A general framework for modeling population abundance data

Time-series data resulting from surveying wild animals are often described using state-space population dynamics models, in particular with Gompertz, Beverton-Holt, or Moran-Ricker latent processes. We show how hidden Markov model methodology provides a flexible framework for fitting a wide range of models to such data. This general approach makes it possible to model abundance on the natural or log scale, include multiple observations at each sampling occasion and compare alternative models using information criteria. It also easily accommodates unequal sampling time intervals, should that possibility occur, and allows testing for density dependence using the bootstrap. The paper is illustrated by replicated time series of red kangaroo abundances, and a univariate time series of ibex counts which are an order of magnitude larger. In the analyses carried out, we fit different latent process and observation models using the hidden Markov framework. Results are robust with regard to the necessary discretization of the state variable. We find no effective difference between the three latent models of the paper in terms of maximized likelihood value for the two applications presented, and also others analyzed. Simulations suggest that ecological time series are not sufficiently informative to distinguish between alternative latent processes for modeling population survey data when data do not indicate strong density dependence.     

The Measurement of Dynamic Latent Variables in Longitudinal Aging Research: Quantifying Adult Development

Dynamic latent variables involve systematic intraindividual change over time. Although it seems natural to apply traditional measurement theory to dynamic latent variables, in fact this is often inappropriate. Traditional measurement theory is based on the idea of static latent variables and offers little guidance to the researcher who wishes to measure a dynamic latent variable with a high degree of accuracy and validity. It is the contention of this article that measurement of a dynamic latent variable must start from a clearly defined substantive theory about human development. Two approaches that take this perspective are presented; the longitudinal Guttman simplex (LGS), a measurement model for dynamic latent variables undergoing irreversible cumulative, unitary development; and latent transition analysis (LTA), a more general latent class measurement model.     

Bayesian Latent Factor Regression for Functional and Longitudinal Data

Summary In studies involving functional data, it is commonly of interest to model the impact of predictors on the distribution of the curves, allowing flexible effects on not only the mean curve but also the distribution about the mean. Characterizing the curve for each subject as a linear combination of a high‐dimensional set of potential basis functions, we place a sparse latent factor regression model on the basis coefficients. We induce basis selection by choosing a shrinkage prior that allows many of the loadings to be close to zero. The number of latent factors is treated as unknown through a highly‐efficient, adaptive‐blocked Gibbs sampler. Predictors are included on the latent variables level, while allowing different predictors to impact different latent factors. This model induces a framework for functional response regression in which the distribution of the curves is allowed to change flexibly with predictors. The performance is assessed through simulation studies and the methods are applied to data on blood pressure trajectories during pregnancy.     

Bayesian Finite Markov Mixture Model for Temporal Multi‐Tissue Polygenic Patterns

Finite mixture models can provide the insights about behavioral patterns as a source of heterogeneity of the various dynamics of time course gene expression data by reducing the high dimensionality and making clear the major components of the underlying structure of the data in terms of the unobservable latent variables. The latent structure of the dynamic transition process of gene expression changes over time can be represented by Markov processes. This paper addresses key problems in the analysis of large gene expression data sets that describe systemic temporal response cascades and dynamic changes to therapeutic doses in multiple tissues, such as liver, skeletal muscle, and kidney from the same animals. Bayesian Finite Markov Mixture Model with a Dirichlet Prior is developed for the identifications of differentially expressed time related genes and dynamic clusters. Deviance information criterion is applied to determine the number of components for model comparisons and selections. The proposed Bayesian models are applied to multiple tissue polygenetic temporal gene expression data and compared to a Bayesian model‐based clustering method, named CAGED. Results show that our proposed Bayesian Finite Markov Mixture model can well capture the dynamic changes and patterns for irregular complex temporal data (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bayesian inference for stochastic kinetic models using a diffusion approximation

This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m- 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network.     

