Weibull Dose-response Model Research Articles

Probabilistic framework for assessing the arsenic exposure risk from cooked fish consumption.

Geogenic arsenic (As) contamination of groundwater is a major ecological and human health problem in southwestern and northeastern coastal areas of Taiwan. Here, we present a probabilistic framework for assessing the human health risks from consuming raw and cooked fish that were cultured in groundwater As-contaminated ponds in Taiwan by linking a physiologically based pharmacokinetics model and a Weibull dose-response model. Results indicate that As levels in baked, fried, and grilled fish were higher than those of raw fish. Frying resulted in the greatest increase in As concentration, followed by grilling, with baking affecting the As concentration the least. Simulation results show that, following consumption of baked As-contaminated fish, the health risk to humans is <10(-6) excess bladder cancer risk level for lifetime exposure; as the incidence ratios of liver and lung cancers are generally acceptable at risk ranging from 10(-6) to 10(-4), the consumption of baked As-contaminated fish is unlikely to pose a significant risk to human health. However, contaminated fish cooked by frying resulted in significant health risks, showing the highest cumulative incidence ratios of liver cancer. We also show that males have higher cumulative incidence ratio of liver cancer than females. We found that although cooking resulted in an increase for As levels in As-contaminated fish, the risk to human health of consuming baked fish is nevertheless acceptable. We suggest the adoption of baking as a cooking method and warn against frying As-contaminated fish. We conclude that the concentration of contaminants after cooking should be taken into consideration when assessing the risk to human health.

Assessing the arsenic-contaminated rice ( Oryza sativa) associated children skin lesions

The purpose of this study was to assess the potential risk of children skin lesions from arsenic-contaminated rice ( Oryza sativa) consumption in West Bengal (India). Published age- and gender-specific skin lesions data in West Bengal were reanalyzed and incorporated into a Weibull dose–response model to predict children skin lesion prevalence. Monomethylarsonous acid (MMA(III)) levels in urine was used as a biomarker that could be predicted from a human physiologically based pharmacokinetic (PBPK) model. This study integrated arsenic contents in irrigation water, bioaccumulation factors of paddy soil, cooking methods, and arsenic bioavailability of cooked rice in gastrointestinal tract into a probabilistic risk model. Results indicated that children aged between 13 and 18 years might pose a relative higher potential risk of skin lesions to arsenic-contaminated cooked rice (odds ratios (ORs) = 1.18 (95% CI 1.12–2.15)) than those of 1–6 years children (ORs = 0.98 (0.85–1.40)). This study revealed the need to consider the relationships between cooking method and arsenic in cooked rice when assessing the risk associated with children skin lesions from rice consumption. This study suggested that arsenic-associated skin lesions risk from arsenic-contaminated rice consumption would be reduced significantly by adopting traditional rice cooking method (wash until clean; rice:water = 1:6; discard excess water) as followed in West Bengal (India) and using water containing lower arsenic (e.g., <10 μg L −1) for cooking.

Risk assessment of arsenic-induced internal cancer at long-term low dose exposure

Previous epidemiological studies have indicated that ingested inorganic arsenic is strongly associated with a wide spectrum of internal cancers. Little is conducted, however, to assess health effects at long-term low dose exposures by linking biologically based mechanistic models and arsenic epidemiological data. We present an integrated approach by linking the Weibull dose–response function and a physiologically based pharmacokinetic (PBPK) model to estimate reference arsenic guideline. The proposed epidemiological data are based on an 8 years follow-up study of 10,138 residents in arseniasis-endemic areas in southwestern and northeastern Taiwan. The 0.01% and 1% excess lifetime cancer risk based point-of-departure analysis were adopted to quantify the internal cancer risks from arsenic in drinking water. Positive relationships between arsenic exposures and cumulative incidence ratios of bladder, lung, and urinary-related cancers were found using Weibull dose–response model r 2 = 0.58–0.89). The result shows that the reference arsenic guideline is recommended to be 3.4 μg L −1 based on male bladder cancer with an excess risk of 10 −4 for a 75-year lifetime exposure. The likelihood of reference arsenic guideline and excess lifetime cancer risk estimates range from 1.9–10.2 μg L −1 and 2.84 × 10 −5 to 1.96 × 10 −4, respectively, based on the drinking water uptake rates of 1.08–6.52 L d −1. This study implicates that the Weibull model-based arsenic epidemiological and the PBPK framework can provide a scientific basis to quantify internal cancer risks from arsenic in drinking water and to further recommend the reference drinking water arsenic guideline.

