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.     

Conditional Rejection Probabilities of Student's t‐test and Design Adaptations

For clinical trials with interim analyses conditional rejection probabilities play an important role when stochastic curtailment or design adaptations are performed. The conditional rejection probability gives the conditional probability to finally reject the null hypothesis given the interim data. It is computed either under the null or the alternative hypothesis. We investigate the properties of the conditional rejection probability for the one sided, one sample t‐test and show that it can be non monotone in the interim mean of the data and non monotone in the non‐centrality parameter for the alternative. We give several proposals how to implement design adaptations (that are based on the conditional rejection probability) for the t‐test and give a numerical example. Additionally, the conditional rejection probability given the interim t‐statistic is investigated. It does not depend on the unknown σ and can be used in stochastic curtailment procedures. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimating age‐dependent survival from age‐aggregated ringing data—extending the use of historical records

Bird ring‐recovery data have been widely used to estimate demographic parameters such as survival probabilities since the mid‐20th century. However, while the total number of birds ringed each year is usually known, historical information on age at ringing is often not available. A standard ring‐recovery model, for which information on age at ringing is required, cannot be used when historical data are incomplete. We develop a new model to estimate age‐dependent survival probabilities from such historical data when age at ringing is not recorded; we call this the historical data model. This new model provides an extension to the model of Robinson, 2010, Ibis, 152, 651–795 by estimating the proportion of the ringed birds marked as juveniles as an additional parameter. We conduct a simulation study to examine the performance of the historical data model and compare it with other models including the standard and conditional ring‐recovery models. Simulation studies show that the approach of Robinson, 2010, Ibis, 152, 651–795 can cause bias in parameter estimates. In contrast, the historical data model yields similar parameter estimates to the standard model. Parameter redundancy results show that the newly developed historical data model is comparable to the standard ring‐recovery model, in terms of which parameters can be estimated, and has fewer identifiability issues than the conditional model. We illustrate the new proposed model using Blackbird and Sandwich Tern data. The new historical data model allows us to make full use of historical data and estimate the same parameters as the standard model with incomplete data, and in doing so, detect potential changes in demographic parameters further back in time.     

Integration of stochastic simulation with multivariate analysis: Short‐term facility fit prediction

This article describes a decision‐support tool to help pinpoint the potential root causes of sub‐optimal short‐term facility fit issues in biopharmaceutical facilities. This was achieved by creating a tool that integrated stochastic simulation with advanced multivariate statistical analysis. Process fluctuations in product titers in cell culture, step yields, and chromatography eluate volumes were mimicked using Monte Carlo simulation data derived using a stochastic discrete‐event simulation model. The resulting stochastic datasets, with the computed consequences on key metrics such as product mass loss and cost of goods, were examined using advanced multivariate statistical techniques. Principal component analysis combined with clustering algorithms was used to analyze the complex datasets from complete industrial batch processes for biopharmaceuticals. The challenge of visualizing the multidimensional nature of the dataset was addressed using hierarchical and k‐means clustering as well as stacked parallel co‐ordinate plots to help identify process fingerprints and characteristics of clusters leading to sub‐optimal facility fit issues. Industrially‐relevant case studies are presented that focus on technology transfer challenges for therapeutic antibodies moving from early phase to late phase clinical trials. The case study details how sub‐optimal facility fit can be alleviated by allocating alternative product pool tanks. The impact of this operational change is then assessed by reviewing an updated process fingerprint. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29: 368–377, 2013     

Highly Infectious CJD Particles Lack Prion Protein but Contain Many Viral‐Linked Peptides by LC‐MS/MS

It is widely believed that host prion protein (PrP), without nucleic acid, converts itself into an infectious form (PrP‐res) that causes transmissible encephalopathies (TSEs), such as human sporadic CJD (sCJD), endemic sheep scrapie, and epidemic BSE. There are many detailed investigations of PrP, but proteomic studies of other proteins in verified infectious TSE particles have not been pursued, even though brain homogenates without PrP retain their complete infectious titer. To define proteins that may be integral to, process, or protect an agent genome, we developed a streamlined, high‐yield purification of infectious FU‐CJD mouse brain particles with minimal PrP. Proteinase K (PK) abolished all residual particle PrP, but did not reduce infectivity, and viral‐size particles lacking PrP were ～70S (vs. 90–120S without PK). Furthermore, over 1,500 non‐PrP proteins were still present and positively identified in high titer FU‐CJD particles without detectable PrP by mass spectrometry (LC‐MS/MS); 114 of these peptides were linked to viral motifs in the environmental–viral database, and not evident in parallel uninfected controls. Host components were also identified in both PK and non‐PK treated particles from FU‐CJD mouse brain and human sCJD brain. This abundant cellular data had several surprises, including finding Huntingtin in the sCJD but not normal human brain samples. Similarly, the neural Wiskott–Aldrich sequence and multivesicular and endosome components associated with retromer APP (Alzheimer amyloid) processing were only in sCJD. These cellular findings suggest that new therapies directed at retromer–vesicular trafficking in other neurodegenerative diseases may also counteract late‐onset sCJD PrP amyloid pathology. J. Cell. Biochem. 115: 2012–2021, 2014. © 2014 Wiley Periodicals, Inc.

