Robust benchmark dose determination based on profile score methods

We investigate several methods commonly used to obtain a benchmark dose and show that those based on full likelihood or profile likelihood methods might have severe shortcomings. We propose two new profile likelihood-based approaches which overcome these problems. Another contribution is the extension of the benchmark dose determination to non full likelihood models, such as quasi-likelihood, generalized estimating equations, which are widely used in settings such as developmental toxicity where clustered data are encountered. This widening of the scope of application is possible by the use of (robust) score statistics. Benchmark dose methods are applied to a data set from a developmental toxicity study.     

Qualitative and quantitative assessment of the risk from the exposure to fetotoxic chemical compounds

A new mathematical dose-response model for the expected probability of toxic response and also for the expected measure of the overdispersion parameter for the reproductive and developmental risk assessment is proposed. The model for the expected probability of toxic response is an improvised Weibull dose-response model incorporating the litter-size effect while the model for the overdispersion parameter is a polynomial function of the dose level. A beta-binomial distribution for the number of offspring showing toxic responses in a litter satisfactorily accounts for the extra-binomial variation and the intralitter correlation of responses of these pups. Confidence limits for low-dose extrapolation are based on the asymptotic distribution of the likelihood ratio. The safe dose for human exposure is then calculated by simple linear extrapolation. The model for overdispersion allows us to obtain the estimates of the overdispersion parameter at these dosages. This was not possible in the earlier models. The proposed model is illustrated by an application to a study on the effect of exposure to diethylhexylphthalate in mice. The results are compared with those obtained by Chen and Kodell (1989) who have applied the simple Weibull dose-response model to the same data set.This paper was prepared with partial support from the United States Environmental Protection Agency under a Cooperative Agreement Number CR-815273. The contents have not been subject to Agency review and therefore do not necessarily reflect the views or policies of the Agency and no official endorsement should be inferred.     

Continuous dose-response modeling and risk analysis with the gamma and reciprocal gamma distributions

Kodell and West (1993) describe two methods for calculating pointwise upper confidence limits on the risk function with normally distributed responses and using a certain definition of adverse quantitative effect. But Banga et al. (2000) have shown that these normal theory methods break down when applied to skew data. We accordingly develop a risk analysis model and associated likelihood-based methodology when the response follows either a gamma or reciprocal gamma distribution. The model supposes that the shape (index) parameter k of the response distribution is held fixed while the logarithm of the scale parameter is a linear model in terms of the dose level. Existence and uniqueness of the maximum likelihood estimates is established. Asymptotic likelihood-based upper and lower confidence limits on the risk are solutions of the Lagrange equations associated with a constrained optimization problem. Starting values for an iterative solution are obtained by replacing the Lagrange equations by the lowest order terms in their asymptotic expansions. Three methods are then compared for calculating confidence limits on the risk: (i) the aforementioned starting values (LRAL method), (ii) full iterative solution of the Lagrange equations (LREL method), and (iii) bounds obtained using approximate normality of the maximum likelihood estimates with standard errors derived from the information matrix (MLE method). Simulation is used to assess coverage probabilities for the resulting upper confidence limits when the log of the scale parameter is quadratic in the dose level. Results indicate that coverage for the MLE method can be off by as much as 15% points and converges very slowly to nominal coverage levels as the sample size increases. Coverage for the LRAL and LREL methods, on the other hand, is close to nominal levels unless (a) the sample size is small, say N < 25, (b) the index parameter is small, say k 1, and (c) the direction of adversity is to the left for the gamma distribution or to the right for the reciprocal gamma distribution.     

Dose-response modeling for developmental neurotoxicity data

The fact that maternal exposures to some chemicals during pregnancy can adversely affect the structure and function of the nervous system in the offspring is well established. Government agencies have for a long time been concerned with regulation of developmental neurotoxicants and safe perinatal exposures. However, despite this concern, current guidelines provide only broad and nonspecific recommendations and lack clear directions for a model based approach to risk estimation. In this paper we propose a dose-response model for the nonquantal data obtained from developmental neurotoxicological experiments. To account for the critical issue of the correlation among responses from pups in the same litter, the so called intralitter correlation, a hierarchical distributional structure is used to derive the underlying unconditional distribution of responses. The maximum likelihood method is used to estimate model parameters and the covariance matrix of the estimates is derived. An example is used to illustrate the results.     

