For short-term chemical inhalation exposures to hazardous chemicals, the incidence of a health effect in biological testing usually conforms to a general linear model with a probit link function dependent on inhalant concentration ^{n} ×

A key step in determining short-term inhalation exposure levels for hazardous vapors and gases is extrapolation to durations that were not tested experimentally (

For deriving AEGLs, NAS recommends using a generalized linear model (GLM) to relate concentration and exposure duration to the health effect incidence monitored in inhalation experiments in animals. GLM with a probit link function is also known as the multivariate probit regression. This is similar to the classical toxicological median lethal dose (LD_{50}) concept, but with the added dimension of time (

Such an analysis allows calculation of a chemical concentration that has a certain probability of causing an adverse health effect at the specified duration of exposure. For AEGL-3 (i.e. mortality) points of departure (POD), this is often the LC_{01} concentration, or the concentration with a 1% probability of causing death after a specified exposure duration (however, the NAS-preferred method is the lower 95% bound on the 5% probability).

Experiments confirm that for a given toxic effect, almost all airborne chemicals show a linear relationship on the log-log scale of

_{01} level of effect,

The constant

When incidence data allow, the probit regression is effective at interval estimation of the TLE (and even directly PODs). However, for many chemicals such information is unavailable. For these chemicals, the NAS recommends an alternative method. A point estimation of the TLE can be carried out based on _{50} level of effect) at multiple durations (

This method may be appealing when LC_{50}s are reported without experimental incidence data; however, this method does not carry over the statistical uncertainties of the LC_{50}s into the interval estimation of the TLE. It is also enticing for the risk assessor to pool LC_{50}s from multiple studies in order to derive a TLE, without regard to the heterogeneity between these studies. A number of TLEs from the AEGL technical support documents (TSDs) are derived this way.

AEGL TSDs represent the largest compendium of peer-reviewed toxicological information pertinent to short-term inhalation exposures. Therefore, it was chosen as the source of information for the present study. In the present study, incidence data for chemicals meta-analyzed by the AEGL Committee were scrutinized using the full range of statistical tests of the probit meta-analysis framework. These data satisfy two conditions: availability of incidence information from

Upon analyzing the data from 273 AEGL TSDs, it was found that 115 empirically-derived TLEs were identified by the AEGL Committee. Of them, 90 TLEs originated from mortality studies. Relevant experimental details such as study source, species, and the method of TLE derivation were also collected. Of the collected TLEs, 14 were based on pharmacokinetic modeling, 62 were calculated by the AEGL Committee using simple linear regression and 39 stemmed from probit analysis. For 41 chemicals, the AEGL Committee pooled data from multiple studies. These were either binomial incidence data (15 chemicals) or LC_{50}s (26 chemicals). For some chemicals, multiple TLEs have been derived for different severity tiers or species. For both 13 chemicals with pooled LC_{50}s and 15 chemicals for which the probit analysis was used, the binomial incidence data were available. For the remaining 13 chemicals, multiple-duration incidence data were not available so these chemicals were not processed further in this study. Thus, the final dataset contained binomial incidence data for 28 AEGL chemicals either directly from AEGL TSDs or from their cited literature (refer to

The first step for analysis of the AEGL incidence data was to calculate probit regressions using a procedure similar to the “Concentration × Time” option in the USEPA’s Benchmark Dose Software (BMDS) 2.7 (USEPA, Washington, DC). The procedure was encoded in MatLab^{®} 2017b (MathWorks, Inc., Natick, MA) to facilitate batch processing. The results of test calculations were identical to those of BMDS within the machine precision. Using incidence data from the original experimental studies, multivariate probit regressions were calculated for each chemical’s study using the natural logarithm-transformed values for concentration and time as in

After calculating the probit regressions for each study, Pearson’s χ^{2} statistic allowed determination of goodness-of-fit for the probit regression of a single study, ^{2}-distribution with the model’s degrees of freedom;

To test if the pooled studies for an individual chemical are parallel, a probit regression was calculated for each study, as well as a categorical probit regression that allows each study to have its own intercept on the probit axis (the parallel probit regression; ^{2} statistic for goodness-of-fit was then calculated for each probit regression. Studies were deemed parallel if the ^{2} statistics for each study, categorical regression with study intercepts, and the parallelism test, respectively.

