Thermal Inactivation of Salmonella Serotypes in Red Meat as Affected by Fat Content

Survival curves of a cocktail of eight serotypes of Salmonella in ground beef and pork meat of different levels of fat (4% to 28%), at temperatures that ranged from 58°C to 65°C, were examined. Asymptotic D-values (D-values for large times) and initial D-values (D-values for small times, near zero) were estimated by identifying regions where the survival curves were linear, and performing linear regressions on data within the identified regions. The initial lag D-values increase with increasing fat levels for both beef and pork. The relationship of the asymptotic D-values with fat levels and temperature is complex, and definitive conclusions could not be made. It appears that, for ground beef, asymptotic D-values increase with increasing fat levels, but this was not the case for ground pork. The shapes of the survival curves were concave, convex, and sigmoidal, and depended upon the temperature, where for the lower temperatures studied (58°C and 60°C) the curves exhibited tailing. The Gompertz function was found to provide a good fit to the data over the range of temperatures and fat levels studied. These results, particularly for beef, suggest the importance of determining the shape of the survival curves (concave, convex or sigmoidal) when estimating times needed to obtain an adequate margin of safety for thermal processes of red meat.     

样条变换偏最小二乘在肝癌数据分类中的应用

肝癌是中国最常见的恶性肿瘤之一。基于肿瘤基因表达谱数据的分析与研究是当今研究的热点,对于癌症的早期诊断、治疗具有十分重要的意义。针对高维小样本基因表达谱数据所显现的变量间严重共线性、类别变量与预测变量的非线性关系,采用了基于样条变换的偏最小二乘回归新技术。首先通过筛选法去除基因表达谱数据中的冗余信息,然后以3次B基样条变换实现非线性基因表达谱数据的线性化重构,随后将重构的矩阵交由偏最小二乘法构建类别变量与预测变量间的关系模型。最后,通过对肝癌肿瘤基因表达谱数据的分析,结果显示此分类模型对数据重构稳健,有效的解决了高维小样本基因表达谱数据间的过拟合和变量间的共线性,具有较高的拟合和分类正确率。     

The effect of end-point adjustments on smoothing splines used for tree-ring standardization

The cubic smoothing spline has been a popular method for detrending tree-ring data since the 1980s. The common implementation of this procedure (e.g., ARSTAN, dplR) uses a unique method for determining the smoothing parameter that is widely known as the %n criterion. However, this smoothing parameter selection method carries the assumption that end point effects are ignorable. In this paper, we complete the mathematical derivation and show how the original method differs from the complete version, both in the interpretation of the smoothing parameter and in the spline fit. Frequency response curves (FRC) demonstrate how the smoothing parameter is affected by the original assumption. For example, the FRC results indicate that a tree core of 250-year length has a 14% difference in the cut-off frequency when looking at the 67%n criterion. The FRC analysis shows that the existing approach produces a more flexible fit than anticipated, i.e., it is removing more variance than previously thought. For example, a 67%n spline under the existing approach corresponds to a 53%n spline fit. By using both simulated tree-core sequences and a dataset from a Midwest forest, we discuss which conditions result in greater differences between the spline fits and which conditions will have small differences. Tree-core sequences that have more curvature, such as a large-amplitude growth release, will lead to greater differences. Finally, we provide approximations to the end-point effect procedure. For example, using an 83%n criterion under the original approach produces a spline fit approximating the 67%n fit under the complete approach. These approximations could be easily implemented within existing programs like ARSTAN.     

Bayesian semiparametric copula estimation with application to psychiatric genetics

This paper proposes a semiparametric methodology for modeling multivariate and conditional distributions. We first build a multivariate distribution whose dependence structure is induced by a Gaussian copula and whose marginal distributions are estimated nonparametrically via mixtures of B‐spline densities. The conditional distribution of a given variable is obtained in closed form from this multivariate distribution. We take a Bayesian approach, using Markov chain Monte Carlo methods for inference. We study the frequentist properties of the proposed methodology via simulation and apply the method to estimation of conditional densities of summary statistics, used for computing conditional local false discovery rates, from genetic association studies of schizophrenia and cardiovascular disease risk factors.     

