Editorial

2 pages, 150 KiB

Open AccessEditorial

Applications of Information Theory to Epidemiology

by Gareth Hughes

Entropy 2020, 22(12), 1392; https://doi.org/10.3390/e22121392 - 09 Dec 2020

Cited by 1 | Viewed by 1466

This Special Issue of Entropy represents the first wide-ranging overview of epidemiological applications since the 2012 publication of Applications of Information Theory to Epidemiology [...] Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

Research

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20 pages, 2334 KiB

Open AccessArticle

Characterization of Pathogen Airborne Inoculum Density by Information Theoretic Analysis of Spore Trap Time Series Data

by Robin A. Choudhury and Neil McRoberts

Entropy 2020, 22(12), 1343; https://doi.org/10.3390/e22121343 - 27 Nov 2020

Cited by 3 | Viewed by 1960

Abstract

In a previous study, air sampling using vortex air samplers combined with species-specific amplification of pathogen DNA was carried out over two years in four or five locations in the Salinas Valley of California. The resulting time series data for the abundance of [...] Read more.

In a previous study, air sampling using vortex air samplers combined with species-specific amplification of pathogen DNA was carried out over two years in four or five locations in the Salinas Valley of California. The resulting time series data for the abundance of pathogen DNA trapped per day displayed complex dynamics with features of both deterministic (chaotic) and stochastic uncertainty. Methods of nonlinear time series analysis developed for the reconstruction of low dimensional attractors provided new insights into the complexity of pathogen abundance data. In particular, the analyses suggested that the length of time series data that it is practical or cost-effective to collect may limit the ability to definitively classify the uncertainty in the data. Over the two years of the study, five location/year combinations were classified as having stochastic linear dynamics and four were not. Calculation of entropy values for either the number of pathogen DNA copies or for a binary string indicating whether the pathogen abundance data were increasing revealed (1) some robust differences in the dynamics between seasons that were not obvious in the time series data themselves and (2) that the series were almost all at their theoretical maximum entropy value when considered from the simple perspective of whether instantaneous change along the sequence was positive. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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35 pages, 4765 KiB

Open AccessArticle

Canine Olfactory Detection of a Non-Systemic Phytobacterial Citrus Pathogen of International Quarantine Significance

by Timothy Gottwald, Gavin Poole, Earl Taylor, Weiqi Luo, Drew Posny, Scott Adkins, William Schneider and Neil McRoberts

Entropy 2020, 22(11), 1269; https://doi.org/10.3390/e22111269 - 09 Nov 2020

Cited by 6 | Viewed by 3052

Abstract

For millennia humans have benefitted from application of the acute canine sense of smell to hunt, track and find targets of importance. In this report, canines were evaluated for their ability to detect the severe exotic phytobacterial arboreal pathogen Xanthomonas citri pv. citri [...] Read more.

For millennia humans have benefitted from application of the acute canine sense of smell to hunt, track and find targets of importance. In this report, canines were evaluated for their ability to detect the severe exotic phytobacterial arboreal pathogen Xanthomonas citri pv. citri (Xcc), which is the causal agent of Asiatic citrus canker (Acc). Since Xcc causes only local lesions, infections are non-systemic, limiting the use of serological and molecular diagnostic tools for field-level detection. This necessitates reliance on human visual surveys for Acc symptoms, which is highly inefficient at low disease incidence, and thus for early detection. In simulated orchards the overall combined performance metrics for a pair of canines were 0.9856, 0.9974, 0.9257 and 0.9970, for sensitivity, specificity, precision, and accuracy, respectively, with 1–2 s/tree detection time. Detection of trace Xcc infections on commercial packinghouse fruit resulted in 0.7313, 0.9947, 0.8750, and 0.9821 for the same performance metrics across a range of cartons with 0–10% Xcc-infected fruit despite the noisy, hot and potentially distracting environment. In orchards, the sensitivity of canines increased with lesion incidence, whereas the specificity and overall accuracy was >0.99 across all incidence levels; i.e., false positive rates were uniformly low. Canines also alerted to a range of 1–12-week-old infections with equal accuracy. When trained to either Xcc-infected trees or Xcc axenic cultures, canines inherently detected the homologous and heterologous targets, suggesting they can detect Xcc directly rather than only volatiles produced by the host following infection. Canines were able to detect the Xcc scent signature at very low concentrations (10,000× less than 1 bacterial cell per sample), which implies that the scent signature is composed of bacterial cell volatile organic compound constituents or exudates that occur at concentrations many fold that of the bacterial cells. The results imply that canines can be trained as viable early detectors of Xcc and deployed across citrus orchards, packinghouses, and nurseries. Full article

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17 pages, 1529 KiB

Open AccessArticle

Analysis of HIV/AIDS Epidemic and Socioeconomic Factors in Sub-Saharan Africa

by Shuman Sun, Zhiming Li, Huiguo Zhang, Haijun Jiang and Xijian Hu

Entropy 2020, 22(11), 1230; https://doi.org/10.3390/e22111230 - 29 Oct 2020

Cited by 5 | Viewed by 2184

Abstract

Sub-Saharan Africa has been the epicenter of the outbreak since the spread of acquired immunodeficiency syndrome (AIDS) began to be prevalent. This article proposes several regression models to investigate the relationships between the HIV/AIDS epidemic and socioeconomic factors (the gross domestic product per [...] Read more.

