Testing for additivity in chemical mixtures using a fixed-ratio ray design and statistical equivalence testing methods

Fixed-ratio ray designs have been used for detecting and characterizing interactions of large numbers of chemicals in combination. Single-chemical dose-response data are used to predict an “additivity curve” along an environmentally relevant ray. A “mixture curve” is estimated from the mixture dose-response data along the ray. A test of additivity is equivalent to a test of coincidence of these two curves, which is based on the traditional hypothesis testing framework that assumes additivity in the null hypothesis and rejects with evidence of interaction. However, failure to reject may be due to lack of statistical power, making the claim of additivity problematic. As a solution we have developed rigorous methodology to test for additivity using statistical equivalence testing logic in which additivity is claimed based on pre-specified biologically important additivity margins, if the data support such a claim. Using the principle of confidence interval inclusion, a confidence region about the difference of meaningful functions of model parameters from the mixture model and that predicted under additivity is computed. When the confidence region is completely contained within the additivity margins then additivity is claimed with a Type I error rate chosen a priori to be some acceptably small value. The method is illustrated using an environmentally relevant fixed-ratio mixture of nine haloacetic acids where cytotoxic response is measured.     

Statistical analysis of interactive cytotoxicity in human epidermal keratinocytes following exposure to a mixture of four metals

Exposure to mixtures of chemicals is an important and relevant environmental issue. Of particular interest is the detection and characterization of departure of biological effects from additivity. Methodology based on the assumption of additivity is used in fitting single-chemicaldata. Interactionsare determined and characterized by making comparisons between the observed and predicted responses at mixtures along a fixed ratio ray of the component substances. Two simultaneous tests are developed for testing for any departure from additivity. Multiple comparisons procedures are used to compare observed responses to that predicted under additivity. A simultaneous confidence band on the predicted responses along the mixture ray is also developed. The methods are illustrated with cytotoxicity data that arise when human epidermal keratinocytes are exposed to a mixture of arsenic, chromium, cadmium, and lead. Synergistic, antagonistic, and additive cytotoxicities were observed at different dose levels of the four-metal mixture.     

Analysis of mixtures of drugs/chemicals along a fixed-ratio ray without single-chemical data to support an additivity model

This article presents and illustrates an approach to designing and analyzing studies involving mixtures/combinations of drugs or chemicals along fixed-ratio rays of the drugs or chemicals for generalized linear models. When interest can be restricted to a specific ray, we consider fixed-ratio ray designs to reduce the amount of experimental effort. When a ray design is used, we have shown that the hypothesis of additivity can be rejected when higher order polynomial terms are required in the total dose-response model. Thus, it is important that we have precise parameter estimates for these higher order polynomial terms in the linear predictor. We have developed methodology for finding a D _s -optimal design based on this subset of the terms in the linear predictor.     

The impact of exposure to a mixture of eighteen polyhalogenated aromatic hydrocarbons on thyroid function: Estimation of an interaction threshold

When an interaction has been detected among the chemicals in a mixture, it may be of interest to predict the interaction threshold. A method is presented for estimation of an interaction threshold along a mixture ray which allows differences in the shapes of the dose-response curves of the individual components (e.g., mixtures of full and partial agonists with differing response maxima). A point estimate and confidence interval for the interaction threshold may be estimated. The methods are illustrated with data from a study of a mixture of 18 polyhalogenated aromatic hydrocarbons (PHAHs) in rats exposed by oral gavage for four consecutive days. Serum total thyroxine (T4) was the response variable. Previous analysis of these data demonstrated a dose-dependent interaction among the 18 chemicals in the mixture, with additivity suggested in the lower portion of the dose-response curve and synergy (greater than additive response) in the higher portion of the dose-response curve. The present work builds on this analysis by construction of an interaction threshold model along the mixture ray. This interaction threshold model has two components: an implicit additivity region and an explicit region that describes the departure from additivity; the interaction threshold is the boundary between the two regions. Estimation of the interaction threshold within the observed experimental region suggested evidence of additivity in the low dose region. Total doses of the mixture that exceed the upper limit of the confidence interval on the interaction threshold were associated with a greater-than-additive interaction.     

Detecting Departure From Additivity Along a Fixed-Ratio Mixture Ray With a Piecewise Model for Dose and Interaction Thresholds

For mixtures of many chemicals, a ray design based on a relevant, fixed mixing ratio is useful for detecting departure from additivity. Methods for detecting departure involve modeling the response as a function of total dose along the ray. For mixtures with many components, the interaction may be dose dependent. Therefore, we have developed the use of a three-segment model containing both a dose threshold and an interaction threshold. Prior to the dose threshold, the response is that of background; between the dose threshold and the interaction threshold, an additive relationship exists; the model allows for departure from additivity beyond the interaction threshold. With such a model, we can conduct a hypothesis test of additivity, as well as a test for a region of additivity. The methods are illustrated with cytotoxicity data that arise when Chinese hamster ovary cells are exposed to a mixture of nine haloacetic acids.     