Note, the use of the goodness-of-fit

For each chemical that was found to have non-parallel studies, the TLEs from the studies were evaluated as a single-group summary effect, with the TLE variance from the single-study probit regression used as the within-study variance. The common-effect model, also known as the fixed-effect model, and the random-effects model were used (

The uniformity among a chemical’s TLEs was evaluated using Cochran’s ^{2} statistic (the ratio of excess dispersion to total dispersion,

Additionally, the ^{2} values for the TLEs of each chemical were evaluated using a statistical rule of thumb, by which ^{2} < 30–40% suggests that heterogeneity might not be important (i.e. supports the common-effect model), while ^{2} > 75% suggest considerable heterogeneity (i.e. supports the random-effects model; ^{2} range in between these extremes is guided by scientific judgement. Further in the text, the latter is illustrated by the case of phosgene, whose ^{2} was 59%. Even though the underlying single-study data passed the

The AEGL Committee identified TLEs from pooled studies for 41 out of 79 unique chemicals with empirically-derived TLEs. For 15 chemicals with pooled data, the AEGL Committee derived meta-analytical TLEs by means of probit analysis. For the remaining chemicals, the Committee carried out simple linear regression analysis using

The first step of analysis involved testing for parallelism of probit planes fitted to the individual study data, as given by

For six of the chemicals, probit three-dimensional planes fitted to their individual study data were parallel and the coefficients for the categorical regression dummy variables were statistically significant,

Incidence data for eight chemicals were comprised of parallel-plane studies, but their categorical regression dummy variables were statistically insignificant,

For the half of studied chemicals, probit planes fitted to the individual study data did not pass the parallel test of Equation (

Hydrogen chloride (HCl). The AEGL Committee relies on an HCl TLE estimate of

Hydrogen sulfide. The AEGL TSD derives a TLE using simple linear regression on rat LC_{50} data compiled from four independent studies (

Oxygen difluoride. The AEGL Committee presents a TLE derived using probit regression on rat mortality incidence data compiled from two independent studies (

Phosgene. The AEGL Committee arrives at a summary TLE based on the

To corroborate these hypotheses, statistical testing for heterogeneity was carried out. The TLEs were evaluated as a single-group summary effect using the TLE variance, considering both the common-effect and random effects models. The TLE variance was used as the within-study variance to calculate the weighted summary effect. The first three chemicals did not pass the ^{2} values greater than 75%. Therefore, they were treated using the random-effects model.

Phosgene represented a special case. Although the phosgene data passed the ^{2} was estimated to 59% (95% CI: 0–90%). A relatively high ^{2}, along with a large uncertainty, did not warrant a common-effect treatment, especially considering the variation in lung tidal volumes at short durations. Instead, the random-effects model was applied to the phosgene data.

The random-effects model uses both the within-study TLE variances and between-studies variance to estimate the summary effect TLE. Unlike the common-effect model, which expects that the true TLE is measured in all studies, the random-effects model assumes that each study estimates a different TLE. Together, these TLEs make a distribution. Because the distribution of TLEs is postulated to be normal, the mean of this distribution was calculated as the summary effect, along with CIs that give the range of TLE variation that may be observed for this chemical in similar studies (

Incidence data for five of the ten remaining non-parallel-plane chemicals could be subjected to meta-analysis as well. For these, there was insufficient evidence to reject the hypothesis that the TLEs for each chemical were homogenous. Therefore, an alternative hypothesis was adopted, and these data were processed using the common-effect model (^{2} statistic. For all common-effect-treated chemicals, ^{2} was less than 3% (see the

The last five chemicals had multiple studies, whose data were neither parallel nor could be modeled using the fixed-effect or random-effects concepts. For each of these chemicals, multiple exposure durations have been reported only in one of the underlying studies. Thus, each chemical had only one study with an interval-estimated TLE (

The methodology of short-term inhalation exposure levels relies on a TLE or directly on a probit regression to carry out temporal extrapolation (