Factor analytic models of clustered multivariate data with informative censoring

This article describes a general class of factor analytic models for the analysis of clustered multivariate data in the presence of informative missingness. We assume that there are distinct sets of cluster-level latent variables related to the primary outcomes and to the censoring process, and we account for dependency between these latent variables through a hierarchical model. A linear model is used to relate covariates and latent variables to the primary outcomes for each subunit. A generalized linear model accounts for covariate and latent variable effects on the probability of censoring for subunits within each cluster. The model accounts for correlation within clusters and within subunits through a flexible factor analytic framework that allows multiple latent variables and covariate effects on the latent variables. The structure of the model facilitates implementation of Markov chain Monte Carlo methods for posterior estimation. Data from a spermatotoxicity study are analyzed to illustrate the proposed approach.     

Dynamic myocardial contractile parameters from left ventricular pressure-volume measurements

A new dynamic model of left ventricular (LV) pressure-volume relationships in beating heart was developed by mathematically linking chamber pressure-volume dynamics with cardiac muscle force-length dynamics. The dynamic LV model accounted for >80% of the measured variation in pressure caused by small-amplitude volume perturbation in an otherwise isovolumically beating, isolated rat heart. The dynamic LV model produced good fits to pressure responses to volume perturbations, but there existed some systematic features in the residual errors of the fits. The issue was whether these residual errors would be damaging to an application where the dynamic LV model was used with LV pressure and volume measurements to estimate myocardial contractile parameters. Good agreement among myocardial parameters responsible for response magnitude was found between those derived by geometric transformations of parameters of the dynamic LV model estimated in beating heart and those found by direct measurement in constantly activated, isolated muscle fibers. Good agreement was also found among myocardial kinetic parameters estimated in each of the two preparations. Thus the small systematic residual errors from fitting the LV model to the dynamic pressure-volume measurements do not interfere with use of the dynamic LV model to estimate contractile parameters of myocardium. Dynamic contractile behavior of cardiac muscle can now be obtained from a beating heart by judicious application of the dynamic LV model to information-rich pressure and volume signals. This provides for the first time a bridge between the dynamics of cardiac muscle function and the dynamics of heart function and allows a beating heart to be used in studies where the relevance of myofilament contractile behavior to cardiovascular system function may be investigated.     

A framework for structural equation models in general pedigrees

Background/Aims: Structural Equation Modeling (SEM) is an analysis approach that accounts for both the causal relationships between variables and the errors associated with the measurement of these variables. In this paper, a framework for implementing structural equation models (SEMs) in family data is proposed. Methods: This framework includes both a latent measurement model and a structural model with covariates. It allows for a wide variety of models, including latent growth curve models. Environmental, polygenic and other genetic variance components can be included in the SEM. Kronecker notation makes it easy to separate the SEM process from a familial correlation model. A limited information method of model fitting is discussed. We show how missing data and ascertainment may be handled. We give several examples of how the framework may be used. Results: A simulation study shows that our method is computationally feasible, and has good statistical properties. Conclusion: Our framework may be used to build and compare causal models using family data without any genetic marker data. It also allows for a nearly endless array of genetic association and/or linkage tests. A preliminary Matlab program is available, and we are currently implementing a more complete and user-friendly R package.     

A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks

Epidemic dynamics pose a great challenge to stochastic modelling because chance events are major determinants of the size and the timing of the outbreak. Reintroduction of the disease through contact with infected individuals from other areas is an important latent stochastic variable. In this study we model these stochastic processes to explain extinction and recurrence of epidemics observed in measles. We develop estimating functions for such a model and apply the methodology to temporal case counts of measles in 60 cities in England and Wales. In order to estimate the unobserved spatial contact process we suggest a method based on stochastic simulation and marginal densities. The estimation results show that it is possible to consider a unified model for the UK cities where the parameters depend on the city size. Stochastic realizations from the dynamic model realistically capture the transitions from an endemic cyclic pattern in large populations to irregular epidemic outbreaks in small human host populations.     