Bayesian testing for trend in a power model for clustered binary data

Developmental toxicity studies are widely used to investigate the potential risk of environmental hazards. In dose–response experiments, subjects are randomly allocated to groups receiving various dose levels. Tests for trend are then often applied to assess possible dose effects. Recent techniques for risk assessment in this area are based on fitting dose–response models. The complexity of such studies implies a number of non-trivial challenges for model development and the construction of dose-related trend tests, including the hierarchical structure of the data, litter effects inducing extra variation, the functional form of the dose–response curve, the adverse event at dam or at fetus level, the inference paradigm, etc. The purpose of this paper is to propose a Bayesian trend test based on a non-linear power model for the dose effect and using an appropriate model for clustered binary data. Our work is motivated by the analysis of developmental toxicity studies, in which the offspring of exposed and control rodents are examined for defects. Simulations show the performance of the method over a number of samples generated under typical experimental conditions.     

Confidence limits on one-stage model parameters in benchmark risk assessment

In modern environmental risk analysis, inferences are often desired on those low dose levels at which a fixed benchmark risk is achieved. In this paper, we study the use of confidence limits on parameters from a simple one-stage model of risk historically popular in benchmark analysis with quantal data. Based on these confidence bounds, we present methods for deriving upper confidence limits on extra risk and lower bounds on the benchmark dose. The methods are seen to extend automatically to the case where simultaneous inferences are desired at multiple doses. Monte Carlo evaluations explore characteristics of the parameter estimates and the confidence limits under this setting.

Analytical methods of data gathering for risk assessment of contaminated soils in agricultural production

For the detection, analysis and assessment of contaminated land a procedure in separate steps is urgently recommended. During screening analyses informations about toxic gases, contents of heavy metals and halogenated organics are provided. When certain threshold values are exceeded, more sophisticated methods of residue analysis may help to decide on soil decontamination or change of exploitation.     

Bootstrap methods for simultaneous benchmark analysis with quantal response data

A primary objective in quantitative risk assessment is the characterization of risk which is defined to be the likelihood of an adverse effect caused by an environmental toxin or chemcial agent. In modern risk-benchmark analysis, attention centers on the “benchmark dose” at which a fixed benchmark level of risk is achieved, with a lower confidence limits on this dose being of primary interest. In practice, a range of benchmark risks may be under study, so that the individual lower confidence limits on benchmark dose must be corrected for simultaneity in order to maintain a specified overall level of confidence. For the case of quantal data, simultaneous methods have been constructed that appeal to the large sample normality of parameter estimates. The suitability of these methods for use with small sample sizes will be considered. A new bootstrap technique is proposed as an alternative to the large sample methodology. This technique is evaluated via a simulation study and examples from environmental toxicology.

Modeling and risk assessment for soil temperatures beneath prescribed forest fires

Prescribed fire is a management tool used by wildland resource management organizations in many ecosystems to reduce hazardous fuels and to achieve a host of other objectives. To study the effects of fire in naturally accumulating fuel conditions, the ambient soil temperature is monitored beneath prescribed burns. In this study we developed a stochastic model for temperature profiles (values at 15 minute intervals) recorded at four depths beneath the soil during a large prescribed burn study. The model was used to assess the temporal fit of the data to particular solutions of the heat equation. We used a random effects model to assess the effects of observed site characteristics on maximum temperatures and to estimate risks of temperatures exceeding critical levels in future similar prescribed fires. Contour plots of estimated risks of temperatures exceeding 60°C for a range of fuel levels and soil depths indicated high risks of occurrence, especially when the moisture levels are low. However, the natural variability among sites seems to be large, even after controlling fuel and moisture levels, resulting in large standard errors of predicted risks.     

TCLP法评价酸性矿山废水污染稻田土壤重金属的生态风险

采用美国最新的法定重金属污染评价方法TCLP(Toxicity Characteristic Leaching Procedure,TCLP)法对粤北大宝山矿山下游受酸性矿山废水长期污染的稻田土壤的重金属(Cd、Zn、Pb、Cu)污染状况进行评价,以国际规定的TCLP法标准评价重金属生态环境风险.结果表明,TCLP试剂提取的土壤重金属Cd、Cu、Pb和Zn含量分别在0.02～0.58、1.42～38.07、0.16-31.01和1.84～75.29 mg·kg-1之间.酸性矿山废水污染稻田土壤不同程度地受到Cd、Cu、Pb、Zn的污染,其中以Pb、Zn污染最为严重,其次为Cu污染,Cd污染程度最轻.     