Toxicological quality and compatibility of combined studies defines the meaning of meta-analysis. The studies may be measuring the same true TLE or may be measuring several different true TLEs. Contingent on that, the resultant meta-analytical estimate may express either the ^{2}), which is postulated as an organic property of the studied data. This implies that additional studies may not necessarily result in reduction of CI on the TLE. A large non-reducible variability would imply that the laboratory data for the given chemical are such that the between-study TLE variability exceeds the within-study variance for different chemicals reported by

For two-thirds of the studied chemicals, however, no statistical justification for denying the hypothesis of a single common TLE was found. For these chemicals, there was no reason to suspect that different studies require different TLEs to explain the data. These data could be explained with just one, an ostensibly

For a few chemicals, no confident conclusion about meta-analytical quality of the TLE could be drawn. For these chemicals, only one multiple concentration-duration study per chemical was available, while single-duration studies disagreed with it. Since the single-duration studies were incompatible with the sole multiple duration study for a chemical, the latter was the designated study for the chemical’s TLE. The designated-study and random-effects TLEs were summarized in the same table (

If there is a need to combine more than two studies, the decision logic may need to be looped more than once to converge to a single summary-effect TLE. The below case of ammonia illustrates the procedure and provides an example of how the public health guidance may change depending on the method used to examine multiple studies (_{01} concentrations of 3374 and 3317 ppm from two mice studies, _{01} concentrations at the 5 AEGL durations) from the categorical probit regression also carry less uncertainty. Directly using a pooled data approach results in unrealistically low LC_{01} values with very wide confidence intervals. This may be why the AEGL committee extrapolated from a 1-h LC_{01} with a TLE instead of using a probit regression, despite the availability of the incidence data.

Using categorical regression on the ammonia studies, LC_{01} concentrations were estimated for all five AEGL durations directly from the fitted probit function using not only the most sensitive species (mice), but also engaging the response information from the rat study, because the rat information improves the accuracy of the slope. Such approach yields a lower 1-h LC_{01} for mice of 2669 ppm and a slightly less steep concentration-duration response (_{01} values for mice calculated at the AEGL-designated durations results in decreased short-term inhalation exposure levels by up to 25% (

The uncertainty in a TLE estimate depends on the fit of the probit model to the incidence data. A large uncertainty in coefficients may originate either from a poor probit fit to the data, a small number of the incidence data points, or both. Usually, uncertainty on the TLE can be reduced by recruiting more data. Of the studied chemicals, chloropicrin represents a good example. An interval estimate of chloropicrin’s TLE using only the

Nevertheless, most of the chemicals in the present study garnered small uncertainties in their TLE estimates. However, several present the conundrum of having both their TLEs and associated CIs outside of default bounds of 1 and 3. These precise TLEs outside of the default 1 and 3 suggest that the single-sided 95%-CI defaults proposed based on the original 20-chemical study of

The AEGL committee often derives TLEs by simple linear regression, i.e.

Chemical risk assessment often confronts the challenge of selecting a key study from multiple studies that could be used for deriving health guidance. The studies may vary in species, statistical power, and laboratory methods, and it may be elusive which study to choose. By designating only one study as a key study, information from complementary studies that could contribute to the understanding of a chemical’s toxicological response is lost. However, correct joint analysis of multiple studies requires a valid meta-analytical framework. Without such a framework, results may be skewed in an indeterminate manner. The resulting inhalation guidance levels may be under-protective or needlessly over-protective. In the present work, uncertainty in temporal extrapolation of short-term inhalation exposures levels was quantified. The quantification exposed commonalities and conflicts among the published studies. Examination of probit meta-analyses performed on 28 chemicals with mortality incidence data has suggested a decision tree for incorporating multiple studies in a statistically appropriate manner for risk assessment of short-term inhalation exposures. The decision tree provides a foundation for evidence-based public health assessment of short-term inhalation exposure scenarios pertinent to emergency response, hazard detection, and preparedness planning. Future work may utilize this framework to update inhalation guidance for these and other chemicals of interest to ATSDR.

