Health Risk Assessment of Fluctuating Concentrations Using Lognormal Models

Saltzman, Bernard E.

doi:10.1080/10473289.1997.10464064

Cited by 11 publications

(4 citation statements)

References 5 publications

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“…To provide further intuition we consider the case in which concentration levels are log‐normally distributed as typically assumed in the literature (e.g., Lyles & Kupper, ; Rappaport, ; Saltzman, ; Meng et al, ). In particular, we assume that

ε_{t} \sim N false(0, σ^{2} false)

, so the (adjusted) natural log of the concentration

c_{t}^{a}

is distributed as

N false(μ^{H}, σ^{2} false)

or as

N false(μ^{L}, σ^{2} false)

.…”

Section: Characterization With Log‐normal Concentration Levelsmentioning

confidence: 99%

Sampling strategies in the assessment of long‐term exposures to toxic substances in air

Nocetti

Crimi

Rossner

2019

Remediation Journal

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The decision to mitigate exposures from vapor intrusion (VI) is typically based on limited data from 24-hour air samples. It is well documented that these data do not accurately represent long-term average exposures linked to adverse health effects. Limited decision guidance is currently available to determine the most appropriate sampling strategy, considering the cost of sampling alternatives along with the economic consequences of exposure-related health effects. We present a decision model that introduces economic and statistical considerations in evaluating alternative VI sampling methods. The model characterizes the best sampling method by factoring economic and health consequences of exposure, the variability of exposure, the cost of sampling and mitigation, and the likelihood of false-negatives and false-positives. Decision-makers can use results to select the sample size that maximizes net benefit. Conceptual and mathematical models are presented linking biological, statistical, and economic considerations to assess the cost and effectiveness of different sampling strategies. The model relates an average exposure concentration, determined statistically, to abatement costs and to the monetary value of health deterioration. The value of the information provided by different strategies is calculated and used to select the optimum sampling method.Simulations show that longer-term sampling methods tend to be more accurate and cost-effective than short-term samples. The ideal sampling strategy shows significant seasonal variation (it is typically optimal to use longer samples in the winter) and also varies significantly with the stringency of regulatory standards. Longer-term sample collection provides a more accurate representation of average VI exposure and reduces the likelihood of type I and type II errors. This reduces expected costs of mitigation and exposure (e.g., health consequences, legal and regulatory penalties), which in some cases can be quite significant. The model herein shows how these savings are balanced against the additional costs of longer-term sampling.

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ε_{t} \sim N false(0, σ^{2} false)

, so the (adjusted) natural log of the concentration

c_{t}^{a}

is distributed as

N false(μ^{H}, σ^{2} false)

or as

N false(μ^{L}, σ^{2} false)

.…”

Section: Characterization With Log‐normal Concentration Levelsmentioning

confidence: 99%

Sampling strategies in the assessment of long‐term exposures to toxic substances in air

Nocetti

Crimi

Rossner

2019

Remediation Journal

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“…Lu (2003) concluded in a study that the lognormal distribution can closely predict the particulate matter concentrations as compared to type V Pearson and Weibull distributions which over-estimated and under-estimated the actual values respectively. Further, concentrations of air pollutants and the frequency distributions are important factors in assessments of human health risks (Saltzman 1997 ). This is of paramount significance for potential policy-making for mitigating pollution episodes over the Indian megacities.…”

Section: Introductionmentioning

confidence: 99%

Frequency distribution of pollutant concentrations over Indian megacities impacted by the COVID-19 lockdown

