on (a) the number of observations less than a fixed point r, (b) the nembers less than s and greater than t, and (c) the sample mean. Optimal choices of the points r, s and t are considered, and the efficiencies of the estimators relative to maximum likelihood estimators (MLE) using the full data are obtained. The simple estimators often perform sufficiently well to make the collection of full data not worthwhile in practice.     

Sensitivity Analysis of an Individual-Based Model for Simulation of Influenza Epidemics

Individual-based epidemiology models are increasingly used in the study of influenza epidemics. Several studies on influenza dynamics and evaluation of intervention measures have used the same incubation and infectious period distribution parameters based on the natural history of influenza. A sensitivity analysis evaluating the influence of slight changes to these parameters (in addition to the transmissibility) would be useful for future studies and real-time modeling during an influenza pandemic.In this study, we examined individual and joint effects of parameters and ranked parameters based on their influence on the dynamics of simulated epidemics. We also compared the sensitivity of the model across synthetic social networks for Montgomery County in Virginia and New York City (and surrounding metropolitan regions) with demographic and rural-urban differences. In addition, we studied the effects of changing the mean infectious period on age-specific epidemics. The research was performed from a public health standpoint using three relevant measures: time to peak, peak infected proportion and total attack rate. We also used statistical methods in the design and analysis of the experiments.The results showed that: (i) minute changes in the transmissibility and mean infectious period significantly influenced the attack rate; (ii) the mean of the incubation period distribution appeared to be sufficient for determining its effects on the dynamics of epidemics; (iii) the infectious period distribution had the strongest influence on the structure of the epidemic curves; (iv) the sensitivity of the individual-based model was consistent across social networks investigated in this study and (v) age-specific epidemics were sensitive to changes in the mean infectious period irrespective of the susceptibility of the other age groups. These findings suggest that small changes in some of the disease model parameters can significantly influence the uncertainty observed in real-time forecasting and predicting of the characteristics of an epidemic.     

A model of the effect of fungicides on disease-induced yield loss, for use in wheat disease management decision support systems

A model of the effect of foliar-applied fungicides on disease-induced yield loss is described, parameterised and tested. The effects of fungicides on epidemics of Septoria tritici (leaf blotch), Puccinia striiformis (yellow rust), Blumeria graminis f.sp. tritici (powdery mildew) and Puccinia triticina (brown rust) on winter wheat were simulated using dose–response curve parameters. Where two or more active substances were applied together, their joint action was estimated using an additive dose model where the active substances had the same mode of action or a multiplicative survival model where the modes of action differed. By coupling the model with models of wheat canopy growth and foliar disease published previously, it was possible to estimate disease-induced yield loss for a prescribed fungicide programme. The difference in green canopy area and, hence, interception of photosynthetically active radiation between simulated undiseased and diseased (but treated) crop canopies was used to estimate yield loss. The model was tested against data from field experiments across a range of sites, seasons and wheat cultivars and was shown to predict the observed disease-induced yield loss with sufficient accuracy to support fungicide treatment decisions. A simple method of accounting for uncertainty in the predictions of yield loss is described. Fungicide product, dose and spray timing combinations selected using the coupled models responded appropriately to disease pressure and cultivar disease resistance.     

Patterns of density dependence in measles dynamics.

An important question in metapopulation dynamics is the influence of external perturbations on the population''s long-term dynamic behaviour. In this paper we address the question of how spatiotemporal variations in demographic parameters affect the dynamics of measles populations in England and Wales. Specifically, we use nonparametric statistical methods to analyse how birth rate and population size modulate the negative density dependence between successive epidemics as well as their periodicity. For the observed spatiotemporal data from 60 cities, and for simulated model data, the demographic variables act as bifurcation parameters on the joint density of the trade-off between successive epidemics. For increasing population size, a transition occurs from an irregular unpredictable pattern in small communities towards a regular, predictable endemic pattern in large places. Variations in the birth rate parameter lead to a bifurcation from annual towards biennial cyclicity in both observed data and model data.     

