Estimation of the Joint Risk from Multiple-Compound Exposure Based on Single-Compound Experiments

In the absence of data from multiple-compound exposure experiments, the health risk from exposure to a mixture of chemical carcinogens is generally based on the results of the individual single-compound experiments. A procedure to obtain an upper confidence limit on the total risk is proposed under the assumption that total risk for the mixture is additive. It is shown that the current practice of simply summing the individual upper-confidence-limit risk estimates as the upper-confidence-limit estimate on the total excess risk of the mixture may overestimate the true upper bound. In general, if the individual upper-confidence-limit risk estimates are on the same order of magnitude, the proposed method gives a smaller upper-confidence-limit risk estimate than the estimate based on summing the individual upper-confidence-limit estimates; the difference increases as the number of carcinogenic components increases.     

Reducing Conservatism in Risk Estimation for Mixtures of Carcinogens

The excess cancer risk that might result from exposure to a mixture of chemical carcinogens usually must be estimated using data from experiments conducted with individual chemicals. In estimating such risk, it is commonly assumed that the total risk due to the mixture is the sum of the risks of the individual components, provided that the risks associated with individual chemicals at levels present in the mixture are low. This assumption, while itself not necessarily conservative, has led to the conservative practice of summing individual upper-bound risk estimates in order to obtain an upper bound on the total excess cancer risk for a mixture. Less conservative procedures are described here and are illustrated for the case of a mixture of four carcinogens.     

基于MCMC的金融市场风险VaR的估计

针对现有 Va R计算中主流方法的缺陷 ,创新性地提出了一种基于马尔科夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)模拟的 Va R计算方法 ,以克服传统 Monte Carlo模拟的高维、静态性缺陷 ,提高估算精度 .通过对美元国债的实证分析和计算 ,验证了 MCMC方法的优越性 .     

Correlations Between Parameters in Risk Models: Estimation and Propagation of Uncertainty by Markov Chain Monte Carlo

Monte Carlo simulation has become the accepted method for propagating parameter uncertainty through risk models. It is widely appreciated, however, that correlations between input variables must be taken into account if models are to deliver correct assessments of uncertainty in risk. Various two-stage methods have been proposed that first estimate a correlation structure and then generate Monte Carlo simulations, which incorporate this structure while leaving marginal distributions of parameters unchanged. Here we propose a one-stage alternative, in which the correlation structure is estimated from the data directly by Bayesian Markov Chain Monte Carlo methods. Samples from the posterior distribution of the outputs then correctly reflect the correlation between parameters, given the data and the model. Besides its computational simplicity, this approach utilizes the available evidence from a wide variety of structures, including incomplete data and correlated and uncorrelated repeat observations. The major advantage of a Bayesian approach is that, rather than assuming the correlation structure is fixed and known, it captures the joint uncertainty induced by the data in all parameters, including variances and covariances, and correctly propagates this through the decision or risk model. These features are illustrated with examples on emissions of dioxin congeners from solid waste incinerators.     

Calculating the Hazard Function and Probability of Tumor for Cancer Risk Assessment When the Parameters Are Time-Dependent

The probability of tumor and hazard function are calculated in a stochastic two-stage model for carcinogenesis when the parameters of the mode are time-dependent. The method used is called the method of characteristics.     

Measures of Compounding Conservatism in Probabilistic Risk Assessment

Concern about the degree of uncertainty and potential conservatism in deterministic point estimates of risk has prompted researchers to turn increasingly to probabilistic methods for risk assessment. With Monte Carlo simulation techniques, distributions of risk reflecting uncertainty and/or variability are generated as an alternative. In this paper the compounding of conservatism⁽¹⁾ between the level associated with point estimate inputs selected from probability distributions and the level associated with the deterministic value of risk calculated using these inputs is explored. Two measures of compounded conservatism are compared and contrasted. The first measure considered, F , is defined as the ratio of the risk value, R _d, calculated deterministically as a function of n inputs each at the j th percentile of its probability distribution, and the risk value, R _j that falls at the j th percentile of the simulated risk distribution (i.e., F=R_d/R_j). The percentile of the simulated risk distribution which corresponds to the deterministic value, R_d , serves as a second measure of compounded conservatism. Analytical results for simple products of lognormal distributions are presented. In addition, a numerical treatment of several complex cases is presented using five simulation analyses from the literature to illustrate. Overall, there are cases in which conservatism compounds dramatically for deterministic point estimates of risk constructed from upper percentiles of input parameters, as well as those for which the effect is less notable. The analytical and numerical techniques discussed are intended to help analysts explore the factors that influence the magnitude of compounding conservatism in specific cases.     