栖息地适宜度评价方法研究进展

栖息地模拟法是根据指示物种所需的物理生境条件确定河流流量,评价栖息地适宜度,为水生生物提供一个适宜的物理生境。与其他方法相比,栖息地模拟法考虑了生物本身对物理生境的要求,需要建立物种-生境评价指标。文章总结了目前用于描述物种—生境关系的栖息地适宜度评价方法,包括栖息地适宜度指数、多元统计方法、模糊逻辑方法、人工神经网络、对多物种和群落的统计分析,归纳了各个方法的进展和应用情况,重点分析了统计学方法在评估栖息地适宜度时的优势和不足。栖息地适宜度指数有二元、单变量、多变量3种格式,前2种方法只考虑单一因子,实际应用中多变量格式应用较多。多变量格式方法直观、所需数据容易获取、实际操作性强,是栖息地定量化的经典方法,也是目前应用最多的方法,然而其对专家经验依赖较多,主观性较强。近些年来,多元统计方法在栖息地适宜度评价方面的应用不断增加,它考虑物理变量之间的相互作用和相关性。模糊逻辑法在处理栖息地模拟中的不确定性方面具有优势,能更好地利用专家知识,更合理的处理建模过程中测量的不准确性和不确定性,同时也考虑了多个变量之间的相互作用,但是当考虑的变量数增加时,模糊规则的数量会迅速增加,给计算带来不便。人工神经网络能够隐性地找出响应变量和环境变量之间的复杂关系,但是其解释能力不足,并需要大量的实测数据对其进行训练,实际应用受到限制。通过排序分析或梯度分析可以对多物种和群落进行统计分析。这些方法都各有优劣,在实际应用中,应结合实际情况选择最合适的栖息地适宜度评价方法。     

Ecological issues and risk assessment in China

As a result of economic development and population explosion, global ecological environments have been severely disturbed and markedly changed. An ecological crisis involving desertification, soil erosion, degradation of land quality, loss of biodiversity and global climate change has been brought about all over the world. In order to manage ecosystems efficiently, it is necessary to assess ecological risk at multiple scales. Ecological risk is the probability that a region and/or site will experience defined ecological or environmental problems. In this paper, the ecological risks of soil erosion, desertification, and acid deposition have been assessed on a national scale according to natural and human factors, such as topography, soil, vegetation and climate. This assessment has provided very useful information for ecological environmental management in China.     

Monitoring the growth of American beech affected by beech bark disease in Maine using the Kalman filter

The effect of beech bark disease on tree growth was tracked using paired resistant and susceptible American beech trees in two locations in Maine. Within each site, the paired trees were chosen in close proximity and with similar morphological characteristics (e.g. stem diameter and crown class) to minimize environment effects in subsequent analysis. A Kalman filter approach was employed to analyse the yearly time-dependent mean differences between paired susceptible and resistant tree-ring widths using simple structural time series models in state space form. On one site, under the influence of a moderate maritime climate, stand dynamics is hypothesized to account for the 34 year difference in onset of decline of trees in codominant, versus those in the intermediate crown classes. The harsher winter conditions associated with the second, more northerly site and known to limit the insect component of the disease complex, are hypothesized to be more of a factor in the close (six year) difference in decline onset between the two crown classes on this site. Some strengths and cautions in the Kalman filter approach are discussed in relation to the analysis of time-dependent trends in tree-ring series.     

Maximum likelihood method for parameter estimation in non-linear models with below detection data

The maximum likelihood (ML) method for regression analyzes of censored data (below detection limit) for nonlinear models is presented. The proposed ML method has been translated into an equivalent least squares method (ML-LS). A two stage iterative algorithm is proposed to estimate statistical parameters from the derived least squares translation. The developed algorithm is applied to a nonlinear model for prediction of ambient air CO concentration in terms of concentrations of respirable particulate matter (RSPM) and NO₂. It has been shown that if censored data are ignored or estimated through simplifications such as (i) censored data are equal to detection limit, (ii) censored data are half of the difference between detection limit and lower limit (e.g., zero or background level) or (iii) censored data are equal to lower limit, this can cause significant bias in estimated parameters. The developed ML-LS method provided better estimates of parameters than any of the simplifications in censored data.     