Evaluation of Root-n Bandwidth Selectors for Kernel Density Estimation

ABSTRACT The kernel density estimator is used commonly for estimating animal utilization distributions from location data. This technique requires estimation of a bandwidth, for which ecologists often use least-squares cross-validation (LSCV). However, LSCV has large variance and a tendency to under-smooth data, and it fails to generate a bandwidth estimate in some situations. We compared performance of 2 new bandwidth estimators (root-n) versus that of LSCV using simulated data and location data from sharp-shinned hawks (Accipter striatus) and red wolves (Canis rufus). With simulated data containing no repeat locations, LSCV often produced a better fit between estimated and true utilization distributions than did root-n estimators on a case-by-case basis. On average, LSCV also provided lower positive relative error in home-range areas with small sample sizes of simulated data. However, root-n estimators tended to produce a better fit than LSCV on average because of extremely poor estimates generated on occasion by LSCV. Furthermore, the relative performance of LSCV decreased substantially as the number of repeat locations in the data increased. Root-n estimators also generally provided a better fit between utilization distributions generated from subsamples of hawk data and the local densities of locations from the full data sets. Least-squares cross-validation generated more unrealistically disjointed estimates of home ranges using real location data from red wolf packs. Most importantly, LSCV failed to generate home-range estimates for >20% of red wolf packs due to presence of repeat locations. We conclude that root-n estimators are superior to LSCV for larger data sets with repeat locations or other extreme clumping of data. In contrast, LSCV may be superior where the primary interest is in generating animal home ranges (rather than the utilization distribution) and data sets are small with limited clumping of locations.     

Nonparametric estimation for the three-stage irreversible illness-death model

In this paper, we present new nonparametric estimators of the stage-occupation probabilities in the three-stage irreversible illness-death model. These estimators use a fractional risk set and a reweighting approach and are valid under stage-dependent censoring. Using a simulated data set, we compare the behavior of our estimators with previously proposed estimators. We also apply our estimators to data on time to Pneumocystis pneumonia and death obtained from an AIDS cohort study.     

Mean and variance of ratio estimators used in fluorescence ratio imaging

BACKGROUND: The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple instances of both signals can be combined in different ways to construct different ratio estimators. METHODS: The mean and variance of three estimators for the ratio between two random variables, x and y, are discussed. Given n samples of x and y, we can intuitively construct two different estimators: the mean of the ratio of each x and y and the ratio between the mean of x and the mean of y. The former is biased and the latter is only asymptotically unbiased. Using the statistical characteristics of this estimator, a third, unbiased estimator can be constructed. RESULTS: We tested the three estimators on simulated data, real-world fluorescence test images, and comparative genome hybridization (CGH) data. The results on the simulated and real-world test images confirm the presented theory. The CGH experiments show that our new estimator performs better than the existing estimators. CONCLUSIONS: We have derived an unbiased ratio estimator that outperforms intuitive ratio estimators.     

Estimating the number of channels in patch recordings

The estimation of the number of channels in a patch was assumed to be equivalent to the estimation of the binomial parameter n. Seven estimators were evaluated, using data sets simulated for a range of parameters appropriate for single channel recording experiments. No single estimator was best for all parameters; a combination of estimators is a possible option to avoid the biases of individual estimators. All estimators were highly accurate in estimating n in the case that n = 1. For n ≤ 4 the simplest estimator, the maximum number of simultaneously open channels, was the best, For larger values of n the best estimators were Bayesian.     