J.H., C.R.C., and R.C.S. were supported by a fellowship from the Oak Ridge Institute for Science and Education.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Disclaimer

The findings and conclusions in this report are those of the authors and do not necessarily represent the views of the Agency for Toxic Substances and Disease Registry.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary materials

Supplementary materials to this article can be found online at

_{50}values

Visualization of the relationship between concentration (

Results of categorical regression probit analysis for chemicals with parallel-plane studies. Panel (a) represents a collection of chemicals’ TLE interval estimates arranged as a forest plot. The estimates are baed on incidence data from individual studies, pooled studies, and the categorical probit regression. Panel (b) illustrates a typical parallel relationship between probit planes of a chemical. It represents the second chemical on the list and includes the ammonia data from the

Results of probit analysis for chemicals with pooled-study data. Panel (a) represents TLE estimates for each chemical arranged as a forest plot. The TLE estimates were calculated based on individual study data and when all available data were pooled together. Panel (b) illustrates how the pooled data from four studies for allyl alcohol,

Results of probit meta-analysis for chemicals studied using the common-effect model. Panel (a) represents TLE forest plots for each chemical calculated based on individual studies, pooled studies, and as the common-effect model summary effect. Panel (b) illustrates how the data from two studies for methyl hydrazine may not be parallel (

Results of probit meta-analysis for chemicals examined using the random-effects model. Panel (a) represents TLE forest plots for each chemical calculated based on individual studies, pooled studies, and as the random-effects model summary effect. Panel (b) illustrates how the data from two studies for oxygen difluoride (

Results of probit analysis for chemicals, whose sparse database allows only a single-study TLE estimation. Panel (a) is a forest plot of the TLEs for each chemical calculated based on their main study, and when the main study data were pooled with single-duration studies. Panel (b) illustrates how data from the single-duration studies,

Decision tree with logic for deriving a TLE for a chemical with multiple studies. The resulting decisions for the 28 chemicals analyzed in this study are shown in blue text.

Acute Exposure Guideline Levels (AEGLs) for ammonia. The concentrations of ammonia in the air are in parts per million (ppm).

Severity Tier | 10 min | 30 min | 1 h | 4 h | 8 h |
---|---|---|---|---|---|

AEGL-1 (discomfort) | 30 | 30 | 30 | 30 | 30 |

AEGL-2 (disabling) | 220 | 220 | 160 | 110 | 110 |

AEGL-3 (life-threatening) | 2700 | 1600 | 1100 | 550 | 390 |

Meta-analytical TLEs for chemicals with homogeneous multi-study data (true TLEs).^{a}

Category | Chemical | Species | Dataset^{b} | TLE (95% CIs) |
---|---|---|---|---|