A Weibull-PBPK model for assessing risk of arsenic-induced skin lesions in children

Chronic arsenic exposure and skin lesions (keratosis and hyperpigmentation) are inextricably linked. This paper was to quantify the children skin lesions risks and to further recommend safe drinking water arsenic standard based on reported arsenic epidemiological data. We linked the Weibull dose–response function and a physiologically based pharmacokinetic (PBPK) model to estimate safe drinking water arsenic concentrations and to perform the risk characterization. We calculated odds ratios (ORs) to assess the relative magnitude of the effect of the arsenic exposure on the likelihood of the prevalence of children skin lesions by calculating proposed Weibull-based prevalence ratios of exposed to control groups associated with the age group-specific PBPK model predicted dimethylarsinite (MMA(III)) levels in urine. Positive relationships between arsenic exposures and cumulative prevalence ratios of skin lesions were found using Weibull dose–response model ( r 2 = 0.91–0.96). We reported that the safe drinking water arsenic standards were recommended to be 2.2 and 1 μg/L for male and 6 and 2.8 μg/L for female in 0–6 and 7–18 years age groups, respectively, based on hyperpigmentation with an excess risk of 10 − 3 for a 75 years lifetime exposure. Risk predictions indicate that estimated ORs have 95% confidence intervals of 1.33–5.12, 1.74–19.15, and 2.81–19.27 based on mean drinking water arsenic contents of 283.19, 282.65, and 468.81 μg/L, respectively, in West Bengal, India, Bangladesh, and southwestern Taiwan. Our findings also suggest that increasing urinary monomethylarsonic acid (MMA) levels are associated with an increase in risks of arsenic-induced children skin lesions.

Arsenic cancer risk posed to human health from tilapia consumption in Taiwan

Ingested inorganic arsenic is strongly associated with a wide spectrum of adverse health outcomes. We propose a bioaccumulation and the Weibull model-based epidemiological framework to accurately estimate the reference arsenic intake guideline for tilapia consumption and tilapia-cultured water arsenic concentration based on bioaccumulations of tilapia and gender/age/cancer-specific epidemiological data from the arseniasis-endemic area in Taiwan. Our results show a positive relationship between arsenic exposure and age/gender- and cancer-specific cumulative incidence ratio using Weibull dose–response model. Based on male bladder cancer with an excess lifetime cancer risk of 10 −4, we estimate the reference tilapia inorganic arsenic guideline value to be 0.084 μg g −1 dry wt based on the suggested daily consumption rate of 120 g d −1. Our findings show that consumption of tilapia in a blackfoot disease (BFD)-endemic area poses no significant cancer risk (excess cancer risks ranging from 3.4×10 −5 to 9.3×10 −5), implying that people in BFD-endemic areas are not readily associated with higher fatalities for bladder cancer exposed from tilapia consumption. We are confident that our model can be easily adapted for other aquaculture species, and encourage risk managers to use the model to evaluate the potential population-level long-term low-dose cancer risks. We conclude that, by integrating the bioaccumulation concept and epidemiological investigation of humans exposed to arsenic, we can provide a scientific basis for risk analysis to enhance risk management strategies.

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.

Reproducibility of the Dose-Response Curve of Steroid-Induced Cleft Palate in Mice

Pregnant CD-1 mice were exposed to cortisone acetate at doses ranging from 20 to 100 mg/kg/day on days 10-13 by oral and intramuscular routes. Multiple replicate assays were conducted under identical conditions to assess the reproducibility of the dose-response curve for cleft palate. The data were fitted to the probit, logistic, multistage or Armitage-Doll, and Weibull dose-response model separately for each route of exposure. The curves were then tested for parallel slopes (probit and logistic models) or coincidence of model parameters (multistage and Weibull models). The 19 replicate experiments had a wide range of slope estimates, wider for the oral than for the intramuscular experiments. For all models and both routes of exposure the null hypothesis of equality of slopes was rejected at a significant level of p < 0.001. For the intramuscular group of replicates, rejection of slope equality could in part be explained by not maintaining a standard dosing regime. The rejection of equivalence of dose-response curves from replicate studies showed that it is difficult to reproduce dose-response data of a single study within the limits defined by the dose-response model. This has important consequences for quantitative risk assessment, public health measures, or development of mechanistic theories which are typically based on a single animal bioassay.