Bayesian Neural Network Models for Censored Data

Neural networks are considered by many to be very promising tools for classification and prediction. The flexibility of the neural network models often result in over-fit. Shrinking the parameters using a penalized likelihood is often used in order to overcome such over-fit. In this paper we extend the approach proposed by FARAGGI and SIMON (1995a) to modeling censored survival data using the input-output relationship associated with a single hidden layer feed-forward neural network. Instead of estimating the neural network parameters using the method of maximum likelihood, we place normal prior distributions on the parameters and make inferences based on derived posterior distributions of the parameters. This Bayesian formulation will result in shrinking the parameters of the neural network model and will reduce the over-fit compared with the maximum likelihood estimators. We illustrate our proposed method on a simulated and a real example.     

A general approach for two-stage analysis of multilevel clustered non-Gaussian data

In this article, we propose a two-stage approach to modeling multilevel clustered non-Gaussian data with sufficiently large numbers of continuous measures per cluster. Such data are common in biological and medical studies utilizing monitoring or image-processing equipment. We consider a general class of hierarchical models that generalizes the model in the global two-stage (GTS) method for nonlinear mixed effects models by using any square-root-n-consistent and asymptotically normal estimators from stage 1 as pseudodata in the stage 2 model, and by extending the stage 2 model to accommodate random effects from multiple levels of clustering. The second-stage model is a standard linear mixed effects model with normal random effects, but the cluster-specific distributions, conditional on random effects, can be non-Gaussian. This methodology provides a flexible framework for modeling not only a location parameter but also other characteristics of conditional distributions that may be of specific interest. For estimation of the population parameters, we propose a conditional restricted maximum likelihood (CREML) approach and establish the asymptotic properties of the CREML estimators. The proposed general approach is illustrated using quartiles as cluster-specific parameters estimated in the first stage, and applied to the data example from a collagen fibril development study. We demonstrate using simulations that in samples with small numbers of independent clusters, the CREML estimators may perform better than conditional maximum likelihood estimators, which are a direct extension of the estimators from the GTS method.     

Estimation of Parameters for One-Way Layout with Rank Set Sampling

Ranked set sampling (RSS) as suggested by McIntyre (1952) and independently by Takahasi and Wakimoto (1968) may be used to estimate the parameters of the one-way layout. The objective is to use the RSS method to increase the efficiency of the estimators relative to the simple random (SRS) method. Estimators of the populations (treatments) effect are considered. Computer simulated results are given, and an example using real data presented to illustrate the computations.     

Human birth seasonality: latitudinal gradient and interplay with childhood disease dynamics

More than a century of ecological studies have demonstrated the importance of demography in shaping spatial and temporal variation in population dynamics. Surprisingly, the impact of seasonal recruitment on infectious disease systems has received much less attention. Here, we present data encompassing 78 years of monthly natality in the USA, and reveal pronounced seasonality in birth rates, with geographical and temporal variation in both the peak birth timing and amplitude. The timing of annual birth pulses followed a latitudinal gradient, with northern states exhibiting spring/summer peaks and southern states exhibiting autumn peaks, a pattern we also observed throughout the Northern Hemisphere. Additionally, the amplitude of United States birth seasonality was more than twofold greater in southern states versus those in the north. Next, we examined the dynamical impact of birth seasonality on childhood disease incidence, using a mechanistic model of measles. Birth seasonality was found to have the potential to alter the magnitude and periodicity of epidemics, with the effect dependent on both birth peak timing and amplitude. In a simulation study, we fitted an susceptible-exposed-infected-recovered model to simulated data, and demonstrated that ignoring birth seasonality can bias the estimation of critical epidemiological parameters. Finally, we carried out statistical inference using historical measles incidence data from New York City. Our analyses did not identify the predicted systematic biases in parameter estimates. This may be owing to the well-known frequency-locking between measles epidemics and seasonal transmission rates, or may arise from substantial uncertainty in multiple model parameters and estimation stochasticity.     

