The logistic regression model including interactions between the factor variables demonstrated for the detection of E. coli O157.H7 in artificially contaminated minced beef

Logistic regression is a powerful tool to analyse data sets with a dichotomous response variable. However, in most situations it is used as a model without interactions between the factor variables. This is done either by presumption or to avoid difficulties in the interpretation of the statistical results. In this article first the model of simple logistic regression without interactions is introduced followed by the expanded model with pairwise interactions between the factors. The application of both models is demonstrated at the present data set concerning the detection of E. coli O157.H7 in artificially contaminated minced beef. The influencing variables are the factors enrichment time, inoculation density, enrichment broth, subculturing medium, and state of samples (fresh vs. deep frozen). The statistical reanalysis displayed strongly differing results emphasizing the importance of interactions in logistic regression models. In particular, the odds ratio for E. coli detection dependant from the enrichment time (24 h vs. 6 h) (OR = 0.41) was strongly overestimated without simultaneous attention of the E. coli inoculation density (OR approximately equal to 0.2 to 0.02). In this context the possible interpretation of the interaction is discussed.     

A generalized Michaelis-Menten equation for the analysis of growth

The functional form W = (W0Kc + Wf t(c)) /(Kc + t(c)), where W is body size at age t, W0 and Wf are the zero- and infinite-time values of W, respectively, and K and c are constants, is derived. This new generalized Michaelis-Menten-type equation provides a flexible model for animal growth capable of describing sigmoidal and diminishing returns behavior. The parameters of the nonlinear model are open to biological interpretation and can be used to calculate reliable estimates of growth traits, such as maximum or average postnatal growth rates. To evaluate the new model, the derived equation and standard growth functions such as the Gompertz and Richards were used to fit 83 growth data sets of different animal species (fish, mice, hamsters, rats, guinea pigs, rabbits, cats, dogs, broilers, turkeys, sheep, goats, pigs, horses, and cattle) with a large range in body size. A comparative study was carried out based on mathematical, statistical, and biological characteristics of the models. The statistical goodness-of-fit achieved with the new model was similar to that of Richards, and both were slightly superior to the Gompertz. The new model differed from the others with respect to some of the estimated growth traits, but there were highly significant correlation coefficients between estimates obtained with the different models, and the ranking of animals based on growth parameters computed with the new function agreed with the rankings computed by the other models. Therefore, the new model, with its variable inflection point, was able to adequately describe growth in a wide variety of animals, to fit a range of data showing sigmoidal growth patterns, and to provide satisfactory estimates of traits for quantifying the growth characteristics of each type of animal.     

Use of structured antedependence models for the genetic analysis of growth curves

Growth curve analysis is an important issue for many agricultural and laboratory species, for both phenotypic and genetic studies. The aim of this paper is to present the use of a novel statistical approach, namely the structured antedependence (SAD) models, to deal with this issue. The basic idea of these models is that an observation at time t can be explained by the previous observations. These models are especially appropriate to deal with cumulative traits such as growth, as BW at age t clearly depends on BW measures at ages (t -1), (t -2), etc. These models were applied on an INRA experimental Charolais herd data set. The data comprised BW records for 560 cows born over an 11-yr period (from 1988 to 1998) from 60 sires and 369 dams. The proposed SAD models were compared with the well-known random regression (RR) models that are already widely used in various areas of longitudinal data analysis. It was found that the SAD models fit the growth process better with far fewer parameters than the RR models (9 instead of 16 covariance parameters for the phenotypic analysis, and 14 instead of 21 for the genetic analysis). Despite this smaller number of covariance parameters, the likelihood value was found to be much higher with the SAD vs. the RR models, with a difference of 262.9 for the phenotypic analysis with a quartic polynomial for the RR and 751.5 for the genetic analysis with a cubic polynomial for both the genetic and environmental parts of the RR model. The SAD models also proved to be better able to interpolate missing values. Heritability, genetic, and environmental correlation coefficients were estimated for weights from birth to adulthood. The structured antedependence models proved, in this study, to be very appropriate to model growth data in a parsimonious and flexible way.     