Parallel | Acetonitrile | Rats | Pozzani (1959) | 1.38 (0.87, 1.88) |

AEGL probit of pooled studies | 1.55 (0.54, 2.5) | |||

Ammonia | Rats | Appleman (1982) | 2.01 (1.76, 2.26) | |

Mice | 2.18 (2.01, 2.35) | |||

Mice + Rats | AEGL citation of ten Berge TLE | 2.0 (1.6, 2.4) | ||

Probit of pooled studies | −3.33 (−17.64, 10.99) | |||

Chlorine trifluoride | Rats | Dost (1974) | 1.15 (1.03, 1.27) | |

AEGL LC_{50} regression | 1.3 | |||

Probit of pooled studies | 1.31 (1.08, 1.53) | |||

Chloropicrin | Rats | 2.12 (0.16, 4.08) | ||

AEGL probit of pooled studies | 2.31 (1.06, 3.56) | |||

Ethylene oxide | Rats | Nachreiner (1992) | 1.39 (0.99, 1.65) | |

AEGL LC_{50} regression | 1.21 | |||

Probit of pooled studies | 1.24 (0.95, 1.53) | |||

Hydrogen selenide | Rats | Zwart (1992) | 1.96 (1.24, 2.68) | |

AEGL probit of pooled studies | 2.51 (1.37, 3.66) | |||

Pooled | Allyl alcohol | Rats | 0.43 (−5e + 4, 5e + 4) | |

Union Carbide Corp. (1965) | 4.54 (−1e + 6, 1e + 6) | |||

Dimethylamine | Rats | IRDC (1992) | 1.96 (1.43, 2.50) | |

AEGL LC_{50} regression | 2.81 | |||

Hexafluoroacetone | Rats | Dupont (1965) | 1.00 (0.94, 1.06) | |

AEGL LC_{50} regression | 0.93 | |||

Methanesulfonyl chloride | Rats | Pennwalt Corp. (1987) | 0.66 (0.61, 0.71) | |

AEGL probit of pooled studies | 0.71 (0.30, 1.11) | |||

Methyl iodide | Rats | EPA (2006) | 1.14 (0.61, 1.67) | |

Oxamyl | Rats | Dupont (1969) | 1.56 (1.13, 1.99) | |

AEGL LC_{50} regression | 1.59 | |||

Peracetic acid | Rats | Janssen (1989) | 14.44 (−94.0, 122.8) | |

AEGL LC_{50} regression | 1.6 | |||

Sulfuric acid | Mice | Runckle and Hahn (1976) (AEGL used probit of mice only) | 1.27 (0.81, 1.73) | |

Rats | Runckle and Hahn (1976) | 3.25 (1.56, 4.94) | ||

Common-effect meta-analysis | Carbon tetrachloride | Rats | Adams (1952) | 2.42 (1.99, 2.86) |

Dow Chemical (1960) | 2.79 (2.30, 3.28) | |||

Mellon Institute (1947) | 1.61 (−2e + 6, 2e + 6) | |||

AEGL LC_{50} regression | 2.53 | |||

Probit of pooled studies | 2.43 (2.09, 2.77) | |||

Methyl hydrazine | Dogs | 0.97 (0.94, 1.01) | ||

Monkeys | 1.03 (0.92, 1.13) | |||

Dogs + Monkeys | AEGL LC_{50} regression | 0.99 (dogs) 0.97 (monkeys) | ||

Probit of pooled studies | 0.99 (0.82, 1.16) | |||

Nitrogen dioxide | Dogs | Hine (1970) | 5.25 (1.53, 8.89) | |

Guinea pigs | Hine (1970) | 3.85 (2.05, 5.66) | ||

Mice | Hine (1970) | 4.41 (3.84, 4.99) | ||

Rabbits | Hine (1970) | 3.39 (2.10, 4.68) | ||

Rats | Hine (1970) | 3.81 (3.13, 4.49) | ||

Dogs + Guinea pigs + Mice + Rabbits + Rats | AEGL citation of ten Berge TLE | 3.5 (2.7, 4.3) | ||

Probit of pooled studies | 3.98 (3.38, 4.57) | |||

Nitrogen trifluoride | Rats | Vernot (1973) | 1.02 (0.95, 1.09) | |

Dost (1970) | 1.27 (−3e + 4, 3e + 4) | |||

Torkelson (1962) | 1.15 (−6e + 4, 6e + 4) | |||

AEGL probit of pooled studies | 1.23 (1.03, 1.43) | |||

Probit of pooled studies (with 5000 ppm data) | 1.24 (1.06, 1.42) | |||

Tear gas (CS, 2-Chlorobenzylidenemalononitrile) | Rats | McNamara (1969) | −0.58 (−5.22, 4.06) | |

Ballantyne (1972) | 0.71 (0.63, 0.79) | |||

Ballantyne (1978) | 1.21 (−9.83, 12.25) | |||

AEGL probit of pooled studies | 0.70 (0.54, 0.87) | |||

The chemicals are categorized by the statistically most appropriate method of analysis, identified by the bold rows.

Shows dataset labels, not the entire inventory of studies. Refer to

Synthetic and designated study TLEs estimated from heterogeneous data.^{a}

Method of analysis | Chemical | Species | Dataset^{b} | TLE (95% CIs) |
---|---|---|---|---|

Random- effects meta-analysis | Hydrogen chloride | Rats | Darmer (1974) | 0.83 (0.77, 0.89) |