Sub-Saharan Africa has been the epicenter of the outbreak since the spread of acquired immunodeficiency syndrome (AIDS) began to be prevalent. This article proposes several regression models to investigate the relationships between the HIV/AIDS epidemic and socioeconomic factors (the gross domestic product per capita, and population density) in ten countries of Sub-Saharan Africa, for 2011–2016. The maximum likelihood method was used to estimate the unknown parameters of these models along with the Newton–Raphson procedure and Fisher scoring algorithm. Comparing these regression models, there exist significant spatiotemporal non-stationarity and auto-correlations between the HIV/AIDS epidemic and two socioeconomic factors. Based on the empirical results, we suggest that the geographically and temporally weighted Poisson autoregressive (GTWPAR) model is more suitable than other models, and has the better fitting results. Full article

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17 pages, 8866 KiB

Open AccessArticle

Mutual Information as a Performance Measure for Binary Predictors Characterized by Both ROC Curve and PROC Curve Analysis

by Gareth Hughes, Jennifer Kopetzky and Neil McRoberts

Entropy 2020, 22(9), 938; https://doi.org/10.3390/e22090938 - 26 Aug 2020

Cited by 6 | Viewed by 2654

Abstract

The predictive receiver operating characteristic (PROC) curve differs from the more well-known receiver operating characteristic (ROC) curve in that it provides a basis for the evaluation of binary diagnostic tests using metrics defined conditionally on the outcome of the test rather than metrics [...] Read more.

The predictive receiver operating characteristic (PROC) curve differs from the more well-known receiver operating characteristic (ROC) curve in that it provides a basis for the evaluation of binary diagnostic tests using metrics defined conditionally on the outcome of the test rather than metrics defined conditionally on the actual disease status. Application of PROC curve analysis may be hindered by the complex graphical patterns that are sometimes generated. Here we present an information theoretic analysis that allows concurrent evaluation of PROC curves and ROC curves together in a simple graphical format. The analysis is based on the observation that mutual information may be viewed both as a function of ROC curve summary statistics (sensitivity and specificity) and prevalence, and as a function of predictive values and prevalence. Mutual information calculated from a 2 × 2 prediction-realization table for a specified risk score threshold on an ROC curve is the same as the mutual information calculated at the same risk score threshold on a corresponding PROC curve. Thus, for a given value of prevalence, the risk score threshold that maximizes mutual information is the same on both the ROC curve and the corresponding PROC curve. Phytopathologists and clinicians who have previously relied solely on ROC curve summary statistics when formulating risk thresholds for application in practical agricultural or clinical decision-making contexts are thus presented with a methodology that brings predictive values within the scope of that formulation. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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11 pages, 1281 KiB

Open AccessArticle

Establishment and Characterization of an Empirical Biomarker SS/PV-ROC Plot Using Results of the UBC^® Rapid Test in Bladder Cancer

by Peter Oehr and Thorsten Ecke

Entropy 2020, 22(7), 729; https://doi.org/10.3390/e22070729 - 30 Jun 2020

Cited by 4 | Viewed by 2595

Abstract

Background: This investigation included both a study of potential non-invasive diagnostic approaches for the bladder cancer biomarker UBC^® Rapid Test and a study including comparative methods about sensitivity–specificity characteristic (SS-ROC) and predictive receiver operating characteristic (PV-ROC) curves that used bladder cancer as [...] Read more.

Background: This investigation included both a study of potential non-invasive diagnostic approaches for the bladder cancer biomarker UBC^® Rapid Test and a study including comparative methods about sensitivity–specificity characteristic (SS-ROC) and predictive receiver operating characteristic (PV-ROC) curves that used bladder cancer as a useful example. Methods: The study included 289 urine samples from patients with tumors of the urinary bladder, patients with non-evidence of disease (NED) and healthy controls. The UBC^® Rapid Test is a qualitative point of care assay. Using a photometric reader, quantitative data can also be obtained. Data for pairs of sensitivity/specificity as well as positive/negative predictive values were created by variation of threshold values for the whole patient cohort, as well as for the tumor-free control group. Based on these data, sensitivity–specificity and predictive value threshold distribution curves were constructed and transformed into SS-ROC and PV-ROC curves, which were included in a single SS/PV-ROC plot. Results: The curves revealed TPP-asymmetric improper curves which cross the diagonal from above. Evaluation of the PV-ROC curve showed that two or more distinct positive predictive values (PPV) can correspond to the same value of a negative predictive value (NPV) and vice versa, indicating a complexity in PV-ROC curves which did not exist in SS-ROC curves. In contrast to the SS-ROC curve, the PV-ROC curve had neither an area under the curve (AUC) nor a range from 0% to 100%. Sensitivity of the qualitative assay was 58.5% and specificity 88.2%, PPV was 75.6% and NPV 77.3%, at a threshold value of approximately 12.5 µg/L. Conclusions: The SS/PV-ROC plot is a new diagnostic approach which can be used for direct judgement of gain and loss of predictive values, sensitivity and specificity according to varied threshold value changes, enabling characterization, comparison and evaluation of qualitative and quantitative bioassays. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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11 pages, 1949 KiB