Alternative approaches to predicting methane emissions from dairy cows

Previous attempts to apply statistical models, which correlate nutrient intake with methane production, have been of limited value where predictions are obtained for nutrient intakes and diet types outside those used in model construction. Dynamic mechanistic models have proved more suitable for extrapolation, but they remain computationally expensive and are not applied easily in practical situations. The first objective of this research focused on employing conventional techniques to generate statistical models of methane production appropriate to United Kingdom dairy systems. The second objective was to evaluate these models and a model published previously using both United Kingdom and North American data sets. Thirdly, nonlinear models were considered as alternatives to the conventional linear regressions. The United Kingdom calorimetry data used to construct the linear models also were used to develop the three nonlinear alternatives that were all of modified Mitscherlich (monomolecular) form. Of the linear models tested, an equation from the literature proved most reliable across the full range of evaluation data (root mean square prediction error = 21.3%). However, the Mitscherlich models demonstrated the greatest degree of adaptability across diet types and intake level. The most successful model for simulating the independent data was a modified Mitscherlich equation with the steepness parameter set to represent dietary starch-to-ADF ratio (root mean square prediction error = 20.6%). However, when such data were unavailable, simpler Mitscherlich forms relating dry matter or metabolizable energy intake to methane production remained better alternatives relative to their linear counterparts.     

Withdrawal time estimation of veterinary drugs: extending the range of statistical methods

In order to use a drug in a food producing animal, evidence has to be provided that after a certain withdrawal time, drug residues in tissues, such as muscle meat, fat, liver, kidney etc., are below a given maximum residue limit (MRL), for a majority of animals. Several statistical methods, both regression based and nonparametric based methods, have been proposed, each relying on different sets of assumptions, which may or may not hold for the specific data situation. The purpose of this paper is to enrich the range of methods, i.e. to provide approaches for situations where current methods are inappropriate. Bayesian methods, using Markov chain Monte Carlo, are proposed to derive inference on the parameters of interest.     

Remote sensing applications for monitoring rangeland vegetation

Remote sensing techniques hold considerable promise for the inventory and monitoring of natural resources on range‐lands. A significant lack of information concerning basic spectral characteristics of range vegetation and soils has resulted in a lack of rangeland applications. To use remote sensing technology for measuring vegetation and soil changes on rangelands, certain things must be accomplished. First, the spectral characteristics of scene components must be determined for the various vegetation types. Second, determinations must be made of the appropriate kinds of remotely sensed data that should be used for the task. And finally, procedures must be outlined for acquiring the remotely sensed data that will measure changes in the range vegetation and soils. The interpretation of the remotely sensed data for such monitoring purposes will depend upon the use of various vegetation indices, pixel modelling and appropriate statistical tests. The parameters of interest for range condition must be identified and a means of measuring them either directly or indirectly developed. The paper describes an approach to the use of remotely sensed data to accomplish rangeland monitoring.     

An economic comparison of several models fitted to nutritional response data

Nutritional requirements are typically estimated based on feeding trials with animals or birds offered several amounts of the critical nutrient(s). A nutrient response function is then fitted to data from the feeding trials. Modern computer techniques allow for a variety of functional forms to be used as nutrient response functions. However, the performance of these models is almost undistinguishable from a purely statistical perspective. This paper approaches the issue of determining nutrient requirements from an economic prospective. Crude protein amounts that would maximize profits were calculated for combinations of corn, soybean meal, and live broilers prices using several nutrient response models fitted to technical data from a trial with several balanced CP amounts fed to broiler chickens. Under certain combinations of input prices, differences between the models were between 1.5 and 3.0% CP. No model consistently predicted the greatest or least CP amounts or net profits, emphasizing that the (tangential) slopes of the models change at different rates over the range of nutrient (CP) amounts studied. Models providing adequate statistical fits to research data do not necessarily provide functions that are clearly most appropriate for maximizing producer profits.     

Estimation of genetic parameters for hip dysplasia in Czech Labrador Retrievers

The objective of this study was to estimate the genetic parameters, genetic trends and breeding values using linear model (LM) and threshold model (TM) for the development of hip dysplasia (HD) in Labrador Retrievers in the Czech Republic (n = 3151). The right and left hip joints were evaluated separately using the Fédération Cynologique Internationale scoring system. Four linear and four TMs were tested for the correct estimation of genetic parameters. All the tested models utilized fixed effects of sex, assessor, year of birth, regression of age at evaluation, random direct genetic effects and the effect of the animals' permanent environments. The models differed in the inclusion of the following effects: fixed effects of regression of inbreeding coefficient, random maternal effect and random effect of the maternal permanent environment. Compared to the TM, the LM provided lower coefficients of direct (0.25-0.29 versus 0.26-0.35) and maternal heritability (0.01-0.02 versus 0.03-0.05), repeatability (0.76-0.77 versus 0.78-0.83) and of the correlation between direct and maternal effects (-0.55 to -0.21 versus -0.80 to -0.27). In the tested models, no statistical significance was found for fixed regression of inbreeding coefficients or for the random effect of the permanent maternal environment. In spite of the similarity of the LM and TM results, the TM is recommended as the more suitable model for estimating genetic parameters and subsequent breeding values for HD in Labrador Retrievers in the Czech Republic.     

