Explained variation and degrees of necessity and of sufficiency for competing risks survival data

In this contribution, the Schemper–Henderson measure of explained variation for survival outcomes is extended to accommodate competing events (CEs) in addition to events of interest. The extension is achieved by moving from the unconditional and conditional survival functions of the original measure to unconditional and conditional cumulative incidence functions, the latter obtained, for example, from Fine and Gray models. In the absence of CEs, the original measure is obtained as a special case. We define explained variation on the population level and provide two different types of estimates. Recently, the authors have achieved a multiplicative decomposition of explained variation into degrees of necessity and degrees of sufficiency. These measures are also extended to the case of competing risks survival data. A SAS macro and an R function are provided to facilitate application. Interesting empirical properties of the measures are explored on the population level and by an extensive simulation study. Advantages of the approach are exemplified by an Austrian study of breast cancer with a high proportion of CEs.     

Measuring Pairwise Agreement Among Many Observers. II. Some Improvements and Additions

Weighted kappa was defined as a measure of pairwise interobserver agreement for the case where the observers judging one subject are not necessarily the same as those judging another subject. In this paper improved formulas for the large sample variance of the weighted kappa statistic are derived, a new definition of interclass kappa coefficients is suggested, and the intraclass correlation coefficient is shown to be a special case of weighted kappa.     

Monitoring and Mining Animal Sounds in Visual Space

Monitoring animals by the sounds they produce is an important and challenging task, whether the application is outdoors in a natural habitat, or in the controlled environment of a laboratory setting. In the former case, the density and diversity of animal sounds can act as a measure of biodiversity. In the latter case, researchers often create control and treatment groups of animals, expose them to different interventions, and test for different outcomes. One possible manifestation of different outcomes may be changes in the bioacoustics of the animals. With such a plethora of important applications, there have been significant efforts to build bioacoustic classification tools. However, we argue that most current tools are severely limited. They often require the careful tuning of many parameters (and thus huge amounts of training data), are either too computationally expensive for deployment in resource-limited sensors, specialized for a very small group of species, or are simply not accurate enough to be useful. In this work we introduce a novel bioacoustic recognition/classification framework that mitigates or solves all of the above problems. We propose to classify animal sounds in the visual space, by treating the texture of their sonograms as an acoustic fingerprint using a recently introduced parameter-free texture measure as a distance measure. We further show that by searching for the most representative acoustic fingerprint, we can significantly outperform other techniques in terms of speed and accuracy.     

Properties and applications of the average interparticle distance

The first and second moment operators are used to define the origin invariant shape and size of a molecule or functional group, as well as expressions for the distance between two electrons and the distance between an electron and a nucleus. The measure of molecular size correlates quite well with an existing theoretical measure of molecular volume calculated from isodensity contours. Also, the measure of size is effective in predicting steric effects of substituents which have been measured experimentally. The electron-electron and electron-nuclear distances are related to components of the Hartree-Fock energy. The average distance between two-electrons can model the Coulomb energy quite well, especially in the case of localized molecular orbitals. The average distance between an electron and a nucleus is closely related to the electron-nuclear attraction energy of a molecule.     

Measuring pairwise agreement among many observers

Weighted kappa is defined as a measure of pairwise inter observer agreement. A weighted intra class kappa coefficient is proposed to measure agreement on a particular response category. An interclass kappa coefficient is proposed for each pair of response categories. Simple estimation procedures are presented for the case where the observers judging one subject are not necessarily the same as those judging another subject. Large sample standard errors are derived and a numerical example is given.     