Open AccessArticle

On the Binormal Predictive Receiver Operating Characteristic Curve for the Joint Assessment of Positive and Negative Predictive Values

by Gareth Hughes

Entropy 2020, 22(6), 593; https://doi.org/10.3390/e22060593 - 26 May 2020

Cited by 5 | Viewed by 2416

Abstract

The predictive receiver operating characteristic (PROC) curve is a diagrammatic format with application in the statistical evaluation of probabilistic disease forecasts. The PROC curve differs from the more well-known receiver operating characteristic (ROC) curve in that it provides a basis for evaluation using [...] Read more.

The predictive receiver operating characteristic (PROC) curve is a diagrammatic format with application in the statistical evaluation of probabilistic disease forecasts. The PROC curve differs from the more well-known receiver operating characteristic (ROC) curve in that it provides a basis for evaluation using metrics defined conditionally on the outcome of the forecast rather than metrics defined conditionally on the actual disease status. Starting from the binormal ROC curve formulation, an overview of some previously published binormal PROC curves is presented in order to place the PROC curve in the context of other methods used in statistical evaluation of probabilistic disease forecasts based on the analysis of predictive values; in particular, the index of separation (PSEP) and the leaf plot. An information theoretic perspective on evaluation is also outlined. Five straightforward recommendations are made with a view to aiding understanding and interpretation of the sometimes-complex patterns generated by PROC curve analysis. The PROC curve and related analyses augment the perspective provided by traditional ROC curve analysis. Here, the binormal ROC model provides the exemplar for investigation of the PROC curve, but potential application extends to analysis based on other distributional models as well as to empirical analysis. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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31 pages, 5091 KiB

Open AccessArticle

On the Use of Entropy Issues to Evaluate and Control the Transients in Some Epidemic Models

by Manuel De la Sen, Raul Nistal, Asier Ibeas and Aitor J. Garrido

Entropy 2020, 22(5), 534; https://doi.org/10.3390/e22050534 - 09 May 2020

Cited by 9 | Viewed by 2334

Abstract

This paper studies the representation of a general epidemic model by means of a first-order differential equation with a time-varying log-normal type coefficient. Then the generalization of the first-order differential system to epidemic models with more subpopulations is focused on by introducing the [...] Read more.

This paper studies the representation of a general epidemic model by means of a first-order differential equation with a time-varying log-normal type coefficient. Then the generalization of the first-order differential system to epidemic models with more subpopulations is focused on by introducing the inter-subpopulations dynamics couplings and the control interventions information through the mentioned time-varying coefficient which drives the basic differential equation model. It is considered a relevant tool the control intervention of the infection along its transient to fight more efficiently against a potential initial exploding transmission. The study is based on the fact that the disease-free and endemic equilibrium points and their stability properties depend on the concrete parameterization while they admit a certain design monitoring by the choice of the control and treatment gains and the use of feedback information in the corresponding control interventions. Therefore, special attention is paid to the evolution transients of the infection curve, rather than to the equilibrium points, in terms of the time instants of its first relative maximum towards its previous inflection time instant. Such relevant time instants are evaluated via the calculation of an “ad hoc” Shannon’s entropy. Analytical and numerical examples are included in the study in order to evaluate the study and its conclusions. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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16 pages, 3140 KiB

Open AccessArticle

Information Graphs Incorporating Predictive Values of Disease Forecasts

by Gareth Hughes, Jennifer Reed and Neil McRoberts

Entropy 2020, 22(3), 361; https://doi.org/10.3390/e22030361 - 20 Mar 2020

Cited by 4 | Viewed by 2800

Abstract

Diagrammatic formats are useful for summarizing the processes of evaluation and comparison of forecasts in plant pathology and other disciplines where decisions about interventions for the purpose of disease management are often based on a proxy risk variable. We describe a new diagrammatic [...] Read more.