Constructing covariance functions for random regression models for growth in Gelbvieh beef cattle

Genetic parameters for a random regression model of growth in Gelbvieh beef cattle were constructed using existing estimates. Information for variances along ages was provided by parameters used for routine Gelbvieh multiple-trait evaluation, and information on correlations among different ages was provided by random regression model estimates from literature studies involving Nellore cattle. Both sources of information were combined into multiple-trait estimates; corrected for continuity, smoothness, and general agreement with literature estimates; and extrapolated to 730 d. Covariance functions using standardized Legendre polynomials were fit for the following effects: additive genetic (direct and maternal), and animal and maternal permanent environment. Residual variances at different ages were fitted using linear splines with three knots. Fit was by least squares. The order of polynomials was varied from third to sixth. Increasing the fit beyond cubic provided small improvements in R2 and increased the number of small eigenvalues of covariance matrices, especially for the additive effect. Parameters for a random regression model in beef cattle can be constructed with negligible artifacts from literature estimates. Formulas can easily be modified for other types of polynomials and splines.     

Implementation issues for Markov Chain Monte Carlo methods in random regression test-day models

Markov Chain Monte Carlo methods made possible estimation of parameters for complex random regression test‐day models. Models evolved from single‐trait with one set of random regressions to multiple‐trait applications with several random effects described by regressions. Gibbs sampling has been used for models with linear (with respect to coefficients) regressions and normality assumptions for random effects. Difficulties associated with implementations of Markov Chain Monte Carlo schemes include lack of good practical methods to assess convergence, slow mixing caused by high posterior correlations of parameters and long running time to generate enough posterior samples. Those problems are illustrated through comparison of Gibbs sampling schemes for single‐trait random regression test‐day models with different model parameterizations, different functions used for regressions and posterior chains of different sizes. Orthogonal polynomials showed better convergence and mixing properties in comparison with ‘lactation curve’ functions of the same number of parameters. Increasing the order of polynomials resulted in smaller number of independent samples for covariance components. Gibbs sampling under hierarchical model parameterization had a lower level of autocorrelation and required less time for computation. Posterior means and standard deviations of genetic parameters were very similar for chains of different size (from 20 000 to 1 000 000) after convergence. Single‐trait random regression models with large data sets can be analysed by Markov Chain Monte Carlo methods in relatively short time. Multiple‐trait (lactation) models are computationally more demanding and better algorithms are required.     

The analysis—Hierarchical models: Past,present and future

This paper discusses statistical modelling for data with a hierarchical structure, and distinguishes in this context between three different meanings of the term hierarchical model: to account for clustering, to investigate variability and separate predictive equations at different hierarchical levels (multi-level analysis), and in a Bayesian framework to involve multiple layers of data or prior information. Within each of these areas, the paper reviews both past developments and the present state, and offers indications of future directions. In a worked example, previously reported data on piglet lameness are reanalyzed with multi-level methodology for survival analysis, leading to new insights into the data structure and predictor effects. In our view, hierarchical models of all three types discussed have much to offer for data analysis in veterinary epidemiology and other disciplines.     

Egg production forecasting: Determining efficient modeling approaches

Several mathematical or statistical and artificial intelligence models were developed to compare egg production forecasts in commercial layers. Initial data for these models were collected from a comparative layer trial on commercial strains conducted at the Poultry Research Farms, Auburn University. Simulated data were produced to represent new scenarios by using means and SD of egg production of the 22 commercial strains. From the simulated data, random examples were generated for neural network training and testing for the weekly egg production prediction from wk 22 to 36. Three neural network architectures-back-propagation-3, Ward-5, and the general regression neural network-were compared for their efficiency to forecast egg production, along with other traditional models. The general regression neural network gave the best-fitting line, which almost overlapped with the commercial egg production data, with an R(2) of 0.71. The general regression neural network-predicted curve was compared with original egg production data, the average curves of white-shelled and brown-shelled strains, linear regression predictions, and the Gompertz nonlinear model. The general regression neural network was superior in all these comparisons and may be the model of choice if the initial overprediction is managed efficiently. In general, neural network models are efficient, are easy to use, require fewer data, and are practical under farm management conditions to forecast egg production.     