A two-component model for counts of infectious diseases

We propose a stochastic model for the analysis of time series of disease counts as collected in typical surveillance systems on notifiable infectious diseases. The model is based on a Poisson or negative binomial observation model with two components: a parameter-driven component relates the disease incidence to latent parameters describing endemic seasonal patterns, which are typical for infectious disease surveillance data. An observation-driven or epidemic component is modeled with an autoregression on the number of cases at the previous time points. The autoregressive parameter is allowed to change over time according to a Bayesian changepoint model with unknown number of changepoints. Parameter estimates are obtained through the Bayesian model averaging using Markov chain Monte Carlo techniques. We illustrate our approach through analysis of simulated data and real notification data obtained from the German infectious disease surveillance system, administered by the Robert Koch Institute in Berlin. Software to fit the proposed model can be obtained from http://www.statistik.lmu.de/ approximately mhofmann/twins.     

A Mechanistic Model of Botrytis cinerea on Grapevines That Includes Weather,Vine Growth Stage,and the Main Infection Pathways

A mechanistic model for Botrytis cinerea on grapevine was developed. The model, which accounts for conidia production on various inoculum sources and for multiple infection pathways, considers two infection periods. During the first period (“inflorescences clearly visible” to “berries groat-sized”), the model calculates: i) infection severity on inflorescences and young clusters caused by conidia (SEV1). During the second period (“majority of berries touching” to “berries ripe for harvest”), the model calculates: ii) infection severity of ripening berries by conidia (SEV2); and iii) severity of berry-to-berry infection caused by mycelium (SEV3). The model was validated in 21 epidemics (vineyard × year combinations) between 2009 and 2014 in Italy and France. A discriminant function analysis (DFA) was used to: i) evaluate the ability of the model to predict mild, intermediate, and severe epidemics; and ii) assess how SEV1, SEV2, and SEV3 contribute to epidemics. The model correctly classified the severity of 17 of 21 epidemics. Results from DFA were also used to calculate the daily probabilities that an ongoing epidemic would be mild, intermediate, or severe. SEV1 was the most influential variable in discriminating between mild and intermediate epidemics, whereas SEV2 and SEV3 were relevant for discriminating between intermediate and severe epidemics. The model represents an improvement of previous B. cinerea models in viticulture and could be useful for making decisions about Botrytis bunch rot control.     

Modeling, simulation, and kinetic analysis of a heterogeneous reaction system for the enzymatic conversion of poorly soluble substrate.

We developed a kinetic model that describes a heterogeneous reaction system consisting of a solid substrate suspension for the production of D-amino acid using D-hydantoinase. As a biocatalyst, mass-produced free and whole cell enzymes were used. The heterogeneous reaction system involves dissolution of a solid substrate, enzymatic conversion of the dissolved D-form substrate, spontaneous racemization of an L-form substrate to D-form, and deactivation of the enzyme. In the case of using whole cell enzymes, transfer of the dissolved substrate and product through the cell membrane was considered. The kinetic parameters were determined from experiments, literature data, and by using Marquardt's method of nonlinear regression analysis. The model was simulated using the kinetic parameters and compared with experimental data, and a good agreement was observed between the experimental results and the simulation ones. Factors affecting the kinetics of the heterogeneous reaction system were analyzed on the basis of the kinetic model, and the efficiency of the reaction systems using free and whole cell enzymes was also compared.     

An open spatial capture–recapture model for estimating density,movement, and population dynamics from line‐transect surveys

The purpose of many wildlife population studies is to estimate density, movement, or demographic parameters. Linking these parameters to covariates, such as habitat features, provides additional ecological insight and can be used to make predictions for management purposes. Line‐transect surveys, combined with distance sampling methods, are often used to estimate density at discrete points in time, whereas capture–recapture methods are used to estimate movement and other demographic parameters. Recently, open population spatial capture–recapture models have been developed, which simultaneously estimate density and demographic parameters, but have been made available only for data collected from a fixed array of detectors and have not incorporated the effects of habitat covariates. We developed a spatial capture–recapture model that can be applied to line‐transect survey data by modeling detection probability in a manner analogous to distance sampling. We extend this model to a) estimate demographic parameters using an open population framework and b) model variation in density and space use as a function of habitat covariates. The model is illustrated using simulated data and aerial line‐transect survey data for North Atlantic right whales in the southeastern United States, which also demonstrates the ability to integrate data from multiple survey platforms and accommodate differences between strata or demographic groups. When individuals detected from line‐transect surveys can be uniquely identified, our model can be used to simultaneously make inference on factors that influence spatial and temporal variation in density, movement, and population dynamics.     

