Accounting for Sampling Error When Inferring Population Synchrony from Time-Series Data: A Bayesian State-Space Modelling Approach with Applications

Background

Data collected to inform time variations in natural population size are tainted by sampling error. Ignoring sampling error in population dynamics models induces bias in parameter estimators, e.g., density-dependence. In particular, when sampling errors are independent among populations, the classical estimator of the synchrony strength (zero-lag correlation) is biased downward. However, this bias is rarely taken into account in synchrony studies although it may lead to overemphasizing the role of intrinsic factors (e.g., dispersal) with respect to extrinsic factors (the Moran effect) in generating population synchrony as well as to underestimating the extinction risk of a metapopulation.

Methodology/Principal findings

The aim of this paper was first to illustrate the extent of the bias that can be encountered in empirical studies when sampling error is neglected. Second, we presented a space-state modelling approach that explicitly accounts for sampling error when quantifying population synchrony. Third, we exemplify our approach with datasets for which sampling variance (i) has been previously estimated, and (ii) has to be jointly estimated with population synchrony. Finally, we compared our results to those of a standard approach neglecting sampling variance. We showed that ignoring sampling variance can mask a synchrony pattern whatever its true value and that the common practice of averaging few replicates of population size estimates poorly performed at decreasing the bias of the classical estimator of the synchrony strength.

Conclusion/Significance

The state-space model used in this study provides a flexible way of accurately quantifying the strength of synchrony patterns from most population size data encountered in field studies, including over-dispersed count data. We provided a user-friendly R-program and a tutorial example to encourage further studies aiming at quantifying the strength of population synchrony to account for uncertainty in population size estimates.     

Proportionality: A Valid Alternative to Correlation for Relative Data

In the life sciences, many measurement methods yield only the relative abundances of different components in a sample. With such relative—or compositional—data, differential expression needs careful interpretation, and correlation—a statistical workhorse for analyzing pairwise relationships—is an inappropriate measure of association. Using yeast gene expression data we show how correlation can be misleading and present proportionality as a valid alternative for relative data. We show how the strength of proportionality between two variables can be meaningfully and interpretably described by a new statistic ϕ which can be used instead of correlation as the basis of familiar analyses and visualisation methods, including co-expression networks and clustered heatmaps. While the main aim of this study is to present proportionality as a means to analyse relative data, it also raises intriguing questions about the molecular mechanisms underlying the proportional regulation of a range of yeast genes.     

Multi-Formalism Modelling and Simulation: Application to Cardiac Modelling

Cardiovascular modelling has been a major research subject for the last decade. Different cardiac models have been developed at a cellular level as well as at the whole organ level. Most of these models are defined by a comprehensive cellular modelling using continuous formalisms or by a tissue-level modelling often based on discrete formalisms. Nevertheless, both views still suffer from difficulties that reduce their clinical applications: the first approach requires heavy computational resources while the second one is not able to reproduce certain pathologies. This paper presents an original methodology trying to gather advantages from both approaches, by means of a hybrid model mixing discrete and continuous formalisms. This method has been applied to define a hybrid model of cardiac action potential propagation on a 2D grid of endocardial cells, combining cellular automata and a set of cells defined by the Beeler-Reuter model. For simulations under physiological and ischemic conditions, results show that the action potential propagation as well as electrogram reconstructions are consistent with clinical diagnosis. Finally, the advantage of the proposed approach is discussed within the frame of cardiac modelling and simulation.     

Classification and Error Estimation for Discrete Data

Discrete classification is common in Genomic Signal Processing applications, in particular in classification of discretized gene expression data, and in discrete gene expression prediction and the inference of boolean genomic regulatory networks. Once a discrete classifier is obtained from sample data, its performance must be evaluated through its classification error. In practice, error estimation methods must then be employed to obtain reliable estimates of the classification error based on the available data. Both classifier design and error estimation are complicated, in the case of Genomics, by the prevalence of small-sample data sets in such applications. This paper presents a broad review of the methodology of classification and error estimation for discrete data, in the context of Genomics, focusing on the study of performance in small sample scenarios, as well as asymptotic behavior.Key Words: Genomics, classification, error estimation, discrete histogram rule, sampling distribution, resubstitution, leave-one-out, ensemble methods, coefficient of determination.     