喀斯特石漠化地区不同恢复和重建措施对土壤质量的影响

采取4种不同恢复和重建措施对典型喀斯特石漠化地区进行了13年的生态治理研究.结果表明,喀斯特严重石漠化区（对照）植物多样性极低,土壤肥力极差,生态环境极为恶劣;改为花椒种植或多种乔-灌-藤混交种植后,植物多样性明显增大,土壤质量得到一定程度恢复,生态系统朝着良性循环方向发展;采取封山育林措施后,林下植被层和群落多样性恢复得最快,林地土壤质量得到较快的恢复;保留较好的喀斯特次生林中植物多样性较高,土壤质量最好.采用合适的生物措施,辅以必要的工程措施,是促进严重喀斯特石漠化地区生态重建的有效途径之一.     

A Comparison of MCC and CEN Error Measures in Multi-Class Prediction

We show that the Confusion Entropy, a measure of performance in multiclass problems has a strong (monotone) relation with the multiclass generalization of a classical metric, the Matthews Correlation Coefficient. Analytical results are provided for the limit cases of general no-information (n-face dice rolling) of the binary classification. Computational evidence supports the claim in the general case.     

严重退化生态系统不同恢复和重建措施的植物多样性与地力差异研究

对花岗岩区土壤严重退化生态系统（对照）及４种不同恢复和重建措施建筑多样性和地力研究结果表明,花岗岩区红壤严重退化生态系统（对照）植物多样地性极低,土壤肥力极差,生态环境极为恶劣,改为杨梅果园（措施Ａ）或多树种混交（措施Ｂ）后,植物多样性明显增大,林地土壤肥力得到一定程度恢复,生态系统朝着良性循环方向发展,采取封山育林（措施Ｃ）方法,林下植被层和群落多样性恢复最快,林地土壤肥力亦得到较快的恢复,保留     

Dissimilarity for partially ranked data and its application to cover-abundance data

Cover-abundance estimates are commonly employed in phytosociological investigations to record the performance of species. Because the coded values are on an ordinal scale of measure, various authors have suggested that some transformation is necessary before such values can be used for classification and ordination. However, it is not clear that transformation is a sufficient treatment, and it would seem preferable to use ordinal data directly. In this paper we examine such direct use of partial rankings and show that several dissimilarity measures can be defined for this case without invoking any transformations. They include dissimilarity measures associated with various rank correlation measures and with distances between strings; all the measure are variant forms of Hausdorf's interset distance. Certain other kinds of data, such as those employing dominant and subdominant species and the dry-weight-rank estimation of biomass, are also on an ordinal scale and could be analysed using similar techniques.To illustrate the approach, a string dissimilarity measure is used to analyse a set of data from Slovakian grasslands which appear to reflect a simple gradient. The original data were recorded with 10 classes of performance and are analysed using hierarchical and nondeterministic, overlapping, classifications.     

Chemistry of proton abstraction by glycolytic enzymes (aldolase, isomerases and pyruvate kinase)

Intermediates have been synthesized that are rapidly utilized by triose phosphate isomerase, yeast aldolase and pyruvate kinase. In each case the compounds have the properties of an enol expected for a stepwise proton transfer mechanism. Apparently the apparatus required for doing this chemistry is sufficiently unique for a large measure of structural homology to have been imposed upon the enzymes of this class during evolution.     

Dendrograms and measuring functional diversity

Patterns and changes in functional diversity can inform about spatial and temporal variation in trait diversity, about the processes that drive assembly, and whether assemblages are likely to contain redundant species. We recently provided a new measure (termed FD) and detailed its advantages over previous ones. Since then an increasing amount of research effort has been directed towards both developing appropriate measures of functional diversity and critiquing previous ones, including FD. Podani and Schmera (2006) attempt to do both, though here we argue that they accomplish neither. First, they suggest that a particular distance measure and clustering method are appropriate. We suggest that this is not the case, and show that they may have little effect on quantitative patterns in FD. Second, they suggest that values of functional diversity must be insensitive to the number of functional traits used. We do not agree because we can envisage no relevant ecological question. Third, they observe that we originally defined an FD of zero for an empty assemblage, whereas it is more appropriate for single species assemblages to have FD of zero. We agree. Their solution, however, is to create a measure of functional diversity which violates set monotonicity. Our solution is a revised version of FD for which single species assemblages have FD=0, and which does not violate set monotonicity. In conclusion, we are confident that FD behaves appropriately and note that it remains the measure of functional diversity with greatest power to explain variation in ecosystem functioning.     