     

Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study

A stochastic discrete-time susceptible-exposed-infectious-recovered (SEIR) model for infectious diseases is developed with the aim of estimating parameters from daily incidence and mortality time series for an outbreak of Ebola in the Democratic Republic of Congo in 1995. The incidence time series exhibit many low integers as well as zero counts requiring an intrinsically stochastic modeling approach. In order to capture the stochastic nature of the transitions between the compartmental populations in such a model we specify appropriate conditional binomial distributions. In addition, a relatively simple temporally varying transmission rate function is introduced that allows for the effect of control interventions. We develop Markov chain Monte Carlo methods for inference that are used to explore the posterior distribution of the parameters. The algorithm is further extended to integrate numerically over state variables of the model, which are unobserved. This provides a realistic stochastic model that can be used by epidemiologists to study the dynamics of the disease and the effect of control interventions.     

Effects of age‐based movement on the estimation of growth assuming random‐at‐age or random‐at‐length data

Simulation methods were used to generate paired data from a simulated population that included the age‐based process of movement and the length‐based process of gear selection. The age‐based process caused bias in the estimates of growth parameters assuming random at length, even when relatively few age classes were affected. Methods that assumed random at age were biased by the subsequent inclusion of the length‐based process of gear selection. Additional knowledge of the age structure of the sampled area is needed to ensure an unbiased estimate of the growth parameters when using the length‐conditional approach in the presence of age‐based movement. Estimates of the variability in the length‐at‐age relationship were better estimated with the length‐conditional than the traditional method even when the assumptions of random at length were violated. Inclusion of paired observations of length and associated age inside the population dynamics model may be the most appropriate way of estimating growth.     

A stochastic SIR model with contact-tracing: large population limits and statistical inference

This paper is devoted to the presentation and study of a specific stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease. Precisely, one considers here the situation in which individuals identified as infected by the public health detection system may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The control strategy, which consists of examining each individual who has been able to be identified on the basis of the information collected within a certain time period, is expected to efficiently reinforce the standard random-screening-based detection and considerably ease the epidemic. In the novel modelling of the spread of a communicable infectious disease considered here, the population of interest evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size, roughly speaking, becomes larger. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relations of the model with the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out.     

Bayesian Analysis of Growth Curves Using Mixed Models Defined by Stochastic Differential Equations

Summary Growth curve data consist of repeated measurements of a continuous growth process over time in a population of individuals. These data are classically analyzed by nonlinear mixed models. However, the standard growth functions used in this context prescribe monotone increasing growth and can fail to model unexpected changes in growth rates. We propose to model these variations using stochastic differential equations (SDEs) that are deduced from the standard deterministic growth function by adding random variations to the growth dynamics. A Bayesian inference of the parameters of these SDE mixed models is developed. In the case when the SDE has an explicit solution, we describe an easily implemented Gibbs algorithm. When the conditional distribution of the diffusion process has no explicit form, we propose to approximate it using the Euler–Maruyama scheme. Finally, we suggest validating the SDE approach via criteria based on the predictive posterior distribution. We illustrate the efficiency of our method using the Gompertz function to model data on chicken growth, the modeling being improved by the SDE approach.     

The effect of waning immunity on long-term behaviour of stochastic models for the spread of infection

In stochastic modelling of infectious spread, it is often assumed that infection confers permanent immunity, a susceptible-infective-removed (SIR) model. We show how results concerning long-term (endemic) behaviour may be extended to a susceptible-infective-removed-susceptible (SIRS) model, in which immunity is temporary. Since the full SIRS model with demography is rather intractable, we also consider two simpler models: the susceptible-infective-susceptible (SIS) model with demography, in which there is no immunity; and the SIRS model in a closed population. For each model, we first analyse a deterministic model, then approximate the quasi-stationary distribution (equilibrium distribution conditional upon non-extinction of infection) using a moment closure technique. We look in particular at the effect of the immune period upon infection prevalence and upon time to fade-out of infection. Our main findings are that a shorter average immune period leads to higher infection prevalence in quasi-stationarity, and to longer persistence of infection in the population.     