Latent pattern mixture models for informative intermittent missing data in longitudinal studies

A frequently encountered problem in longitudinal studies is data that are missing due to missed visits or dropouts. In the statistical literature, interest has primarily focused on monotone missing data (dropout) with much less work on intermittent missing data in which a subject may return after one or more missed visits. Intermittent missing data have broader applicability that can include the frequent situation in which subjects do not have common sets of visit times or they visit at nonprescheduled times. In this article, we propose a latent pattern mixture model (LPMM), where the mixture patterns are formed from latent classes that link the longitudinal response and the missingness process. This allows us to handle arbitrary patterns of missing data embodied by subjects' visit process, and avoids the need to specify the mixture patterns a priori. One assumption of our model is that the missingness process is assumed to be conditionally independent of the longitudinal outcomes given the latent classes. We propose a noniterative approach to assess this key assumption. The LPMM is illustrated with a data set from a health service research study in which homeless people with mental illness were randomized to three different service packages and measures of homelessness were recorded at multiple time points. Our model suggests the presence of four latent classes linking subject visit patterns to homeless outcomes.     

An information theory based framework for the measurement of population health

This paper proposes a new framework for the measurement of population health and the ranking of the health of different geographies. Since population health is a latent variable, studies which measure and rank the health of different geographies must aggregate observable health attributes into one summary measure. We show that the methods used in nearly all the literature to date implicitly assume that all attributes are infinitely substitutable. Our method, based on the measurement of multidimensional welfare and inequality, minimizes the entropic distance between the summary measure of population health and the distribution of the underlying attributes. This summary function coincides with the constant elasticity of substitution and Cobb–Douglas production functions and naturally allows different assumptions regarding attribute substitutability or complementarity. To compare methodologies, we examine a well-known ranking of the population health of U.S. states, America's Health Rankings. We find that states’ rankings are somewhat sensitive to changes in the weight given to each attribute, but very sensitive to changes in aggregation methodology. Our results have broad implications for well-known health rankings such as the 2000 World Health Report, as well as other measurements of population and individual health levels and the measurement and decomposition of health inequality.     

Measurement error in a random walk model with applications to population dynamics

Population abundances are rarely, if ever, known. Instead, they are estimated with some amount of uncertainty. The resulting measurement error has its consequences on subsequent analyses that model population dynamics and estimate probabilities about abundances at future points in time. This article addresses some outstanding questions on the consequences of measurement error in one such dynamic model, the random walk with drift model, and proposes some new ways to correct for measurement error. We present a broad and realistic class of measurement error models that allows both heteroskedasticity and possible correlation in the measurement errors, and we provide analytical results about the biases of estimators that ignore the measurement error. Our new estimators include both method of moments estimators and "pseudo"-estimators that proceed from both observed estimates of population abundance and estimates of parameters in the measurement error model. We derive the asymptotic properties of our methods and existing methods, and we compare their finite-sample performance with a simulation experiment. We also examine the practical implications of the methods by using them to analyze two existing population dynamics data sets.     

Primary brain cell infection by Toxoplasma gondii reveals the extent and dynamics of parasite differentiation and its impact on neuron biology

Toxoplasma gondii is a eukaryotic parasite that forms latent cysts in the brain of immunocompetent individuals. The latent parasite infection of the immune-privileged central nervous system is linked to most complications. With no drug currently available to eliminate the latent cysts in the brain of infected hosts, the consequences of neurons'' long-term infection are unknown. It has long been known that T. gondii specifically differentiates into a latent form (bradyzoite) in neurons, but how the infected neuron responds to the infection remains to be elucidated. We have established a new in vitro model resulting in the production of mature bradyzoite cysts in brain cells. Using dual, host and parasite RNA-seq, we characterized the dynamics of differentiation of the parasite, revealing the involvement of key pathways in this process. Moreover, we identified how the infected brain cells responded to the parasite infection revealing the drastic changes that take place. We showed that neuronal-specific pathways are strongly affected, with synapse signalling being particularly affected, especially glutamatergic synapse signalling. The establishment of this new in vitro model allows investigating both the dynamics of parasite differentiation and the specific response of neurons to long-term infection by this parasite.     