Mlonte Carlo Techniques for Quantitative Uncertainty Analysis in Public Health Risk Assessments

Most public health risk assessments assume and combine a series of average, conservative, and worst-case values to derive a conservative point estimate of risk. This procedure has major limitations. This paper demonstrates a new methodology for extended uncertainty analyses in public health risk assessments using Monte Carlo techniques. The extended method begins as do some conventional methods--with the preparation of a spreadsheet to estimate exposure and risk. This method, however, continues by modeling key inputs as random variables described by probability density functions (PDFs). Overall, the technique provides a quantitative way to estimate the probability distributions for exposure and health risks within the validity of the model used. As an example, this paper presents a simplified case study for children playing in soils contaminated with benzene and benzo(a)pyrene (BaP).     

Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses

Experimental animal studies often serve as the basis for predicting risk of adverse responses in humans exposed to occupational hazards. A statistical model is applied to exposure-response data and this fitted model may be used to obtain estimates of the exposure associated with a specified level of adverse response. Unfortunately, a number of different statistical models are candidates for fitting the data and may result in wide ranging estimates of risk. Bayesian model averaging (BMA) offers a strategy for addressing uncertainty in the selection of statistical models when generating risk estimates. This strategy is illustrated with two examples: applying the multistage model to cancer responses and a second example where different quantal models are fit to kidney lesion data. BMA provides excess risk estimates or benchmark dose estimates that reflects model uncertainty.     

半参数空间ZISF的估计、分类与蒙特卡罗模拟

零无效率随机前沿模型（ZISF）包含随机前沿模型和回归模型,两模型各有一定的发生概率,适用于技术无效生产单元和技术有效生产单元同时存在的情形。本文在ZISF的生产函数中引入空间效应和非参函数,并假设回归模型的发生概率为非参函数,构建了半参数空间ZISF。该模型可有效避免忽略空间效应导致的有偏且不一致估计量,也避免了线性模型的拟合不足。本文对非参函数采用B样条逼近,使用极大似然方法和JLMS法分别估计参数和技术效率。蒙特卡罗结果表明：①本文方法的估计精度和分类精度均较高。随着样本容量的增大,精度增加。②忽略空间效应或者非参数效应,估计精度和分类精度降低,文中模型有存在必要性。③忽略发生概率的非参数效应会严重降低估计和分类精度,远大于忽略生产函数的非参数效应的影响。     

Risk Assessment for Aflatoxin: An Evaluation Based on the Multistage Model

Lifetime cancer potency of alfatoxin was assessed based on the Yeh et al. study from China in which both aflatoxin exposure and hepatitis B prevalence were measured. This study provides the best available information for estimating the carcinogenic risk posed by aflatoxin to the U.S. population. Cancer potency of aflatoxin was estimated using a biologically motivated risk assessment model. The best estimate of aflatoxin potency was 9 (mg/kg/day)⁻¹ for individuals negative for hepatitis B and 230 (mg/kg/day)⁻¹ for individuals positive for hepatitis B.     

Cancer Risk Estimation for Mixtures of Coal Tars

Two-year chronic bioassays were conducted by using B6C3F1 female mice fed several concentrations of two different mixtures of coal tars from manufactured gas waste sites or benzo(a)pyrene (BaP). The purpose of the study was to obtain estimates of cancer potency of coal tar mixtures, by using conventional regulatory methods, for use in manufactured gas waste site remediation. A secondary purpose was to investigate the validity of using the concentration of a single potent carcinogen, in this case benzo(a)pyrene, to estimate the relative risk for a coal tar mixture. The study has shown that BaP dominates the cancer risk when its concentration is greater than 6,300 ppm in the coal tar mixture. In this case the most sensitive tissue site is the forestomach. Using low-dose linear extrapolation, the lifetime cancer risk for humans is estimated to be: Risk < 1.03 × 10⁻⁴ (ppm coal tar in total diet) + 240 × 10⁻⁴ (ppm BaP in total diet), based on forestomach tumors. If the BaP concentration in the coal tar mixture is less than 6,300 ppm, the more likely case, then lung tumors provide the largest estimated upper limit of risk, Risk < 2.55 × 10⁻⁴ (ppm coal tar in total diet), with no contribution of BaP to lung tumors. The upper limit of the cancer potency (slope factor) for lifetime oral exposure to benzo(a)pyrene is 1.2 × 10⁻³ per μg per kg body weight per day from this Good Laboratory Practice (GLP) study compared with the current value of 7.3 × 10⁻³ per μg per kg body weight per day listed in the U.S. EPA Integrated Risk Information System.     