A stochastic SIR model with contact-tracing: large population limits and statistical inference

This paper is devoted to the presentation and study of a specific stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease. Precisely, one considers here the situation in which individuals identified as infected by the public health detection system may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The control strategy, which consists of examining each individual who has been able to be identified on the basis of the information collected within a certain time period, is expected to efficiently reinforce the standard random-screening-based detection and considerably ease the epidemic. In the novel modelling of the spread of a communicable infectious disease considered here, the population of interest evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size, roughly speaking, becomes larger. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relations of the model with the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out.     

Components of morphological variation in Baikalian endemial cyclopid Acanthocyclops signifer complex from different localities

Use of traditional methods for morphological studies only permits the analysis of a small part of the information embodied in morphological structures. Besides comparing populations using the mean values of characters which allows one to estimate their morphological similarity, analysis of variation among individuals within a population can be informative. Variation among individuals consists of factorial and stochastic components. The factorial component is an upper estimate of genetic heterogeneity and thus permits one to evaluate the population's adaptability. The stochastic component (estimated by fluctuating asymmetry, i.e. random deviations from perfect bilateral symmetry), being a measure of developmental stability, is an indicator of a population's fitness. Assessment of measurement error is necessary for assessment of the true value of the stochastic component and for selection of the most informative characters. Such analysis allows one to extract additional information from morphological data in comparison with methods traditionally used on copepods. This approach was applied to an analysis of morphological variation in the study of the Baikalian endemic cyclopoid Acanthocyclops signifer (Mazepova) from three different isolated localities. Characters typically used in studies of taxonomy of this group are considered here. Measurement error was rather high (more than 50% of the stochastic component), which can be explained by technical difficulties of measuring the characters. All populations differ in the mean values of the characters. This shows the taxonomic heterogeneity of this group and reveals the necessity of its taxonomic revision. Populations also differ in the level of stochastic and factorial components of the total variance. The data are interpreted from the point of view of taxonomy and the possible evolution of the group.     

Dependent competing risks: a stochastic process model

Analyses of human mortality data classified according to cause of death frequently are based on competing risk theory. In particular, the times to death for different causes often are assumed to be independent. In this paper, a competing risk model with a weaker assumption of conditional independence of the times to death, given an assumed stochastic covariate process, is developed and applied to cause specific mortality data from the Framingham Heart Study. The results generated under this conditional independence model are compared with analogous results under the standard marginal independence model. Under the assumption that this conditional independence model is valid, the comparison suggests that the standard model overestimates by 4% the effect on life expectancy at age 30 due to the hypothetical elimination of cancer and by 7% the effect for cardiovascular/cerebrovascular disease. By age 80 the overestimates were 11% for cancer and 16% for heart disease. These results suggest the importance of avoiding the marginal independence assumption when appropriate data are available — especially when focusing on mortality at advanced ages.     

Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas

We present a mathematical model for malaria treatment and spread of drug resistance in an endemic population. The model considers treated humans that remain infectious for some time and partially immune humans who are also infectious to mosquitoes although their infectiousness is always less than their non immune counterparts. The model is formulated by considering delays in the latent periods in both mosquito and human populations and in the period within which partial immunity is lost. Qualitative analysis of the model including positivity and boundedness of solutions is performed. Analysis of the reproductive numbers shows that if the treated humans become immediately uninfectious to mosquitoes then treatment will always reduce the number of sensitive infections. If however treated humans are infectious then for treatment to effectively reduce the number of sensitive infections, the ratio of the infectious period of the treated humans to the infectious period of the untreated humans multiplied by the ratio of the transmission rate from a treated human to the transmission rate of an untreated human should be less than one. Our results show that the spread of drug resistance with treatment as a control strategy depends on the ratio of the infectious periods of treated and untreated humans and on the transmission rates from infectious humans with resistant and sensitive infections. Numerical analysis is performed to assess the effects of treatment on the spread of resistance and infection. The study provides insight into the possible intervention strategies to be employed in malaria endemic populations with resistant parasites by identifying important parameters.     

A random effects model for multistate survival analysis with application to bone marrow transplants

We present an extension of the non-homogeneous Markov model for a bone marrow transplant recovery process which allows for possible associations between the transition intensities. The associations between intensities are modeled by a correlated gamma frailty model. Based on a parametric model for the conditional transition intensities, we obtain estimates of the model parameters. We use these estimates to make predictions of patient’s eventual prognosis given the current medical history of the patient. Estimates of the uncertainty in our predictions are obtained by a modified bootstrap technique.     