Parameters Estimation in a Simple Linear Regression Using Rank Set Sampling

Ranked set sampling (RSS) as suggested by MCINTYRE (1952) and TAKAHASI and WAKIMOTO (1968) may be used to estimate the parameters of the simple regression line. The objective is to use the RSS method to increase the efficiency of the estimators relative to the simple random sampling (SRS) method. Estimators of the slope and intercept are considered. Computer simulated results are given, and an example using real data presented to illustrate the computations.     

Effects of Point Pattern Shape on Home-Range Estimates

Abstract: Home-range estimators are commonly tested with simulated animal locational data in the laboratory before the estimators are used in practice. Although kernel density estimation (KDE) has performed well as a home-range estimator for simulated data, several recent studies have reported its poor performance when used with data collected in the field. This difference may be because KDE and other home-range estimators are generally tested with simulated point locations that follow known statistical distributions, such as bivariate normal mixtures, which may not represent well the space-use patterns of all wildlife species. We used simulated animal locational data of 5 point pattern shapes that represent a range of wildlife utilization distributions to test 4 methods of home-range estimation: 1) KDE with reference bandwidths, 2) KDE with least-squares cross-validation, 3) KDE with plug-in bandwidths, and 4) minimum convex polygon (MCP). For the point patterns we simulated, MCP tended to produce more accurate area estimates than KDE methods. However, MCP estimates were markedly unstable, with bias varying widely with both sample size and point pattern shape. The KDE methods performed best for concave distributions, which are similar to bivariate normal mixtures, but still overestimated home ranges by about 40–50% even in the best cases. For convex, linear, perforated, and disjoint point patterns, KDE methods overestimated home-range sizes by 50–300%, depending on sample size and method of bandwidth selection. These results indicate that KDE does not produce home-range estimates that are as accurate as the literature suggests, and we recommend exploring other techniques of home-range estimation.     

Predictive Validation of an Influenza Spread Model

Background

Modeling plays a critical role in mitigating impacts of seasonal influenza epidemics. Complex simulation models are currently at the forefront of evaluating optimal mitigation strategies at multiple scales and levels of organization. Given their evaluative role, these models remain limited in their ability to predict and forecast future epidemics leading some researchers and public-health practitioners to question their usefulness. The objective of this study is to evaluate the predictive ability of an existing complex simulation model of influenza spread.

Methods and Findings

We used extensive data on past epidemics to demonstrate the process of predictive validation. This involved generalizing an individual-based model for influenza spread and fitting it to laboratory-confirmed influenza infection data from a single observed epidemic (1998–1999). Next, we used the fitted model and modified two of its parameters based on data on real-world perturbations (vaccination coverage by age group and strain type). Simulating epidemics under these changes allowed us to estimate the deviation/error between the expected epidemic curve under perturbation and observed epidemics taking place from 1999 to 2006. Our model was able to forecast absolute intensity and epidemic peak week several weeks earlier with reasonable reliability and depended on the method of forecasting-static or dynamic.

Conclusions

Good predictive ability of influenza epidemics is critical for implementing mitigation strategies in an effective and timely manner. Through the process of predictive validation applied to a current complex simulation model of influenza spread, we provided users of the model (e.g. public-health officials and policy-makers) with quantitative metrics and practical recommendations on mitigating impacts of seasonal influenza epidemics. This methodology may be applied to other models of communicable infectious diseases to test and potentially improve their predictive ability.