Comparison of cancer slope factors using different statistical approaches.

The U.S. Environmental Protection Agency's cancer guidelines ( USEPA, 2005 ) present the default approach for the cancer slope factor (denoted here as s*) as the slope of the linear extrapolation to the origin, generally drawn from the 95% lower confidence limit on dose at the lowest prescribed risk level supported by the data. In the past, the cancer slope factor has been calculated as the upper 95% confidence limit on the coefficient (q*₁) of the linear term of the multistage model for the extra cancer risk over background. To what extent do the two approaches differ in practice? We addressed this issue by calculating s* and q*₁ for 102 data sets for 60 carcinogens using the constrained multistage model to fit the dose‐response data. We also examined how frequently the fitted dose‐response curves departed appreciably from linearity at low dose by comparing q₁, the coefficient of the linear term in the multistage polynomial, with a slope factor, s_c, derived from a point of departure based on the maximum liklihood estimate of the dose‐response. Another question we addressed is the extent to which s* exceeded s_c for various levels of extra risk. For the vast majority of chemicals, the prescribed default EPA methodology for the cancer slope factor provides values very similar to that obtained with the traditionally estimated q*₁. At 10% extra risk, q*₁/s* is greater than 0.3 for all except one data set; for 82% of the data sets, q*₁ is within 0.9 to 1.1 of s*. At the 10% response level, the interquartile range of the ratio, s*/s_c, is 1.4 to 2.0.     

基于VaR的现金流风险度量模型研究

与金融企业不同,非金融类企业拥有更多非经常交易且不易估值的资产,因此更关注其在将来某一时刻现金流的不确定性.把现金流在险值与金融工程技术中在险值的概念相结合,运用风险敞口模型分析和蒙特卡洛模拟等计量方法,为非金融类公司管理层、投资者和分析家提供一个简单具体而直接的现金流不确定性的评判指标.通过对在险值和现金流在险值的比较以及对现金流在险值度量模型发展脉络的分析,发现现金流在险值技术更能刻画出非金融类公司的财务风险;通过引入管理决策风险作为风险因子并改进风险敞口模型,计算样本公司的现金流在险值;进一步提出现金流在险值的应用价值和研究方向.     

An Exact Analysis of the Multistage Model Explaining Dose-Response Concavity

The traditional multistage (MS) model of carcinogenesis implies several empirically testable properties for dose-response functions. These include convex (linear or upward-curving) cumulative hazards as a function of dose; symmetric effects on lifetime tumor probability of transition rates at different stages; cumulative hazard functions that increase without bound as stage-specific transition rates increase without bound; and identical tumor probabilities for individuals with identical parameters and exposures. However, for at least some chemicals, cumulative hazards are not convex functions of dose. This paper shows that none of these predicted properties is implied by the mechanistic assumptions of the MS model itself. Instead, they arise from the simplifying "rare-tumor" approximations made in the usual mathematical analysis of the model. An alternative exact probabilistic analysis of the MS model with only two stages is presented, both for the usual case where a carcinogen acts on both stages simultaneously, and also for idealized initiation-promotion experiments in which one stage at a time is affected. The exact two-stage model successfully fits bioassay data for chemicals (e.g., 1,3-butadiene) with concave cumulative hazard functions that are not well-described by the traditional MS model. Qualitative properties of the exact two-stage model are described and illustrated by least-squares fits to several real datasets. The major contribution is to show that properties of the traditional MS model family that appear to be inconsistent with empirical data for some chemicals can be explained easily if an exact, rather than an approximate model, is used. This suggests that it may be worth using the exact model in cases where tumor rates are not negligible (e.g., in which they exceed 10%). This includes the majority of bioassay experiments currently being performed.     

