On criteria for evaluating models of absolute risk

Absolute risk is the probability that an individual who is free of a given disease at an initial age, a, will develop that disease in the subsequent interval (a, t]. Absolute risk is reduced by mortality from competing risks. Models of absolute risk that depend on covariates have been used to design intervention studies, to counsel patients regarding their risks of disease and to inform clinical decisions, such as whether or not to take tamoxifen to prevent breast cancer. Several general criteria have been used to evaluate models of absolute risk, including how well the model predicts the observed numbers of events in subsets of the population ("calibration"), and "discriminatory power," measured by the concordance statistic. In this paper we review some general criteria and develop specific loss function-based criteria for two applications, namely whether or not to screen a population to select subjects for further evaluation or treatment and whether or not to use a preventive intervention that has both beneficial and adverse effects. We find that high discriminatory power is much more crucial in the screening application than in the preventive intervention application. These examples indicate that the usefulness of a general criterion such as concordance depends on the application, and that using specific loss functions can lead to more appropriate assessments.     

基于遗传算法和支持向量机的乳杆菌发酵过程建模

由于生化反应过程的复杂性和高度非线性,多数简单的数学模型不能准确描述。该文基于Matlab软件,利用改进的支持向量机(υ-SVR)对植物乳酸杆菌发酵这一典型生化过程进行研究,应用遗传算法估计模型最优参数,建立植物乳杆菌的菌体密度预测模型。同时建立传统的logistic动力学模型以进行比较。结果表明,采用结合遗传算法的υ-SVR预测模型拟合误差小,皮尔森相关系数(R)更高,可以较好地预测乳酸杆菌的发酵过程,为其优化控制及放大提供依据。     

Does GARP really fail miserably? A response to Stockman et al. (2006)

Stockman et al. (2006 ) found that ecological niche models built using DesktopGARP ‘failed miserably’ to predict trapdoor spider (genus Promyrmekiaphila) distributions in California. This apparent failure of GARP (Genetic Algorithm for Rule‐Set Production) was actually a failure of the authors’ methods, that is, attempting to build ecological niche models using single data points. In this paper, we present a re‐analysis of their original data using standard methods with the data appropriately partitioned into training/testing subsets. This re‐evaluation generated accurate distributional predictions that we contrast with theirs. We address the consequences of model‐building using single data points and the need for a foundational understanding of the principles of ecological niche modelling.     

In vitro effects of water activity, temperature and solutes on the growth rate of P. italicum Wehmer and P. digitatum Sacc

AIMS: To evaluate the effect of water activity (a(w) 0.98-0.89, adjusted with glycerol, sorbitol, glucose, or NaCl) and temperature (5-25 degrees C) on the lag phase and radial growth rate (mm day(-1)) of the important citrus spoilage fungi, such as Penicillium italicum and Penicillium digitatum grown in potato dextrose agar (PDA) medium. To select, among models based on the use of different solutes, a model fitting accurately the growth of these species in relation to a(w) and temperature. METHODS AND RESULTS: Extensive data analyses showed for both Penicillium species a highly significant effect of a(w), temperature, solutes and their interactions on radial growth rate (P < 0.0001). Radial growth rate was inhibited and the lag phase (i.e. the time required for growth) lengthened as the a(w) of the medium decreased. NaCl appeared to causes the greatest stress on growth when compared with other nonionic solutes. Penicillium italicum stopped growing at 0.96 a(w) and P. digitatum at 0.93 a(w). Under the dry conditions where growth was observed, P. italicum grew faster than P. digitatum at low temperature and P. digitatum remained more active at ambient temperature. Multiple regression analysis applied to the square roots of the growth rates observed in the presence of each solute showed that both the 'glycerol model' and the 'sorbitol model' yielded a good prediction of P. italicum growth and the 'sorbitol model' gave an accurate fit for P. digitatum growth, offering high-quality prediction within the experimental limits described. CONCLUSIONS: Mathematical models describing and predicting, as a function of a(w) and temperature, the square root of the radial growth rate of the agents responsible for blue and green decays are important tools for understanding the behaviour of these fungi under natural conditions and for predicting citrus fruit spoilage. SIGNIFICANCE AND IMPACT OF THE STUDY: Implementation of these results should contribute towards a more rational control strategy against citrus spoilage fungi.     

Development and Application of a Predictive Model of Freshwater Fish Assemblage Composition to Evaluate River Health in Eastern Australia

Multivariate predictive models are widely used tools for assessment of aquatic ecosystem health and models have been successfully developed for the prediction and assessment of aquatic macroinvertebrates, diatoms, local stream habitat features and fish. We evaluated the ability of a modelling method based on the River InVertebrate Prediction and Classification System (RIVPACS) to accurately predict freshwater fish assemblage composition and assess aquatic ecosystem health in rivers and streams of south-eastern Queensland, Australia. The predictive model was developed, validated and tested in a region of comparatively high environmental variability due to the unpredictable nature of rainfall and river discharge. The model was concluded to provide sufficiently accurate and precise predictions of species composition and was sensitive enough to distinguish test sites impacted by several common types of human disturbance (particularly impacts associated with catchment land use and associated local riparian, in-stream habitat and water quality degradation). The total number of fish species available for prediction was low in comparison to similar applications of multivariate predictive models based on other indicator groups, yet the accuracy and precision of our model was comparable to outcomes from such studies. In addition, our model developed for sites sampled on one occasion and in one season only (winter), was able to accurately predict fish assemblage composition at sites sampled during other seasons and years, provided that they were not subject to unusually extreme environmental conditions (e.g. extended periods of low flow that restricted fish movement or resulted in habitat desiccation and local fish extinctions).     