Mondal

Sharma

Mandal

et al. 2021

Environ Sci Pollut Res

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The megacities experience poor air quality frequently due to stronger anthropogenic emissions. India had one of the longest lockdowns in 2020 to curb the spread of COVID-19, leading to reductions in the emissions from anthropogenic activities. In this article, the frequency distributions of different pollutants have been analysed over two densely populated megacities: Delhi (28.70° N; 77.10° E) and Kolkata (22.57° N; 88.36° E). In Delhi, the percentage of days with PM 2.5 levels exceeding the National Ambient Air Quality Standards (NAAQS) between 25 March and 17 June dropped from 98% in 2019 to 61% in 2020. The lockdown phase 1 brought down the PM 10 (particulate matter having an aerodynamic diameter ≤ 10 μm) levels below the daily NAAQS limit over Delhi and Kolkata. However, PM 10 exceeded the limit of 100 μgm −3 during phases 2–5 of lockdown over Delhi due to lower temperature, weaker winds, increased relative humidity and commencement of limited traffic movement. The PM 2.5 levels exhibit a regressive trend in the highest range from the year 2019 to 2020 in Delhi. The daily mean value for PM 2.5 concentrations dropped from 85–90 μgm −3 to 40–45 μgm −3 bin, whereas the PM 10 levels witnessed a reduction from 160–180 μgm −3 to 100–120 μgm −3 bin due to the lockdown. Kolkata also experienced a shift in the peak of PM 10 distribution from 80–100 μgm −3 in 2019 to 20–40 μgm −3 during the lockdown. The PM 2.5 levels in peak frequency distribution were recorded in the 35–40 μgm −3 bin in 2019 which dropped to 15–20 μgm −3 in 2020. In line with particulate matter, other primary gaseous pollutants (NO x , CO, SO 2 , NH 3 ) also showed decline. However, changes in O 3 showed mixed trends with enhancements in some of the phases and reductions in other phases. In contrast to daily mean O 3 , 8-h maximum O 3 showed a reduction over Delhi during lockdown phases except for phase 3. Interestingly, the time of daily maximum was observed to be delayed by ~ 2 h over Delhi (from 1300 to 1500 h) and ~ 1 h over Kolkata (from 1300 to 1400 h) almost coinciding with the time of maximum temperature, highlighting the role of meteorology versus precursors. Emission reductions weakened the chemical sink of O 3 leading to enhancement (120%; 11 ppbv) in night-time O 3 over Delhi during phases 1–3. Supplementary Information The online version contains supplementary material available at 10.1007/s11356-021-16874-z.

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“…A log-normal probability distribution of sensitivity thresholds f ( x ) yields a cumulative log-normal dose-response relationship F ( x ) that is cumbersome and not suited for nonlinear regression procedures. However, the cumulative log-normal function is closely approximated by the simple log-logistic model , , which can be expressed in terms of parameters that are readily interpretable and useful in the fields of toxicology and pharmacology: y = M i n + M a x − M i n 1 + false( ϵ / x false) β where the independent variable x is the “dose,” that is, the amount, concentration, or intensity of the affecter; the dependent variable y is the expected amount of the effect or proportion of the population experiencing the effect; parameter Min is the minimum effect or proportion affected; parameter Max is the maximum effect or proportion; parameter ϵ is the dose at the inflection point of the dose-response curve, i.e., the ED50, the dose at which the effect is reduced by 50% or half the population is affected; β is a parameter related to the maximum slope of the curve, which occurs at dose ϵ.…”

Section: Introductionmentioning

confidence: 99%

“…Contaminant concentrations are well described by log-normal distributions (13), and an assumption of log-normal frequency distributions of sensitivity thresholds underlies the widely-used probit analysis of dose-response relationships (14). A log-normal probability distribution of sensitivity thresholds f(x) yields a cumulative log-normal dose-response relationship F(x) (15) that is cumbersome and not suited for nonlinear regression procedures. However, the cumulative log-normal function is closely approximated by the simple log-logistic model (16,17), which can be expressed in terms of parameters that are readily interpretable and useful in the fields of toxicology and pharmacology:…”

Section: Introductionmentioning

confidence: 99%

A General Approach to Modeling Biphasic Relationships

Beckon

Parkins

Maximovich

et al. 2008

Environ. Sci. Technol.

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Biphasic relationships can be found throughout the sciences, especially in the dose-response relationships of pharmacology, toxicology, agriculture, and nutrition. Accurate modeling of biphasic dose-response is an essential step in establishing effective guidelines for the protection of human and ecosystem health, yet currently-used biphasic mathematical models lack biological rationale and fit only limited sets of biphasic data. To model biphasic relationships more closely over wider ranges of exposures, we suggest a simple, general, biologically reasonable modeling approach leading to a family of mathematical models that combine log-logistic functions: at least one for the upslope and one forthe downslope of the biphasic relationship. All parameters employed are meaningfully interpretable. These models can be used to test for the presence of biphasic effects, and they simplify to a standard log-logistic model in the special case where no biphasic effect can be detected. They offer the promise of improvement in assessment of the safety and efficacy of pharmaceuticals and nutrients as well as in determination of the toxicity of contaminants. Additionally, they may be useful in modeling nonmonotonic cause-effect relationships in other scientific disciplines.

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Health Risk Assessment of Fluctuating Concentrations Using Lognormal Models

Cited by 11 publications

References 5 publications

Sampling strategies in the assessment of long‐term exposures to toxic substances in air

Sampling strategies in the assessment of long‐term exposures to toxic substances in air

Frequency distribution of pollutant concentrations over Indian megacities impacted by the COVID-19 lockdown

A General Approach to Modeling Biphasic Relationships

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