Additional Evidence for Errors in DS86 Neutron Kerma for Hiroshima Based on Biological Dosimetry and Implications for Radiation Protection and Attributable Risk Evaluation

Results of neutron activation measurements in Hiroshima indicate that calculated neutron doses based on the DS86 dosimetry system may be too low. In this study, adjusted radiation doses (neutron dose multiplied by neutron RBE, plus gamma ray dose) to bone marrow in units of equivalent gamma ray Gy were estimated as a function of distance from the hypocentre using data for fatalities occurring between 2 days and 2 months after exposure to mixed neutron and gamma radiations, among people inside Japanese-style wooden houses. A Weibull dose-response model was used to relate mortality frequency to the adjusted dose to bone marrow. Adjusted doses calculated based on DS86 neutron and gamma kerma were compared to estimates based on biological dosimetry

Quantitative Risk Assessment for Teratological Effects

Abstract This article presents a quantitative procedure for using a “benchmark dose” to obtain low-dose risk estimates for reproductive and developmental toxic effects. This procedure combines the best features of the previously proposed methods for handling litter effects for teratology data and the currently used methods for quantitative risk assessment. The beta-binomial distribution is used to account for litter effects, and the Weibull dose—response model is used for modeling teratogenic effects. A benchmark dose, defined to be the lowest dose at which the excess risk does not exceed 1% with 95% confidence, is proposed to replace the no-observed-effect level (NOEL). The NOEL is generally the highest experimental dose that is not statistically different from the control; the NOEL approach does not use experimental data effectively for quantitative risk estimation. In this article, a lower limit on the safe dose is estimated by linearly extrapolating downward from the benchmark dose; this procedure is recommended because it is not strongly dependent on the model used in the data range. Linear extrapolation from a benchmark dose is essentially equivalent to the use of a safety factor in determining a safe dose from a NOEL. However, the linear extrapolation procedure reflects the risk at the estimated safe dose. Confidence limits on excess risks and safe doses are based on the beta-binomial likelihood ratio criterion rather than on the asymptotic distribution of the maximum likelihood estimates, because the latter have been shown to exhibit poor properties in the low-dose extrapolation problem. The proposed method is illustrated by application to a real data set.

Experimental design strategy for the Weibull dose response model

The objective of this research was to determine optimum design point allocation for estimation of relative yield losses from ozone pollution when the true and fitted yield-ozone dose response relationship follows the Weibull. The optimum design is dependent on the values of the Weibull model parameters. A transformation was developed which allowed the optimum design (by the determinant criterion) for one parametric situation to be translated to any other, and permitted the search for optimum designs to be restricted to one set of Weibull parameters. Optimum designs were determined for the case where the Weibull parameters are assumed known, and effects of deviating from the optimum designs were investigated. Several alternative design strategies were considered for protecting against incorrectly guessing the Weibull model parameters when their true values are not known.

The Weibull Function as a Dose‐Response Model to Describe Ozone Effects on Crop Yields1

Field experiments have demonstrated that ozone (O3) pollution can reduce yields of important crop species. The assessment of the impact of O3 is facilitated by the use of a family of dose response models that covers the range of responses observed in field O3 dose response studies. The Weibull dose response model is a flexible, biologically realistic, model that has been found useful for this purpose. The purposes of this study are i) to discuss analyses of dose response data using the Weibull model and its extensions, ii) to identify some of the problems inherent in the use of a nonlinear dose response model, and iii) to show application of the model to two sets of experimental data. The basic Weibuil model is a modification of the Weibull probability distribution function. Extensions of the basic model allow for class variables and other continuous variables in the experimental design. A bivariate form of the Weibull allows for independent effects of two pollutants. The use of the Weibull model with class variables (cultivars) is demonstrated using a 1977 winter wheat (Triticum aestivum L.) experiment grown at Raleigh, NC involving four cultivars exposed to four levels of O3 pollution. Tests of homogeneity over cultivars of the proportional yield responses show differential cultivar response to O3. The bivariate Weibull model is demonstrated using a 1981 soybean [Glycine max (L.) Merr.] experiment involving one cultivar exposed to the factorial set of treatments consisting of six levels of O3 and four levels of SO2 pollution. The test of lack of fit of the bivariate Weibuil model was nonsignificant, supporting the hypothesis that O3 and SO2 were acting independently. The percent predicted relative yield losses and their standard errors are given for two of the wheat cultivars and for the soybean cultivar.

A General Noninteractive Multiple Toxicity Model Including Probit, Logit, and Weibull Transformations

A multiple toxicity model for the quantal response of organisms is constructed based on an existing bivariate theory. The main assumption is that the tolerances follow a multivariate normal distribution function. However, any monotone tolerance distribution can be applied by mapping the integration region in the n-dimensional space of transforms on the n-dimensional space of normal equivalent deviates. General requirements to noninteractive bivariate tolerance distributions are discussed, and it is shown that bivariate logit and Weibull distributions, constructed according to the mapping procedure, meet these criteria. The univariate Weibull dose-response model is given a novel interpretation in terms of reactions between toxicant molecules and a hypothetical key receptor of the organism. The application of the multiple toxicity model is demonstrated using literature data for the action of gamma-benzene hexachloride and pyrethrins on flour beetles (Tribolium castaneum). Nonnormal tolerance distributions are needed when the mortality data include extreme response probabilities.