Stochastic simulations of a multi-group compartmental model for Johne's disease on US dairy herds with test-based culling intervention

Infection elimination may be an important goal of control programs. Only in stochastic infection models can true infection elimination be observed as a fadeout. The phenomena of fadeout and variable prevalence are important in understanding the transmission dynamics of infectious diseases and these phenomena are essential to evaluate the effectiveness of control measures. To investigate the stochastic dynamics of Mycobacterium avium subsp. paratuberculosis (MAP) infection on US dairy herds with test-based culling intervention, we developed a multi-group stochastic compartmental model (a continuous time Markov chain model) with both horizontal and vertical transmission. The stochastic model predicted fadeout and within-herd prevalence to have a large variance. Although test-based culling intervention generally decreased prevalence over time, it took longer than desired by producers to eliminate the endemic MAP infection from a herd. Uncertainty analysis showed that, using annual culture test and culling of only high shedders or culling of both low and high shedders with a 12-month delay in culling of low shedders, MAP infection persisted in many herds beyond 20 years. While using semi-annual culture test and culling of low and high shedders with a 6-month delay in culling of low shedders, MAP infection in many herds would be extinct within 20 years. Sensitivity analysis of the cumulative density function of fadeout suggested that combining test-based culling intervention and reduction of transmission rates through improved management between susceptible calves and shedding animals may be more effective than either alone in eliminating endemic MAP infection. We also discussed the effects of other factors such as herd size, heifer replacement, and adult cow infection on the probability of fadeout.     

Precise Estimates of Persistence Time for SIS Infections in Heterogeneous Populations

For a susceptible–infectious–susceptible infection model in a heterogeneous population, we derive simple and precise estimates of mean persistence time, from a quasi-stationary endemic state to extinction of infection. Heterogeneity may be in either individuals’ levels of infectiousness or of susceptibility, as well as in individuals’ infectious period distributions. Infectious periods are allowed to follow arbitrary non-negative distributions. We also obtain a new and accurate approximation to the quasi-stationary distribution of the process, as well as demonstrating the use of our estimates to investigate the effects of different forms of heterogeneity. Our model may alternatively be interpreted as describing an infection spreading through a heterogeneous directed network, under the annealed network approximation.     

On the global stability of a generalized cholera epidemiological model

In this paper, we conduct a careful global stability analysis for a generalized cholera epidemiological model originally proposed in [J. Wang and S. Liao, A generalized cholera model and epidemic/endemic analysis, J. Biol. Dyn. 6 (2012), pp. 568–589]. Cholera is a water- and food-borne infectious disease whose dynamics are complicated by the multiple interactions between the human host, the pathogen, and the environment. Using the geometric approach, we rigorously prove the endemic global stability for the cholera model in three-dimensional (when the pathogen component is a scalar) and four-dimensional (when the pathogen component is a vector) systems. This work unifies the study of global dynamics for several existing deterministic cholera models. The analytical predictions are verified by numerical simulation results.     

An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks

Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the prevention and control of infectious diseases and computer viruses. Here we consider Markovian susceptible-infectious-susceptible (SIS) dynamics on finite strongly connected networks, applicable to several sexually transmitted diseases and computer viruses. In this context, a theoretical definition of endemic prevalence is easily obtained via the quasi-stationary distribution (QSD). By representing the model as a percolation process and utilising the property of duality, we also provide a theoretical definition of invasion probability. We then show that, for undirected networks, the probability of invasion from any given individual is equal to the (probabilistic) endemic prevalence, following successful invasion, at the individual (we also provide a relationship for the directed case). The total (fractional) endemic prevalence in the population is thus equal to the average invasion probability (across all individuals). Consequently, for such systems, the regions or individuals already supporting a high level of infection are likely to be the source of a successful invasion by another infectious agent. This could be used to inform targeted interventions when there is a threat from an emerging infectious disease.     

Statistical Methods for Analyzing Right‐Censored Length‐Biased Data under Cox Model

Summary Length‐biased time‐to‐event data are commonly encountered in applications ranging from epidemiological cohort studies or cancer prevention trials to studies of labor economy. A longstanding statistical problem is how to assess the association of risk factors with survival in the target population given the observed length‐biased data. In this article, we demonstrate how to estimate these effects under the semiparametric Cox proportional hazards model. The structure of the Cox model is changed under length‐biased sampling in general. Although the existing partial likelihood approach for left‐truncated data can be used to estimate covariate effects, it may not be efficient for analyzing length‐biased data. We propose two estimating equation approaches for estimating the covariate coefficients under the Cox model. We use the modern stochastic process and martingale theory to develop the asymptotic properties of the estimators. We evaluate the empirical performance and efficiency of the two methods through extensive simulation studies. We use data from a dementia study to illustrate the proposed methodology, and demonstrate the computational algorithms for point estimates, which can be directly linked to the existing functions in S‐PLUS or R .