Sample size and power determination for detecting interactions in mixtures of chemicals

In the analysis of mixtures of drugs/chemicals it is often of interest to test for the presence of interaction. If the hypothesis of no interaction (additivity) is not rejected, then the analyst may reasonably claim additivity if and only if the study is powered to a desired (e.g., biologically meaningful) level. The objective of this article is to address the sample size and power issues related to testing the hypothesis of additivity at specified mixture points. The study of disinfectant by-products (DBPs) found in drinking water, described in earlier literature, is used to illustrate the procedures for estimating power and sample sizes for detecting interactions at specified mixtures. The four trihalomethanes used in the study are bromodichloromethane (BDCM), chlorodibromomethane (CDBM), chloroform (CHCl₃), and bromoform (CHBr₃)     

基于三维姿态拟合的非接触式红鳍东方鲀全长精准估算方法

鱼类生物量无损测算是智能化水产养殖的重要环节,如何实现鱼体全长精准估算是该环节稳定运行的重要前提。该研究以红鳍东方鲀为对象,提出了一种鱼体全长精准估算方法,可在非接触情况下对自由游动的红鳍东方鲀进行精准的体长估算。首先,利用双目立体视觉技术对原始图像进行校正和立体匹配获得深度图像,并通过SOLOv2模型进行鱼体分割;然后,通过自主设计的独立分类器对图像进行高效分类,自动获取可用于全长估算的鱼类侧面图像,其分类准确率达95.3%;最后,耦合图像平面特征和深度信息,对鱼类进行三维姿态拟合,实现鱼类全长精准估算。结果表明,该方法全长估算的平均相对误差为2.67%,标准差为9.45%,且全长估算值与质量表现出良好相关性（R2=0.88）。该研究将为鱼类生物量无损测算提供关键技术支撑,对水产养殖的信息化管理、鱼类生长状况评估、投饵控制等具有重要意义。     

Comparison of Models Analyzing a Small Number of Observed Meningitis Cases in Navrongo,Ghana

The “meningitis belt” is a region in sub-Saharan Africa where annual outbreaks of meningitis occur, with epidemics observed cyclically. While we know that meningitis is heavily dependent on seasonal trends, the exact pathways for contracting the disease are not fully understood and warrant further investigation. Most previous approaches have used large sample inference to assess impacts of weather on meningitis rates. However, in the case of rare events, the validity of such assumptions is uncertain. This work examines the meningitis trends in the context of rare events, with the specific objective of quantifying the underlying seasonal patterns in meningitis rates. We compare three main classes of models: the Poisson generalized linear model, the Poisson generalized additive model, and a Bayesian hazard model extended to accommodate count data and a changing at-risk population. We compare the accuracy and robustness of the models through the bias, RMSE, and standard deviation of the estimators, and also provide a detailed case study of meningitis patterns for data collected in Navrongo, Ghana.Supplementary materials accompanying this paper appear online.     

Empirical evaluation of sufficient similarity in dose—Response for environmental risk assessment of chemical mixtures

When toxicity data are not available for a chemical mixture of concern, U.S. Environmental Protection Agency (EPA) guidelines allow risk assessment to be based on data for a surrogate mixture considered “sufficiently similar” in terms of chemical composition and component proportions. As a supplementary approach, using statistical equivalence testing logic and mixed model theory we have developed methodology to define sufficient similarity in dose—response for mixtures of many chemicals containing the same components with different ratios. Dose—response data from a mixture of 11 xenoestrogens and the endogenous hormone, 17ß-estradiol are used to illustrate the method.     

Relationship between corn yield and chemical composition of the ear leaf measured with different regression models

Abstract

Corn yields and leaf samples were obtained from experimental plots receiving varying rates of N, P and K. Yields were regressed on leaf levels of N, P, K, Ca, Mg, B, Cu, Fe, Mn and Zn as independent variables. Various polynomial regressions were fitted to the yields and “goodness of fit”; of particular mathematical models was used as a basis for evaluating particular biological and statistical concepts.

It was found that no regression, where chemical elements were used as ratios, fit the observations as well as a quadratic polynomial or its square root transformation. This suggests that within the set of data used, emphasis on particular cation or anion ratios does not necessarily result in the “best”; explanation of variation in yield.