Statistical and biological considerations in evaluating drug efficacy in equine strongyle parasites using fecal egg count data

Anthelmintic resistance (AR) is a serious problem for the control of equine gastrointestinal nematodes, particularly in the cyathostomins. The fecal egg count reduction test (FECRT) is the most common method for diagnosing AR and serves as the practical gold standard. However, accurate quantification of resistance and especially accurate diagnosis of emerging resistance to avermectin/milbemycin (A/M) drugs, is hampered by a lack of accepted standards for study design, data analysis, and data interpretation. In order to develop rational evidence-based standards for diagnosis of resistance, one must first take into account the numerous sources of variability, both biological and technical, that affect the measurement of fecal egg counts (FECs). Though usually ignored, these issues can greatly impact the observed efficacy. Thus, to accurately diagnose resistance on the basis of FECRT data, it is important to reduce levels of variability through improved study design, and then deal with inherent variability that cannot be removed, by performing thorough and proper statistical analysis. In this paper we discuss these issues in detail, and provide an explanation of the statistical models and methods that are most appropriate for analyzing these types of data. We also provide several examples using data from laboratory, field, and simulation experiments illustrating the benefits of these approaches.     

A comparison of methods of fitting several models to nutritional response data

A variety of models have been proposed to fit nutritional input-output response data. The models are typically nonlinear; therefore, fitting the models usually requires sophisticated statistical software and training to use it. An alternative tool for fitting nutritional response models was developed by using widely available and easier-to-use Microsoft Excel software. The tool, implemented as an Excel workbook (NRM.xls), allows simultaneous fitting and side-by-side comparisons of several popular models. This study compared the results produced by the tool we developed and PROC NLIN of SAS. The models compared were the broken line (ascending linear and quadratic segments), saturation kinetics, 4-parameter logistics, sigmoidal, and exponential models. The NRM.xls workbook provided results nearly identical to those of PROC NLIN. Furthermore, the workbook successfully fit several models that failed to converge in PROC NLIN. Two data sets were used as examples to compare fits by the different models. The results suggest that no particular nonlinear model is necessarily best for all nutritional response data.     

紫花苜蓿茎秆和叶片的解吸等温线模型及参数优化

为掌握苜蓿(Medicago sativa)收获干燥过程中的解吸等温线,控制干燥过程和贮藏稳定性。文章采用镜面冷凝露点法研究了20℃,30℃,40℃条件下苜蓿顶部茎秆、中部茎秆、根部茎秆以及叶片的解吸等温线。依据5种常用等温线模型对试验数据进行了拟合,并对各拟合模型的适用性进行了分析评价,在此基础上对模型的表达式及参数进行了优化和修正,以确定最佳拟合模型及其参数。结果表明:苜蓿叶片属于Ⅱ型解吸等温线,苜蓿顶部茎秆、中部茎秆、根部茎秆都属于Ⅲ型等温线。在同一水活度条件下,苜蓿茎秆和叶片的储藏温度不同对安全含水率的要求也不同,且它们的安全含水率存在较大差异,环境温度越低对应的安全含水率越高。在20℃,30℃和40℃条件下,苜蓿叶片采用修正GAB模型拟合效果最好,顶部茎秆的最佳解吸等温线方程为GAB和Henderson模型,中部茎秆和根部茎秆适用于GAB和Oswin模型。     

Considerations for analysis of time-to-event outcomes subject to competing risks in veterinary clinical studies

In veterinary medicine, prospective clinical trials are increasingly utilized to address questions regarding effectiveness of therapies and patient prognosis. A large number of these trials involve time-to-event (TTE) endpoints, which require special methods of analysis to handle data in which not all subjects are observed to have the event of interest. Analyses and interpretation of the results can be further complicated when an endpoint of interest is not observed in some patients because they incur a competing risk, such as death from an unrelated cause. Competing risks have been the source of confusion in many epidemiologic analyses leading to the potential for misinterpretation. In this article, we review key considerations for the TTE analysis in the setting of competing risks. We briefly review standard TTE tools, namely Kaplan–Meier survival curves and Cox regression. In the setting of outcomes with competing risks, we provide guidance on the appropriate analysis techniques, such as cumulative incidence curves, to estimate the risk of an event of interest. We also describe a common pitfall of treating competing risks as censoring in Kaplan–Meier survival curve analysis, which can overestimate the event rate of interest. We describe two common regression methods that examine associated risk factors in the presence of competing risks and highlight the different research questions these methods address. This article provides an introductory overview and illustrates concepts with examples from veterinary trials and with example data sets.     