Diagrammatic formats are useful for summarizing the processes of evaluation and comparison of forecasts in plant pathology and other disciplines where decisions about interventions for the purpose of disease management are often based on a proxy risk variable. We describe a new diagrammatic format for disease forecasts with two categories of actual status and two categories of forecast. The format displays relative entropies, functions of the predictive values that characterize expected information provided by disease forecasts. The new format arises from a consideration of earlier formats with underlying information properties that were previously unexploited. The new diagrammatic format requires no additional data for calculation beyond those used for the calculation of a receiver operating characteristic (ROC) curve. While an ROC curve characterizes a forecast in terms of sensitivity and specificity, the new format described here characterizes a forecast in terms of relative entropies based on predictive values. Thus it is complementary to ROC methodology in its application to the evaluation and comparison of forecasts. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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9 pages, 1085 KiB

Open AccessArticle

An Information-Theoretic Measure for Balance Assessment in Comparative Clinical Studies

by Jarrod E. Dalton, William A. Benish and Nikolas I. Krieger

Entropy 2020, 22(2), 218; https://doi.org/10.3390/e22020218 - 15 Feb 2020

Cited by 3 | Viewed by 2322

Abstract

Limitations of statistics currently used to assess balance in observation samples include their insensitivity to shape discrepancies and their dependence upon sample size. The Jensen–Shannon divergence (JSD) is an alternative approach to quantifying the lack of balance among treatment groups that does not [...] Read more.

Limitations of statistics currently used to assess balance in observation samples include their insensitivity to shape discrepancies and their dependence upon sample size. The Jensen–Shannon divergence (JSD) is an alternative approach to quantifying the lack of balance among treatment groups that does not have these limitations. The JSD is an information-theoretic statistic derived from relative entropy, with three specific advantages relative to using standardized difference scores. First, it is applicable to cases in which the covariate is categorical or continuous. Second, it generalizes to studies in which there are more than two exposure or treatment groups. Third, it is decomposable, allowing for the identification of specific covariate values, treatment groups or combinations thereof that are responsible for any observed imbalance. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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32 pages, 937 KiB

Open AccessArticle

Dynamics of Ebola Disease in the Framework of Different Fractional Derivatives

by Khan Muhammad Altaf and Abdon Atangana

Entropy 2019, 21(3), 303; https://doi.org/10.3390/e21030303 - 21 Mar 2019

Cited by 73 | Viewed by 4479

Abstract

In recent years the world has witnessed the arrival of deadly infectious diseases that have taken many lives across the globe. To fight back these diseases or control their spread, mankind relies on modeling and medicine to control, cure, and predict the behavior [...] Read more.

In recent years the world has witnessed the arrival of deadly infectious diseases that have taken many lives across the globe. To fight back these diseases or control their spread, mankind relies on modeling and medicine to control, cure, and predict the behavior of such problems. In the case of Ebola, we observe spread that follows a fading memory process and also shows crossover behavior. Therefore, to capture this kind of spread one needs to use differential operators that posses crossover properties and fading memory. We analyze the Ebola disease model by considering three differential operators, that is the Caputo, Caputo–Fabrizio, and the Atangana–Baleanu operators. We present brief detail and some mathematical analysis for each operator applied to the Ebola model. We present a numerical approach for the solution of each operator. Further, numerical results for each operator with various values of the fractional order parameter

α

are presented. A comparison of the suggested operators on the Ebola disease model in the form of graphics is presented. We show that by decreasing the value of the fractional order parameter

α

, the number of individuals infected by Ebola decreases efficiently and conclude that for disease elimination, the Atangana–Baleanu operator is more useful than the other two. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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Review

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20 pages, 1424 KiB

Open AccessReview

A Review of the Application of Information Theory to Clinical Diagnostic Testing

by William A. Benish

Entropy 2020, 22(1), 97; https://doi.org/10.3390/e22010097 - 14 Jan 2020

Cited by 14 | Viewed by 4266

Abstract

The fundamental information theory functions of entropy, relative entropy, and mutual information are directly applicable to clinical diagnostic testing. This is a consequence of the fact that an individual’s disease state and diagnostic test result are random variables. In this paper, we review [...] Read more.

The fundamental information theory functions of entropy, relative entropy, and mutual information are directly applicable to clinical diagnostic testing. This is a consequence of the fact that an individual’s disease state and diagnostic test result are random variables. In this paper, we review the application of information theory to the quantification of diagnostic uncertainty, diagnostic information, and diagnostic test performance. An advantage of information theory functions over more established test performance measures is that they can be used when multiple disease states are under consideration as well as when the diagnostic test can yield multiple or continuous results. Since more than one diagnostic test is often required to help determine a patient’s disease state, we also discuss the application of the theory to situations in which more than one diagnostic test is used. The total diagnostic information provided by two or more tests can be partitioned into meaningful components. Full article

(This article belongs to the Special Issue Applications of Information Theory to Epidemiology)

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