Characterization of structure and properties of bone by spectral measure method

Novel mathematical method called spectral measure method (SMM) is developed for characterization of bone structure and indirect estimation of bone properties. The spectral measure method is based on an inverse homogenization technique which allows to derive information about the structure of composite material from measured effective electric or viscoelastic properties. The mechanical properties and ability to withstand fracture depend on the structural organization of bone as a hierarchical composite. Information about the bone structural parameters is contained in the spectral measure in the Stieltjes integral representation of the effective properties. The method is based on constructing the spectral measure either by calculating it directly from micro-CT images or using measurements of electric or viscoelastic properties over a frequency range. In the present paper, we generalize the Stieltjes representation to the viscoelastic case and show how bone microstructure, in particular, bone volume or porosity, can be characterized by the spectral function calculated using measurements of complex permittivity or viscoelastic modulus. For validation purposes, we numerically simulated measured data using micro-CT images of cancellous bone. Recovered values of bone porosity are in excellent agreement with true porosity estimated from the micro-CT images. We also discuss another application of this method, which allows to estimate properties difficult to measure directly. The spectral measure method based on the derived Stieltjes representation for viscoelastic composites, has a potential for non-invasive characterization of bone structure using electric or mechanical measurements. The method is applicable to sea ice, porous rock, and other composite materials.     

On the evolution of virulence and the relationship between various measures of mortality

Smallpox causes roughly 20% mortality whereas chickenpox causes less than 0.1%. Most 'verbal' (i.e. non-mathematical) discussions using a mortality definition of virulence would therefore label smallpox as more virulent. Indeed, the virulence of many diseases is measured using such case mortalities, chi, or related measures such as expected host lifespan, T, or lethal dose, LD(x). But chi, T and LD(x) are only indirectly related to parasite-induced instantaneous mortality rate, alpha, which is the mortality measure used in much of the theory developed to explain virulence evolution. Here I point out that relatively deadly pathogens can actually have lower values of alpha than benign pathogens, demonstrating that alpha does not, by itself, reflect the extent to which a parasite causes host mortality. I present mathematical relationships between alpha and chi, T and LD(x), and use these to demonstrate that predictions about virulence evolution can be qualitatively altered depending upon which measure is used as the definition of virulence. Two simple examples are presented to illustrate this point, one of which demonstrates that the well-cited prediction that virulence should evolve to be higher when disease-independent host mortality increases need not hold. This prediction has been made in terms of parasite-induced instantaneous mortality, alpha, but if virulence is measured using case mortality (or T or LD(x)) then this prediction can easily be reversed. Theoretical and empirical researchers must use compatible mortality measures before a productive exchange between the two can take place, and it is suggested that case mortality (or lethal dose) is best suited as a single (mortality) measure of parasite virulence.     

Diffusion from gel in brain: Modelisation and identification

A mathematical model is proposed for describing the mechanism of diffusion from gel (Tissucol) into the extracellular space. After diffusion of the antibiotic in one dimension, the gradient concentration was determined with microvoltametric electrodes. These microelectrodes measure the free diffusible form of electroactive antibiotics in the extracellular brain space. The aim of this study was to find simultaneously the coefficient of diffusion and extraction of some antibiotics (in our case the Fotemustin) using the Alienor Algorithm. These coefficients are useful for predicting the concentration gradient into abscesses, fibrin, etc.     