Modeling and testing treated tumor growth using cubic smoothing splines

Human tumor xenograft models are often used in preclinical study to evaluate the therapeutic efficacy of a certain compound or a combination of certain compounds. In a typical human tumor xenograft model, human carcinoma cells are implanted to subjects such as severe combined immunodeficient (SCID) mice. Treatment with test compounds is initiated after tumor nodule has appeared, and continued for a certain time period. Tumor volumes are measured over the duration of the experiment. It is well known that untreated tumor growth may follow certain patterns, which can be described by certain mathematical models. However, the growth patterns of the treated tumors with multiple treatment episodes are quite complex, and the usage of parametric models is limited. We propose using cubic smoothing splines to describe tumor growth for each treatment group and for each subject, respectively. The proposed smoothing splines are quite flexible in modeling different growth patterns. In addition, using this procedure, we can obtain tumor growth and growth rate over time for each treatment group and for each subject, and examine whether tumor growth follows certain growth pattern. To examine the overall treatment effect and group differences, the scaled chi-squared test statistics based on the fitted group-level growth curves are proposed. A case study is provided to illustrate the application of this method, and simulations are carried out to examine the performances of the scaled chi-squared tests.     

Estimates of the genetic parameters of turkey body weight using random regression analysis

Random regression (RR) analysis has been recommended to estimate the genetic parameters of longitudinal data. The objective of this study was to evaluate the growth of turkeys using RR models. Data were collected from 957 turkeys and included 15,478 individual body weight recorded during the first week of life and between weeks 2 and 32 by 2-week intervals. To take into account the repeated measurements of weight for each animal, a specific overall growth curve was modelled using a cubic smoothing spline. Animal deviation to this curve was also modelled using an RR function. All data were analysed with the ASReml package. The results showed an increase in heritability estimates over the trajectory and peaked at 0.60 around 20 to 32 weeks of age. Genetic correlations showed that turkeys could be selected at earlier time points, at 12 weeks of age, in order to increase the growth rate. In general, genetic correlation estimates were higher among adjacent ages, decreasing markedly with the increase of distance between ages. Negative genetic correlations were observed between ages.     

A Random Intercepts–Functional Slopes Model for Flexible Assessment of Susceptibility in Longitudinal Designs

Summary In many biomedical investigations, a primary goal is the identification of subjects who are susceptible to a given exposure or treatment of interest. We focus on methods for addressing this question in longitudinal studies when interest focuses on relating susceptibility to a subject's baseline or mean outcome level. In this context, we propose a random intercepts–functional slopes model that relaxes the assumption of linear association between random coefficients in existing mixed models and yields an estimate of the functional form of this relationship. We propose a penalized spline formulation for the nonparametric function that represents this relationship, and implement a fully Bayesian approach to model fitting. We investigate the frequentist performance of our method via simulation, and apply the model to data on the effects of particulate matter on coronary blood flow from an animal toxicology study. The general principles introduced here apply more broadly to settings in which interest focuses on the relationship between baseline and change over time.     

Assessment of agreement under nonstandard conditions using regression models for mean and variance

The total deviation index of Lin and Lin et al. is an intuitive approach for the assessment of agreement between two methods of measurement. It assumes that the differences of the paired measurements are a random sample from a normal distribution and works essentially by constructing a probability content tolerance interval for this distribution. We generalize this approach to the case when differences may not have identical distributions -- a common scenario in applications. In particular, we use the regression approach to model the mean and the variance of differences as functions of observed values of the average of the paired measurements, and describe two methods based on asymptotic theory of maximum likelihood estimators for constructing a simultaneous probability content tolerance band. The first method uses bootstrap to approximate the critical point and the second method is an analytical approximation. Simulation shows that the first method works well for sample sizes as small as 30 and the second method is preferable for large sample sizes. We also extend the methodology for the case when the mean function is modeled using penalized splines via a mixed model representation. Two real data applications are presented.