Likelihood-Based Modeling and Analysis of Data Underdispersed Relative to the Poisson Distribution

By using a generalization of the Poisson process, distributions can be constructed that show appropriate amounts of underdispersion relative to the Poisson distribution that may be apparent from observed data. These are then used to examine the differences between the distributions of numbers of fetal implants in mice corresponding to different doses of the herbicide 2,4,5-T.     

The Power of Relative Rates Tests Depends on the Data

One of the most useful features of molecular phylogenetic analyses is the potential for estimating dates of divergence of evolutionary lineages from the DNA of extant species. But lineage-specific variation in rate of molecular evolution complicates molecular dating, because a calibration rate estimated from one lineage may not be an accurate representation of the rate in other lineages. Many molecular dating studies use a ``clock test' to identify and exclude sequences that vary in rate between lineages. However, these clock tests should not be relied upon without a critical examination of their effectiveness at removing rate variable sequences from any given data set, particularly with regard to the sequence length and number of variable sites. As an illustration of this problem we present a power test of a frequently employed triplet relative rates test. We conclude that (1) relative rates tests are unlikely to detect moderate levels of lineage-specific rate variation (where one lineage has a rate of molecular evolution 1.5 to 4.0 times the other) for most commonly used sequences in molecular dating analyses, and (2) this lack of power is likely to result in substantial error in the estimation of dates of divergence. As an example, we show that the well-studied rate difference between murid rodents and great apes will not be detected for many of the sequences used to date the divergence between these two lineages and that this failure to detect rate variation is likely to result in consistent overestimation the date of the rodent–primate split. Received: 9 June 1999 / Accepted: 22 October 1999     

Management of Evolving Map Data: Data Structures and Algorithms Based on the Framework Map

A consensus framework map of a chromosome is the single most useful map of the chromosome, because of the amount of information it holds as well as the quality of the supporting data backing the putative order of its objects. We describe data structures and algorithms to assist in framework map maintenance and to answer queries about order and distance on genomic objects. We show how these algorithms are efficiently implemented in a client-server relational database. We believe that our data structures are particularly suitable for databases to support collaborative mapping efforts that use heterogeneous methodologies. We summarize two applications that use these algorithms: CHROMINFO, a database specifically designed for framework map maintenance; and the shared client-server database for the chromosome 12 genome center.     

Response of Insect Relative Growth Rate to Temperature and Host-Plant Phenology: Estimation and Validation from Field Data

Between 1975 to 2011, aphid Relative Growth Rates (RGR) were modelled as a function of mean outdoor temperature and host plant phenology. The model was applied to the grain aphid Sitobion avenae using data on aphid counts in winter wheat at two different climate regions in France (oceanic climate, Rennes (western France); continental climate, Paris). Mean observed aphid RGR was higher in Paris compared to the Rennes region. RGR increased with mean temperature, which is explained by aphid reproduction, growth and development being dependent on ambient temperature. From the stem extension to the heading stage in wheat, there was either a plateau in RGR values (Rennes) or an increase with a maximum at heading (Paris) due to high intrinsic rates of increase in aphids and also to aphid immigration. From the wheat flowering to the ripening stage, RGR decreased in both regions due to the low intrinsic rate of increase in aphids and high emigration rate linked to reduced nutrient quality in maturing wheat. The model validation process showed that the fitted models have more predictive power in the Paris region than in the Rennes region.     

Magnetic Resonance Assessment of Response to Therapy: Tumor Change Measurement,Truth Data and Error Sources

This article describes methods and issues that are specific to the assessment of change in tumor characteristics as measured using quantitative magnetic resonance (MR) techniques and how this relates to the establishment of quantitative MR imaging (MRI) biomarkers of patient response to therapy. The initial focus is on the various sources of bias and variance in the measurement of microvascular parameters and diffusion parameters as such parameters are being used relatively commonly as secondary or exploratory end points in current phase 1/2 clinical trails of conventional and targeted therapies. Several ongoing initiatives that seek to identify the magnitude of some of the sources of measurement variations are then discussed. Finally, resources being made available through the National Cancer Institute Reference Image Database to Evaluate Response (RIDER) project that might be of use in investigations of quantitative MRI biomarker change analysis are described. These resources include 1) data from phantom-based assessment of system response, including short-term (1 hour) and moderate-term (1 week) contrast response and relaxation time measurement, 2) data obtained from repeated dynamic contrast agent-enhanced MRI studies in intracranial tumors, and 3) data obtained from repeated diffusion MRI studies in both breast and brain. A concluding section briefly discusses issues that must be addressed to allow the transition of MR-based imaging biomarker measures from their current role as secondary/exploratory end points in clinical trials to primary/surrogate markers of response and, ultimately, in clinical application.     