Measurable prediction for the single patient and the results of large double blind controlled randomized trials

BACKGROUND: It has been shown that the clinical state of one patient can be represented by known measured variables of interest, each of which then form the element of a fuzzy set as point in the unit hypercube. We hypothesized that precise comparison of a single patient with the average patient of a large double blind controlled randomized study is possible using fuzzy theory. METHODS/PRINCIPLE FINDINGS: The sets as points unit hypercube geometry allows fuzzy subsethood to define in measures of fuzzy cardinality different conditions, similarity and comparison between fuzzy sets. A fuzzy measure of prediction is defined from fuzzy measures of similarity and comparison. It is a measure of the degree to which fuzzy set A is similar to fuzzy set B when different conditions are taken into account and removed from the comparison. When represented as a fuzzy set as point in the unit hypercube, a clinical patient can be compared to an average patient of a large group study in a precise manner. This comparison is expressed by the fuzzy prediction measure. This measure in itself is not a probability. Once thus precisely matched to the average patient of a large group study, risk reduction is calculated by multiplying the measured similarity of the clinical patient to the risk of the average trial patient. CONCLUSION/SIGNIFICANCE: Otherwise not precisely translatable to the single case, the result of group statistics can be applied to the single case through the use of fuzzy subsethood and measured in fuzzy cardinality. This measure is an alternative to a Bayesian or other probability based statistical approach.     

First and second moments and the mean hamming distance in a stochastic replication-mutation model for biological macromolecules

In this work first and second moments for a many species Moran model are calculated. The model describes by means of a time-continuous birth- and death process the evolution of an ensemble of N macromolecules out of n possible species. The molecules may replicate (correct or erroneous, in the latter case producing mutants) and may undergo elimination. Replication and elimination will be coupled in order to keep population size constant. In the case of arbitrary replication rates an expansion of the moments in powers of 1/N is found. For equal replication rates exact calculation of the moments is possible. In the case of a v-cube model (binary macromolecules) the second moments may be used to find a simple expression for the mean Hamming distance in the system. This quantity provides a measure for the localization of the ensemble.Supported by Stiftung Volkswagenwerk     

Predictive influence in the accelerated failure time model

We develop case deletion diagnostics for prediction of future observations in the accelerated failure time model. We view prediction to be an important inferential goal in a survival analysis and thus it is important to identify whether particular observations may be influencing the quality of predictions. We use the Kullback-Leibler divergence as a measure of the discrepancy between the estimated probability distributions for the full and the case-deleted samples. In particular, we focus on the effect of case deletion on estimated survival curves but where we regard the survival curve estimate as a vehicle for prediction. We also develop a diagnostic for assessing the effect of case deletion on inferences for the median time to failure. The estimated median can be used with both predictive and estimative purposes in mind. We also discuss the relationship between our suggested measures and the corresponding Cook distance measure, which was designed with the goal of assessing estimative influence. Several applications of the proposed diagnostics are presented.     

A versatile approach to determine instantaneous co-activation: Development,implementation and comparison to existing measures

Abstract

An adaptable method of computing muscle co-activity is presented. Instantaneous muscle activities from multiple muscles are reduced into commonality and activity level dimensions. Both dimensions are weighted independently and combined into a co-activation measure, Φ. Myoelectric data from relaxed and braced simulated rear vehicle impacts were used to compare Φ to two existing co-activity measures in muscle pair and multi-muscle cases, Φ showed greater sensitivity in the muscle pair case and could better discriminate the relaxed and braced conditions in the multi-muscle case than previous measures. The flexibility of Φ allowed tailoring to reflect the current purpose.     

The how and why of branch support and partitioned branch support, with a new index to assess partition incongruence

An introduction and step‐by‐step guide to the calculation of branch support (BS) and partitioned branch support (PBS) is provided, along with a new summary measure of conflict among data partitions, the partition congruence index (PCI). Patterns of PCI vs. BS are compared for two data matrices from butterflies. PCI is a close mirror of BS unless BY is relatively low and there is a lot of conflict among data partitions, in which case PCI becomes negative. Some theoretical concerns relating to PBS are noted. © The Willi Hennig Society 2006.