Mice | Darmer (1974) | 1.21 (0.99, 1.44) | ||

Mice + Rats | AEGL citation of ten Berge TLE | 1.0 (0.7, 1.3) | ||

Hydrogen sulfide | Rats | 8.27 (3.38, 13.17) | ||

Prior (1988) | 2.07 (1.57, 2.56) | |||

AEGL LC_{50} regression | 4.35 | |||

Probit of pooled studies | 3.69 (2.97, 4.41) | |||

Oxygen difluoride | Rats | 0.86 (0.81 0.92) | ||

1.94 (0.95, 2.94) | ||||

AEGL citation of ten Berge TLE | 1.1 (1.0, 1.2) | |||

AEGL probit of pooled studies | 1.11 (0.82, 1.40) | |||

Phosgene | Rats | 0.79 (0.74, 0.84) | ||

Mice | 0.74 (0.65, 0.79) | |||

Rats + Mice | AEGL LC_{50} regression | 1 | ||

Probit of pooled studies | 0.77 (0.70, 0.83) | |||

Designated study analysis | Acrylonitrile | Rats | ||

AEGL citation of ten Berge TLE | 1.1 (1.0, 1.2) | |||

AEGL probit of pooled studies | 1.09 (0.98, 1.21) | |||

Fenamiphos | Rats | Thyssen (1979) | ||

AEGL probit of pooled studies | 4.78 (1.42, 8.15) | |||

Probit of pooled studies | 4.78 (0.93, 8.63) | |||

Methyl bromide | Rats | |||

AEGL LC_{50} regression | 1.2 | |||

Probit of pooled studies | 1.58 (1.33, 1.83) | |||

Perfluoroisobutylene | Rats | |||

AEGL LC_{50} regression | 1.04 | |||

Probit of pooled studies | 1.06 (0.99, 1.13) | |||

1,1,1-Trichloroethane | Rats | |||

AEGL LC_{50} regression | 3 | |||

Probit of pooled studies | 2.23 (1.23, 3.23) |

The summary effect TLE is bolded for each chemical’s random-effects meta-analysis. For chemicals requiring a designated study, the study and its resulting TLE are also bolded.

Shows dataset labels, not the entire inventory of studies. Refer to

Comparison of the published and recalculated AEGLs for gaseous hydrogen chloride. The concentrations are in parts per million (ppm).

Time | 10 min | 30 min | 1 h | 4 h | 8 h |
---|---|---|---|---|---|

AEGL-3 | 620 | 210 | 100 | 26 | 26 |

Recalculated | 381 | 172 | 100 | 12 | 12^{a} |

Difference | 40% | 20% | 0% | 2-fold | 2-fold |

The AEGL TSD ackowledges uncertainty in extrapolation from 1-h to 8-h duration, however, adopts the least health protective approach extrapolating from a shorter 4-h duration to longer 8-h duration, essentially, using an infinitely large TLE. With evidence-based uncertainty in mind, an 8-h exposure level would be 4 ppm, i.e. the difference would increase 7-fold.

Comparison of short-term inhalation exposure levels for ammonia derived using three meta-analytical procedures.

Ammonia inhalation guidance (concentrations in ppm) | 10 min | 30 min | 1 h | 4 h | 8 h | |
---|---|---|---|---|---|---|

AEGL Committee procedure | 1-h LC_{01} from mice studies | 3300 | ||||

Divide by total UF of 3 | 1100 | |||||

Extrapolate to other durations using TLE = 2 from pooled mice and rat studies (AEGL-3 levels) | 2700 | 1600 | 1100 | 550 | 390 | |

Pooled probit regression | LC_{01} for rat & mice studies in a pooled regression (95% CI) | 2.5 (0.00009–54) | 3.6 (0.0003–57) | 4.3 (0.0007–61) | 6.4 (0.003–78) | 7.9 (0.005–94) |

Divide by total UF of 3 (recalculated AEGL-3 levels) | 0.83 | 1.2 | 1.4 | 2.3 | 2.6 | |

Categorical probit regression approach | LC_{01} for mice studies in categorical regression (95% CI) | 6100 (5400–6700) | 3700 (3200–4000) | 2700 (2300–2900) | 1400 (1200–1600) | 1000 (850–1200) |

Divide by total UF of 3 (recalculated AEGL-3 levels) | 2000 | 1200 | 890 | 470 | 340 |