River condition assessment may depend on the sub-sampling method: field live-sort versus laboratory sub-sampling of invertebrates for bioassessment

Aquatic macroinvertebrates are commonly used biological indicators for assessing the health of freshwater ecosystems. However, counting all the invertebrates in the large samples that are usually collected for rapid site assessment is time-consuming and costly. Therefore, sub-sampling is often done with fixed time or fixed count live-sorting in the field or with preserved material using sample splitters in the laboratory. We investigate the differences between site assessments provided when the two sub-sampling approaches (Live-sort and Lab-sort) were used in conjunction with predictive bioassessment models. The samples showed a method bias. The Live-sort sub-samples tended to have more large, conspicuous invertebrates and often fewer small and, or cryptic animals that were more likely to be found in Lab-sort samples where a microscope was used. The Live-sort method recovered 4–6 more taxa than Lab-sorting in spring, but not in autumn. The magnitude of the significant differences between Live-sort and Lab-sort predictive model outputs, observed to expected (O/E) taxa scores, for the same sites ranged from 0.12 to 0.53. These differences in the methods resulted in different assessments of some sites only and the number of sites that were assessed differently depended on the season, with spring samples showing most disparity. The samples may differ most in spring because many of the invertebrates are larger at that time (and thus are more conspicuous targets for live-sorters). The Live-sort data cannot be run through a predictive model created from Lab-sort data (and vice versa) because of the taxonomic differences in sub-sample composition and the sub-sampling methods must be standardized within and among studies if biological assessment is to provide valid comparisons of site condition. Assessments that rely on the Live-sorting method may indicate that sites are ‘less impaired’ in spring compared to autumn because more taxa are retrieved in spring when they are larger and more visible. Laboratory sub-sampling may return fewer taxa in spring, which may affect assessments relying on taxonomic richness.     

Evaluating prognostic accuracy of biomarkers under competing risk

To develop more targeted intervention strategies, an important research goal is to identify markers predictive of clinical events. A crucial step toward this goal is to characterize the clinical performance of a marker for predicting different types of events. In this article, we present statistical methods for evaluating the performance of a prognostic marker in predicting multiple competing events. To capture the potential time-varying predictive performance of the marker and incorporate competing risks, we define time- and cause-specific accuracy summaries by stratifying cases based on causes of failure. Such definition would allow one to evaluate the predictive accuracy of a marker for each type of event and compare its predictiveness across event types. Extending the nonparametric crude cause-specific receiver operating characteristics curve estimators by Saha and Heagerty (2010), we develop inference procedures for a range of cause-specific accuracy summaries. To estimate the accuracy measures and assess how covariates may affect the accuracy of a marker under the competing risk setting, we consider two forms of semiparametric models through the cause-specific hazard framework. These approaches enable a flexible modeling of the relationships between the marker and failure times for each cause, while efficiently accommodating additional covariates. We investigate the asymptotic property of the proposed accuracy estimators and demonstrate the finite sample performance of these estimators through simulation studies. The proposed procedures are illustrated with data from a prostate cancer prognostic study.     

Goodness-of-fit diagnostics for Bayesian hierarchical models

This article proposes methodology for assessing goodness of fit in Bayesian hierarchical models. The methodology is based on comparing values of pivotal discrepancy measures (PDMs), computed using parameter values drawn from the posterior distribution, to known reference distributions. Because the resulting diagnostics can be calculated from standard output of Markov chain Monte Carlo algorithms, their computational costs are minimal. Several simulation studies are provided, each of which suggests that diagnostics based on PDMs have higher statistical power than comparable posterior-predictive diagnostic checks in detecting model departures. The proposed methodology is illustrated in a clinical application; an application to discrete data is described in supplementary material.     

Postglacial colonization of Europe by the barbastelle bat: agreement between molecular data and past predictive modelling

The barbastelle (Barbastella barbastellus) is a rare forest bat with a wide distribution in Europe. Here, we combine results from the analysis of two mtDNA fragments with species distribution modelling to determine glacial refugia and postglacial colonization routes. We also investigated whether niche conservatism occurs in this species. Glacial refugia were identified in the three southern European peninsulas: Iberia, Italy and the Balkans. These latter two refugia played a major role in the postglacial colonization process, with their populations expanding to England and central Europe, respectively. Palaeo‐distribution models predicted that suitable climatic conditions existed in the inferred refugia during the last glacial maximum (LGM). Nevertheless, the overlap between the current and the LGM distributions was almost inexistent in Italy and in the Balkans, meaning that B. barbastellus populations were forced to shift range between glacial and interglacial periods, a process that probably caused some local extinctions. In contrast, Iberian populations showed a ‘refugia within refugium’ pattern, with two unconnected areas containing stable populations (populations that subsisted during both glacial and interglacial phases). Moreover, the match between LGM models and the refugial areas determined by molecular analysis supported the hypothesis of niche conservatism in B. barbastellus. We argue that geographic patterns of genetic structuring, altogether with the modelling results, indicate the existence of four management units for conservation: Morocco, Iberia, Italy and UK, and Balkans and central Europe. In addition, all countries sampled possessed unique gene pools, thus stressing the need for the conservation of local populations.