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle

The objective of this work was to estimate covariance functions using random regression models on B-splines functions of animal age, for weights from birth to adult age in Canchim cattle. Data comprised 49,011 records on 2435 females. The model of analysis included fixed effects of contemporary groups, age of dam as quadratic covariable and the population mean trend taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were modelled through a step function with four classes. The direct and maternal additive genetic effects, and animal and maternal permanent environmental effects were included as random effects in the model. A total of seventeen analyses, considering linear, quadratic and cubic B-splines functions and up to seven knots, were carried out. B-spline functions of the same order were considered for all random effects. Random regression models on B-splines functions were compared to a random regression model on Legendre polynomials and with a multitrait model. Results from different models of analyses were compared using the REML form of the Akaike Information criterion and Schwarz' Bayesian Information criterion. In addition, the variance components and genetic parameters estimated for each random regression model were also used as criteria to choose the most adequate model to describe the covariance structure of the data. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most adequate to describe the covariance structure of the data. Random regression models using B-spline functions as base functions fitted the data better than Legendre polynomials, especially at mature ages, but higher number of parameters need to be estimated with B-splines functions.     

基于Landsat 8 OLI影像的渭-库绿洲植被地上生物量估算

干旱区绿洲植被地上生物量估算研究可为绿洲生态系统稳定性评价与区域碳储量估算提供重要依据。以渭干河-库车河三角洲绿洲为研究区，利用ENVI 5.3软件对Landsat 8 OLI 影像数据进行预处理，提取反映植被地上生物量信息的植被指数和波段因子，并结合样地实测数据，采用常规统计模型、多元逐步回归和偏最小二乘回归方法建立研究区植被地上生物量最优估测模型，从而揭示该绿洲植被地上生物量的空间分布特征。结果表明：1）所选的20个遥感因子与实测植被地上生物量呈极显著正相关关系，相关系数为0.5~0.7（P<0.01）。2）乔木与灌木地上生物量最优估测模型均为多元逐步回归模型，草本与农作物地上生物量的估测模型以偏最小二乘回归模型为最优，模型验证决定系数均在0.6以上，均方根误差和平均绝对误差均较小。3）研究区植被地上生物量主要在280~1450 g·m^-2 分布，面积约为6973.82 km²，低水平地上生物量（ABG<65 g·m^-2）分布区域约占研究区总面积的15.02%。地上生物量由高到低依次为：农作物>乔木>灌木>草本。根据不同的植被类型，基于地物光谱特征构建的遥感估测模型可准确估算干旱区绿洲植被地上生物量，并对其空间分布特征进行遥感定量反演。     

Use of heterogeneous operation-specific contact parameters changes predictions for foot-and-mouth disease outbreaks in complex simulation models

The role of contact parameters in a complex spatial simulation model of foot-and-mouth disease spread was determined by comparing predictions of number of infected premises, epidemic duration, and relative infection risk for different production sectors between a model that included the Full, heterogeneous (differing by production type) type-specific information about animal, vehicle and personnel movement between premises, and models that used partial and homogeneous (similar across production types) weighted-mean or proxy parameter sets for contacts between premises of all types. The model was run using a dataset of known premises locations in a three-county area in the Central Valley of California and categorized into 13 premises types and six production sectors.Results from models run with homogeneous contact parameters were always different from those obtained from the Full model, demonstrating that model predictions are affected by heterogeneity in contact parameters. Models simplified by using weighted-mean parameters predicted fewer infected premises. Models that were simplified by using medium dairy farm or large swine operation proxy parameters predicted longer epidemics with more infected premises, while those using small beef operation proxy parameters predicted shorter epidemics with fewer infected premises. Simplified-parameter models underestimated the impact on the economically important dairy sector, while overestimating the impact on beef and backyard operations. Results establish a need for heterogeneous, operation-specific contact parameters in complex stochastic simulation models that must be weighed against the cost of obtaining and coding premises type-specific contact information.     

A statistical model to optimize indirect sandwich enzyme-linked immunosorbent assay parameters of antigen and antibody: a microcomputer program

A new computer software program "AVCRV" was developed using a statistical model to analyze the data from the indirect sandwich enzyme-linked immunosorbent assay (ELISA). The software program calculates a sigmoid type of regression analysis and can be run on most microcomputers in the laboratory. The program permits those who are not familiar with computers to complete this type of analysis in a few seconds without a large mainframe computer or complicated software. This statistical model for a sigmoid type of regression analysis of ELISA data may improve the analysis of research data for various avian pathogens from several different experiments.