Latent Coinfection and the Maintenance of Strain Diversity

Technologies for strain differentiation and typing have made it possible to detect genetic diversity of pathogens, both within individual hosts and within communities. Coinfection of a host by more than one pathogen strain may affect the relative frequency of these strains at the population level through complex within- and between-host interactions; in infectious diseases that have a long latent period, interstrain competition during latency is likely to play an important role in disease dynamics. We show that SEIR models that include a class of latently coinfected individuals can have markedly different long-term dynamics than models without coinfection, and that coinfection can greatly facilitate the stable coexistence of strains. We demonstrate these dynamics using a model relevant to tuberculosis in which people may experience latent coinfection with both drug sensitive and drug resistant strains. Using this model, we show that the existence of a latent coinfected state allows the possibility that disease control interventions that target latency may facilitate the emergence of drug resistance.     

Bayesian dynamic modeling of latent trait distributions

Studies of latent traits often collect data for multiple items measuring different aspects of the trait. For such data, it is common to consider models in which the different items are manifestations of a normal latent variable, which depends on covariates through a linear regression model. This article proposes a flexible Bayesian alternative in which the unknown latent variable density can change dynamically in location and shape across levels of a predictor. Scale mixtures of underlying normals are used in order to model flexibly the measurement errors and allow mixed categorical and continuous scales. A dynamic mixture of Dirichlet processes is used to characterize the latent response distributions. Posterior computation proceeds via a Markov chain Monte Carlo algorithm, with predictive densities used as a basis for inferences and evaluation of model fit. The methods are illustrated using data from a study of DNA damage in response to oxidative stress.     

Assessing Toxicities in a Clinical Trial: Bayesian Inference for Ordinal Data Nested within Categories

Summary This article addresses modeling and inference for ordinal outcomes nested within categorical responses. We propose a mixture of normal distributions for latent variables associated with the ordinal data. This mixture model allows us to fix without loss of generality the cutpoint parameters that link the latent variable with the observed ordinal outcome. Moreover, the mixture model is shown to be more flexible in estimating cell probabilities when compared to the traditional Bayesian ordinal probit regression model with random cutpoint parameters. We extend our model to take into account possible dependence among the outcomes in different categories. We apply the model to a randomized phase III study to compare treatments on the basis of toxicities recorded by type of toxicity and grade within type. The data include the different (categorical) toxicity types exhibited in each patient. Each type of toxicity has an (ordinal) grade associated to it. The dependence among the different types of toxicity exhibited by the same patient is modeled by introducing patient‐specific random effects.     

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.     

A semiparametric transition model with latent traits for longitudinal multistate data

SUMMARY: We propose a general multistate transition model. The model is developed for the analysis of repeated episodes of multiple states representing different health status. Transitions among multiple states are modeled jointly using multivariate latent traits with factor loadings. Different types of state transition are described by flexible transition-specific nonparametric baseline intensities. A state-specific latent trait is used to capture individual tendency of the sojourn in the state that cannot be explained by covariates and to account for correlation among repeated sojourns in the same state within an individual. Correlation among sojourns across different states within an individual is accounted for by the correlation between the different latent traits. The factor loadings for a latent trait accommodate the dependence of the transitions to different competing states from a same state. We obtain the semiparametric maximum likelihood estimates through an expectation-maximization (EM) algorithm. The method is illustrated by studying repeated transitions between independence and disability states of activities of daily living (ADL) with death as an absorbing state in a longitudinal aging study. The performance of the estimation procedure is assessed by simulation studies.     

An SEIQR model for childhood diseases

It has been shown that the inclusion of an isolated class in the classical SIR model for childhood diseases can be responsible for self-sustained oscillations. Hence, the recurrent outbreaks of such diseases can be caused by autonomous, deterministic factors. We extend the model to include a latent class (i.e. individuals who are infected with the disease, but are not yet able to pass the disease to others) and study the resulting dynamics. The existence of Hopf bifurcations is shown for the model, as well as a homoclinic bifurcation for a perturbation to the model. For historical data on scarlet fever in England, our model agrees with the epidemiological data much more closely than the model without the latent class. For other childhood diseases, our model suggests that isolation is unlikely to be a major factor in sustained oscillations.