A health risk assessment for fluoride in Central Europe

Like many elements, fluorine (which generally occurs in nature as fluoride) is beneficial to human health in trace amounts, but can be toxic in excess. The links between low intakes of fluoride and dental protection are well known; however, fluoride is a powerful calcium-seeking element and can interfere with the calcified structure of bones and teeth in the human body at higher concentrations causing dental or skeletal fluorosis. One of the main exposure routes is via drinking water and the World Health Organisation currently sets water quality guidelines for the element. In Central Europe, groundwater resources that exceed the guideline value of 1.5 mg l⁻¹ are widespread and effects on health of high fluoride in water have been reported. The aim of the current project was to develop a geographic information system (GIS) to aid the identification of areas where high-fluoride waters and fluorosis may be a problem; hence, where water treatment technologies should be targeted. The development of the GIS was based upon the collation and digitisation of existing information relevant to fluoride risk in Ukraine, Moldova, Hungary and Slovakia assembled for the first time in a readily accessible form. In addition, geochemistry and health studies to examine in more detail the relationships between high-fluoride drinking waters and health effects in the population were carried out in Moldova and Ukraine demonstrating dental fluorosis prevalence rates of 60–90% in adolescents consuming water containing 2–7 mg l⁻¹ fluoride.     

Uncertainty in epidemiology and health risk and impact assessment

Environmental epidemiology and health risk and impact assessment have long grappled with problems of uncertainty in data and their relationships. These uncertainties have become more challenging because of the complex, systemic nature of many of the risks. A clear framework defining and quantifying uncertainty is needed. Three dimensions characterise uncertainty: its nature, its location and its level. In terms of its nature, uncertainty can be both intrinsic and extrinsic. The former reflects the effects of complexity, sparseness and nonlinearity; the latter arises through inadequacies in available observational data, measurement methods, sampling regimes and models. Uncertainty occurs in three locations: conceptualising the problem, analysis and communicating the results. Most attention has been devoted to characterising and quantifying the analysis—a wide range of statistical methods has been developed to estimate analytical uncertainties and model their propagation through the analysis. In complex systemic risks, larger uncertainties may be associated with conceptualisation of the problem and communication of the analytical results, both of which depend on the perspective and viewpoint of the observer. These imply using more participatory approaches to investigation, and more qualitative measures of uncertainty, not only to define uncertainty more inclusively and completely, but also to help those involved better understand the nature of the uncertainties and their practical implications.     

Uncertainty in the assessment of hazard,exposure and risk

The terminology, concepts and current approaches to uncertainty in the assessment of hazard, exposure and risk are reviewed. Five generic questions are discussed on uncertainty, including sources, levels, when and how it should be dealt with or reduced, what are our gaps in understanding and how they can be addressed. A case study of lead exposure of children in Lavrion, Greece, is used to exemplify these questions and possible answers. Estimation of uncertainty may be improved by the use of interorganisational studies to capture sources of uncertainty that are often overlooked. Gaps identified in our understanding of uncertainty include: a limitation in the availability of basic measurements, a lack of knowledge of the environmental processes, an inability to predict the effects of mixtures, the aetiology of disease and devising procedures for optimal resource allocation in impact assessment.     

Air pollution-oriented ecological risk assessment in Xiamen city,China

Urban energy consumption is one of the most important causes of air pollution. Air pollution-oriented ecological risk assessment is of great significance to the promotion of urban environmental protection. This paper focuses on ecological risk in Xiamen city caused by air pollutant discharge from urban energy consumption. The Long-range Energy Alternatives Planning model was used to establish two scenarios of energy consumption in Xiamen city, and based on different scenarios, we estimated urban energy consumption and discharge quantity of air pollutant (DQAP). A box model and an expert scoring method were used to calculate the air pollution burden (APB) of SO₂, NO₂, CO, PM₁₀ and PM_2.5 and to obtain the probabilities of different air pollution loads. An ecological risk assessment model was developed and utilized to predict Xiamen city’s ecological risks in 2020. The results showed that under an energy-saving scenario, the ecological risks for PM_2.5, SO₂ and NO₂ are high, whereas the ecological risks for CO and PM₁₀ are low. Under a baseline scenario, the ecological risks for PM_2.5, SO₂ and NO₂ are moderate, whereas the ecological risks for CO and PM₁₀ are low. In addition, the APB of SO₂, NO₂, CO, and PM_2.5, but not of PM₁₀, is predicted to rise. In the simulation, energy generation from coal is the main source of air pollution. Although the DQAP from automobiles is not high, it is predicted to rise year-on-year. In summary, the ecological risk due to pollution in Xiamen city is high, and the main pollutants are SO₂, NO₂ and PM_2.5.