Relative Deprivation and Relative Wealth Enhances Anti-Immigrant Sentiments: The V-Curve Re-Examined

Previous research has shown that negative attitudes towards immigrants and support for anti-immigrant parties are observed both among those experiencing relative deprivation and those experiencing relative gratification (so called v-curve). Whereas the effect of relative deprivation is intuitive, the effect of relative gratification is more difficult to explain. Why would economic prosperity provoke negative attitudes towards immigrants? We first present correlational (Study 1) and experimental (Study 2) support for the v-curve. In Study 1, in a national Swiss referendum, a higher percentage anti-immigrant voting was found in cantons with relatively lower and relatively higher relative disposable income. In Study 2, in a hypothetical society, more opposition to ‘newcomers’ joining society was found among poor or above average wealth group members than among those in a moderate wealth group condition. In Study 3, we replicate this finding and also show that opposition to immigration is higher for all wealth groups when societal inequality is growing rather than declining. In a final study, we examine different forms of relative gratification and mediators of the relationship between relative gratification and opposition to immigration (i.e., identification, collective self-definition as competent and cold, and fear about future wealth). Only fear about future wealth mediates this relationship. We conclude that, paradoxically, relative gratification effects are partly due to the fear of future deprivation.     

Quantitative Imaging to Assess Tumor Response to Therapy: Common Themes of Measurement,Truth Data,and Error Sources

RATIONALE: Early detection of tumor response to therapy is a key goal. Finding measurement algorithms capable of early detection of tumor response could individualize therapy treatment as well as reduce the cost of bringing new drugs to market. On an individual basis, the urgency arises from the desire to prevent continued treatment of the patient with a high-cost and/or high-risk regimen with no demonstrated individual benefit and rapidly switch the patient to an alternative efficacious therapy for that patient. In the context of bringing new drugs to market, such algorithms could demonstrate efficacy in much smaller populations, which would allow phase 3 trials to achieve statistically significant decisions with fewer subjects in shorter trials. MATERIALS AND METHODS: This consensus-based article describes multiple, image modality-independent means to assess the relative performance of algorithms for measuring tumor change in response to therapy. In this setting, we describe specifically the example of measurement of tumor volume change from anatomic imaging as well as provide an overview of other promising generic analytic methods that can be used to assess change in heterogeneous tumors. To support assessment of the relative performance of algorithms for measuring small tumor change, data sources of truth are required. RESULTS: Very short interval clinical imaging examinations and phantom scans provide known truth for comparative evaluation of algorithms. CONCLUSIONS: For a given category of measurement methods, the algorithm that has the smallest measurement noise and least bias on average will perform best in early detection of true tumor change.     

Computed Tomography Assessment of Response to Therapy: Tumor Volume Change Measurement,Truth Data,and Error

RATIONALE AND OBJECTIVES: This article describes issues and methods that are specific to the measurement of change in tumor volume as measured from computed tomographic (CT) images and how these would relate to the establishment of CT tumor volumetrics as a biomarker of patient response to therapy. The primary focus is on the measurement of lung tumors, but the approach should be generalizable to other anatomic regions. MATERIALS AND METHODS: The first issues addressed are the various sources of bias and variance in the measurement of tumor volumes, which are discussed in the context of measurement variation and its impact on the early detection of response to therapy. RESULTS AND RESOURCES: Research that seeks to identify the magnitude of some of these sources of error is ongoing, and several of these efforts are described herein. In addition, several resources for these investigations are being made available through the National Institutes of Health-funded Reference Image Database to Evaluate Response to therapy in cancer project, and these are described as well. Other measures derived from CT image data that might be predictive of patient response are described briefly, as well as the additional issues that each of these metrics may encounter in real-life applications. CONCLUSIONS: The article concludes with a brief discussion of moving from the assessment of measurement variation to the steps necessary to establish the efficacy of a metric as a biomarker for response.     