A Common Rationale for Global Sensitivity Measures and Their Estimation

Measures of sensitivity and uncertainty have become an integral part of risk analysis. Many such measures have a conditional probabilistic structure, for which a straightforward Monte Carlo estimation procedure has a double‐loop form. Recently, a more efficient single‐loop procedure has been introduced, and consistency of this procedure has been demonstrated separately for particular measures, such as those based on variance, density, and information value. In this work, we give a unified proof of single‐loop consistency that applies to any measure satisfying a common rationale. This proof is not only more general but invokes less restrictive assumptions than heretofore in the literature, allowing for the presence of correlations among model inputs and of categorical variables. We examine numerical convergence of such an estimator under a variety of sensitivity measures. We also examine its application to a published medical case study.     

Principles of Good Practice for the Use of Monte Carlo Techniques in Human Health and Ecological Risk Assessments

We propose 14 principles of good practice to assist people in performing and reviewing probabilistic or Monte Carlo risk assessments, especially in the context of the federal and state statutes concerning chemicals in the environment. Monte Carlo risk assessments for hazardous waste sites that follow these principles will be easier to understand, will explicitly distinguish assumptions from data, and will consider and quantify effects that could otherwise lead to misinterpretation of the results. The proposed principles are neither mutually exclusive nor collectively exhaustive. We think and hope that these principles will evolve as new ideas arise and come into practice.     

Uncertainty Evaluation of Human Risk Analysis (HRA) of Chemicals by Multiple Exposure Routes

The application of an ISO standard procedure (Guide to the Expression of Uncertainty in Measurement (GUM)) is here discussed to quantify uncertainty in human risk estimation under chronic exposure to hazardous chemical compounds. The procedure was previously applied to a simple model; in this article a much more complex model is used, i.e., multiple compound and multiple exposure pathways. Risk was evaluated using the usual methodologies: the deterministic reasonable maximum exposure (RME) and the statistical Monte Carlo method. In both cases, the procedures to evaluate uncertainty on risk values are detailed. Uncertainties were evaluated by different methodologies to account for the peculiarity of information about the single variable. The GUM procedure enables the ranking of variables by their contribution to uncertainty; it provides a criterion for choosing variables for deeper analysis. The obtained results show that the application of GUM procedure is easy and straightforward to quantify uncertainty and variability of risk estimation. Health risk estimation is based on literature data on a water table contaminated by three volatile organic compounds. Daily intake was considered by either ingestion of water or inhalation during showering. The results indicate one of the substances as the main contaminant, and give a criterion to identify the key component on which the treatment selection may be performed and the treatment process may be designed in order to reduce risk.     

金融资产风险度量及其在风险投资中的应用——基于稳定分布的新视角

引入稳定分布对沪深两市指数数据进行检验,结果表明两指数具有“尖峰厚尾”的分形特征,在此基础上建立了DaR类风险测度,实证研究表明两指数跌幅时间序列存在协同跌幅共线性效应.其次,给出了蒙特卡洛稳定分布和正态分布模拟下的两类风险测度估计值,建立了离差率模型,结果表明稳定分布下的风险度量适合投资者进行风险管理.最后,研究了不同跟踪时间窗口下的风险测度指标MDD.投资者和风险管理人员不仅要关注VaR类风险,更要警惕DaR类风险指标.     

First-Order Reliability Analysis of Public Health Risk Assessment

This paper demonstrates a new methodology for probabilistic public health risk assessment using the first-order reliability method. The method provides the probability that incremental lifetime cancer risk exceeds a threshold level, and the probabilistic sensitivity quantifying the relative impact of considering the uncertainty of each random variable on the exceedance probability. The approach is applied to a case study given by Thompson et al. ⁽¹⁾ on cancer risk caused by ingestion of benzene-contaminated soil, and the results are compared to that of the Monte Carlo method. Parametric sensitivity analyses are conducted to assess the sensitivity of the probabilistic event with respect to the distribution parameters of the basic random variables, such as the mean and standard deviation. The technique is a novel approach to probabilistic risk assessment, and can be used in situations when Monte Carlo analysis is computationally expensive, such as when the simulated risk is at the tail of the risk probability distribution.