“Classical”; growth equations were fitted to corn yields, but were not as precise in predicting yields as the polynomials. A modified stagewise regression procedure was used for fitting one mathematical model, but results were less satisfactory than those obtained with usual least squares procedures.     

Insights Into the Latent Multinomial Model Through Mark-Resight Data on Female Grizzly Bears With Cubs-of-the-Year

Mark-resight designs for estimation of population abundance are common and attractive to researchers. However, inference from such designs is very limited when faced with sparse data, either from a low number of marked animals, a low probability of detection, or both. In the Greater Yellowstone Ecosystem, yearly mark-resight data are collected for female grizzly bears with cubs-of-the-year (FCOY), and inference suffers from both limitations. To overcome difficulties due to sparseness, we assume homogeneity in sighting probabilities over 16 years of bi-annual aerial surveys. We model counts of marked and unmarked animals as multinomial random variables, using the capture frequencies of marked animals for inference about the latent multinomial frequencies for unmarked animals. We discuss undesirable behavior of the commonly used discrete uniform prior distribution on the population size parameter and provide OpenBUGS code for fitting such models. The application provides valuable insights into subtleties of implementing Bayesian inference for latent multinomial models. We tie the discussion to our application, though the insights are broadly useful for applications of the latent multinomial model.     

Estimating the Risk of Exceeding Thresholds in Environmental Systems

Environmental regulations often rely on limits or thresholds to indicate an acceptable pollutant load. Estimates of the Risk of Exceeding such Thresholds (RET) are often based on a single model deemed to be the best for the particular pollutant or particular case. However, if many models make different predictions but explain the data almost equally well, predictions based on a single model may omit important information contained in other models that fit almost as well as the “best” single model. More accurate assessments of RET may result if multiple models are considered. We compared performance of the single best model relative to that of an ensemble of models estimated by bagging (Bootstrap AGGregatING) using the example of soil P concentrations and the risk of exceeding environmental limits of soil P concentrations in the watershed of Lake Mendota, Wisconsin, USA. Bagging yielded significantly better predictions of the risk of exceeding a threshold level of soil P (99.6% accuracy versus 74% for single-model prediction at a 20 mg kg^?1 threshold). Use of multiple model techniques can improve estimates of RET over a range of realistic thresholds in other management situations where thresholds are important including eutrophication, desertification, fisheries, and many types of pollution control.     

Chronic toxicity of an environmental contaminant mixture to young (or larval) striped bass

Larvae of striped bass (Morone saxatilis (Walbaum)) were exposed to a mixture of organic and inorganic contaminants in fresh well water and 2 g L^?1 saline water for 30 days and in 5 g L^?1 saline water for 90 days. Environmental concentrations (ECs) of organic and inorganic chemicals were estimated for the Chesapeake Bay area. Striped bass were exposed to the EC, 0.25 EC, 0.5 EC, 2 EC, 4 EC, and a solvent control to simulate potential conditions in their spawning and nursery habitats of the Chesapeake Bay. The sensitivities of striped bass as determined by survival depended on the characteristics of the exposure water. Larvae exposed in fresh well water were the most susceptible to the contaminant mixture; the 2 and 4 EC treatments caused significant (P:5 0.05) mortality within 30 days. In the 2 g L^?1 salinity water, the 4 EC treatment caused significant mortality after 30 days of exposure. Larvae exposed to the contaminant mixture for 90 days in the 5 g L^?1 saline water incurred significant mortality in the 2 and 4 EC treatments. We concluded that the age of the larvae, concentration of the contaminants, and salinity of the environment must be considered in evaluating the influence of environmental contaminants on the decline of striped bass along the east coast.     

Response of oat-triticale mixture to post-emergence weed harrowing

ABSTRACT

In experiments with weed harrowing crops are negatively affected by competing weeds but also by the destructive effect of used implement. This research was carried out to find growth stages during which mixture of oat (Avena sativa L.) and triticale (× Triticosecale Wittm.) was resistant to harrowing and was able to effectively recover from this physical disturbance. Plots were harrowed 1–3 times on the same day at six consecutive stages of mixture growth with spring-tine harrow. After the latest harrowing, all plots were sprayed with herbicide to exclude competitive effect of weeds on the mixture. Compared to non-harrowed plots plant density of mixture was significantly reduced after a single cultivation at 1- and 2-leaf stage (20% and 23% respectively), two cultivations at 3-leaf stage (22%) and three at the beginning of the tillering (21%). No yield penalty was noticed for the density reductions, thus showing high ability of mixture to recover from physical disturbance. We recommend plant emergence as an appropriate growth stage for single harrowing of oat-triticale mixture. Two cultivations on the same day should not be planned earlier than at the beginning of tillering.     