PET/CT Assessment of Response to Therapy: Tumor Change Measurement,Truth Data,and Error

We describe methods and issues that are relevant to the measurement of change in tumor uptake of ¹⁸F-fluorodeoxyglucose (FDG) or other radiotracers, as measured from positron emission tomography/computed tomography (PET/CT) images, and how this would relate to the establishment of PET/CT tumor imaging as a biomarker of patient response to therapy. The primary focus is on the uptake of FDG by lung tumors, but the approach can be applied to diseases other than lung cancer and to tracers other than FDG. The first issue addressed is the sources of bias and variance in the measurement of tumor uptake of FDG, and where there are still gaps in our knowledge. These are discussed in the context of measurement variation and how these would relate to the early detection of response to therapy. Some of the research efforts currently underway to identify the magnitude of some of these sources of error are described. In addition, we describe resources for these investigations that are being made available through the Reference Image Database for the Evaluation of Response project. Measures derived from PET image data that might be predictive of patient response as well as the additional issues that each of these metrics may encounter are described briefly. The relationship between individual patient response to therapy and utility for multicenter trials is discussed. We conclude with a discussion of moving from assessing measurement variation to the steps necessary to establish the efficacy of PET/CT imaging as a biomarker for response.     

Modelling Survival Data to Examine Length of Treatment Effectiveness in a Clinical Trial

In some clinical trials where the experimental treatment is found to be effective in increasing survival, an important question is how long should the patient remain under treatment. Although the trial may not be designed to specifically answer this question, comparisons of the hazard curves among the treatment groups can yield some useful information. The survival data may be modelled using a flexible set of hazard functions and specific models are then chosen for further examination. This paper illustrates the approach using data from the Beta-Blocker Heart Attack Trial. Parametric and semi-parametric models are fitted and likelihood methods are used to assess length of treatment effectiveness.     

Global Registration of Subway Tunnel Point Clouds Using an Augmented Extended Kalman Filter and Central-Axis Constraint

Because tunnels generally have tubular shapes, the distribution of tie points between adjacent scans is usually limited to a narrow region, which makes the problem of registration error accumulation inevitable. In this paper, a global registration method is proposed based on an augmented extended Kalman filter and a central-axis constraint. The point cloud registration is regarded as a stochastic system, and the global registration is considered to be a process that recursively estimates the rigid transformation parameters between each pair of adjacent scans. Therefore, the augmented extended Kalman filter (AEKF) is used to accurately estimate the rigid transformation parameters by eliminating the error accumulation caused by the pair-wise registration. Moreover, because the scanning range of a terrestrial laser scanner can reach hundreds of meters, a single scan can cover a tunnel segment with a length of more than one hundred meters, which means that the central axis extracted from the scan can be employed to control the registration of multiple scans. Therefore, the central axis of the subway tunnel is first determined through the 2D projection of the tunnel point cloud and curve fitting using the RANSAC (RANdom SAmple Consensus) algorithm. Because the extraction of the central axis by quadratic curve fitting may suffer from noise in the tunnel points and from variations in the tunnel, we present a global extraction algorithm that is based on segment-wise quadratic curve fitting. We then derive the central-axis constraint as an additional observation model of AEKF to optimize the registration parameters between each pair of adjacent scans. The proposed approach is tested on terrestrial point clouds that were acquired in a subway tunnel. The results show that the proposed algorithm is capable of improving the accuracy of aligning multiple scans by 48%.     

The Interpretation of Low-Angle X-Ray Data from Planar and Concentric Multilayered Structures: The Use of One-Dimensional Electron Density Strip Models

The use of one-dimensional electron density strip models in interpreting low-angle X-ray data from planar and concentric multilayered structures is described. Diffraction formulas for an n-strip model are given. Fourier transforms, normalization constants, and Patterson functions are derived for certain strip models.     

The extended Kalman filter applied to a continuous culture model

The temperature-dependent endogenous metabolism model of single species continuous culture dynamics is utilized in the computer simulation of the Kalman filter state estimation technique. Parameters of the nonlinear equations can be “tracked” while variance in measured states can be damped. The state estimator is illustrated in, the context of conventional control strategies.