采用改进Unet网络的茶园导航路径识别方法

针对目前在茶园垄间导航路径识别存在准确性不高、实时性差和模型解释困难等问题，该研究在Unet模型的基础上进行优化，提出融合Unet和ResNet模型优势的Unet-ResNet34模型，并以该模型所提取的导航路径为基础，生成路径中点，通过多段三次B样条曲线法拟合中点生成茶园垄间导航线。该研究在数据增强后的茶园垄间道路训练集中完成模型训练，将训练完成的模型在验证集进行导航路径识别，根据梯度加权类激活映射法解释模型识别过程，可视化对比不同模型识别结果。Unet-ResNet34模型在不同光照和杂草条件下导航路径分割精度指标平均交并比为91.89%，能够实现茶园垄间道路像素级分割。模型处理RGB图像的推理速度为36.8 帧/s，满足导航路径分割的实时性需求。经过导航线偏差试验可知，平均像素偏差为8.2像素，平均距离偏差为0.022 m，已知茶园垄间道路平均宽度为1 m，道路平均距离偏差占比2.2%。茶园履带车行驶速度在0～1 m/s之间，单幅茶垄图像平均处理时间为0.179 s。研究结果能够为茶园视觉导航设备提供技术和理论基础。     

Local Influence for Spatially Correlated Binomial Data: An Application to the <Emphasis Type="Italic">Spodoptera frugiperda</Emphasis> Infestation in Corn

Influence diagnostics are valuable tools for understanding the influence of data and/or model assumptions on the results of a statistical analysis. This paper proposes local influence for the analysis of spatially correlated binomial data. We consider a spatial model with a binomial marginal distribution and logit link function. Generalized estimating equations via Fisher’s scoring are used for estimating the parameters. We present an application to the spatial Spodoptera frugiperda infestation where the generalized estimating equations are used to identify potential influential observations by the local influence analysis. The spatial prediction with and without the influential points is compared. The results show that the presence of the influential observation in the data changes statistical inference, the predicted values and the respective maps. A simulation study considering different scenarios shows the performance of the local influence diagnostic method.     

超长钝顶螺旋藻的选育及形态和生长特性初步研究

用组织匀浆破碎和离心沉降法制备和分离出钝顶螺旋藻(Spirulina platensis)Sp-Z 的单细胞或少于5个细胞的片段,并用60Coγ射线辐照处理,半致死剂量为1.2 kGy.在2.4kGy的处理组中,筛选出4株藻丝长度、螺旋数、螺旋长分别为Sp-Z的15、10和1.8倍的超长钝顶螺旋藻突变体Sp-Z(E.L).Sp-Z的生长曲线几乎呈直线型,而Sp-Z(E.L)的生长曲线则呈较明显的"S"形.在室外培养时,Sp-Z(E.L)的产量比Sp-Z高11.7%.     

A Zero-Inflated Spatial Gamma Process Model With Applications to Disease Mapping

In this paper, we introduce a novel discrete Gamma Markov random field (MRF) prior for modeling spatial relations among regions in geo-referenced health data. Our proposition is incorporated into a generalized linear mixed model zero-inflated (ZI) framework that accounts for excess zeroes not explained by usual parametric (Poisson or Negative Binomial) assumptions. The ZI framework categorizes subjects into low-risk and high-risk groups. Zeroes arising from the low-risk group contributes to structural zeroes, while the high-risk members contributes to random zeroes. We aim to identify explanatory covariates that might have significant effect on (i) the probability of subjects in low-risk group, and (ii) intensity of the high risk group, after controlling for spatial association and subject-specific heterogeneity. Model fitting and parameter estimation are carried out under a Bayesian paradigm through relevant Markov chain Monte Carlo (MCMC) schemes. Simulation studies and application to a real data on hypertensive disorder of pregnancy confirms that our model provides superior fit over the widely used conditionally auto-regressive proposition.     

A Population-Size Model for Protein Spot Detection in Proteomic Studies

In proteomic studies, a population of proteins are often examined on a gel using a technique called two-dimensional gel eletrophoresis. The technique separates the protein population into individual protein spots on a two-dimensional gel by isoelectric charge and molecular weight. The resulting gel images are then processed by a software system for spot detection and subsequent analysis. The performance of a spot-detection program is evaluated by the total number of spots that are detected. A popular spot-detection program uses the “master–slave” approach, where all spots on “slave images” are subsets of the spots on the “master image.” We argue that this approach potentially misses a large proportion of proteins and propose a model that quantifies the lack of performance. We provide nonparametric estimators for the protein population size and the expected number of proteins to be detected if a “fusion-gel” approach was used. Using the data from a rat liver proteome study, we estimate that more than half of the protein population is missed by the master–slave approach.