Historical Context and Recent Advances in Exposure-Response Estimation for Deriving Occupational Exposure Limits

Figures & data

Figure 1 This figure shows the dichotomous specification of the added risk specification of the benchmark dose. The quantity P₀ is the probability of that response for unexposed subjects; P₀ + BMR represents the increased probability of response at the benchmark dose. Finally, the BMD is the dose associated with the point on f(d) associated with the population P₀ + BMR probability of adverse response.

Figure 2 Graph of the continuous specification of the benchmark dose based upon the figure of Budtz-Jorgensen et al.⁽³⁸⁾ The quantity X₀ is the abnormal response cutoff, P₀ is the probability of that response for unexposed subjects, and P₀ + BMR is represents the increased probability of response at the benchmark dose. Finally, the BMD is the dose associated with the point on f(d) associated with the population P₀ + BMR probability of adverse response.

Table 1 Common Impediments to Inference When Developing an Exposure-Response Relationship from Epidemiological Studies

Issue-Origins	Consequences	Fixes
Confounding bias -Other risk factors (RF) for outcome are associated with exposure^(^49^)	Under- or over-estimation of effects of exposure	Collect explicit information on confounding RFs or useful surrogates and model along with exposure effects.
Effect modification- Estimate of exposure effect depends on other RFs^(^49^)	RF-specific exposure response estimates result; response is not generalizable	Derive estimate for exposure response at some specified level of confounders, e.g., for population average smoking
Selection bias – Entry into study depends jointly on exposure status and outcome status^(^49^)	A problem for retrospective studies only; potentially fatal flaw when present	Achieve high participation rates; blind potential subjects and study operatives on study hypotheses; estimate maximum possible bias resulting
Healthy worker effect (HWE)- A special set of confounding RFs related to unknown health attributes of study participants that influence entry to study such as through hiring or fitness^(^49^)	The HWE can cause substantial underestimation of exposure effects depending on outcomes studied; can affect mortality and morbidity, cancer and non-cancer. The HWE may vary across demographic groups and over period of employment. If disease detection is superior in worker population overestimation of effect can occur.	Use internal comparison populations or, with external comparisons (e.g., national rates), estimate population differences.
Healthy worker survivor effect (HWSE)-Confounding that is time-dependent due to changing composition of workforce with duration of employment. For example, generally healthier workers may stay employed longer than others, long duration workers may smoke less, employed workers may have better healthcare.^(^50^)	Inappropriate comparisons may result depending on study design and analysis, usually causing underestimation of exposure effects.	Sometimes, if there is sufficient variation in exposure levels across study population, modeling employment duration together with exposure metrics can reduce this bias.
Reverse Causation- A special case of survivor bias in which the advent of the disease or health effect itself alters a worker's exposure status through employment termination or other health-induced job changes.^(^51^)	Cases with the outcome effect may exhibit less cumulative exposure than non-cases even though the outcome was caused by the exposure; a fundamental modeling assumption is violated and model fitting can be disabled.	This would be a fatal flaw in most study designs. It is much less important with long latency diseases where recent exposures are discounted (lagged). It occurs particularly with outcomes in which there is a preclinical phase of irritancy, impairment, or hyper-responsiveness to the exposure causing the outcome. Complex analytical approaches based on matching algorithms have been proposed and applied.
Variable susceptibility- A wide gradient of susceptibility resulting in a higher incidence of health effects cases initially from the most susceptible subjects, possibly depleting some high-susceptibility subpopulations over time producing lower overall susceptibility with advancing cumulative exposures^(^52^)	Exposure metrics show supra-linear associations with outcomes – apparent diminishing or attenuating effects with increasing exposure. Low exposure extrapolation pertains increasingly to higher susceptibility subpopulations. Similarly, a low susceptibility subpopulation could be present whose proportion of the population would increase over time.	Impose a linear exposure-response for a subset of observation time with less cumulative exposure, or attempt to accommodate a duration-dependent decline in susceptibility within the exposure-response model.

Table 2 Dose Response Dataset I

Observation	Concentration (PPM)	# on test	# exhibiting the adverse response
1	0	20	1
2	12.5	20	1
3	25	20	4
4	50	20	8
5	100	5	5

Hypothetical dichotomous data set used as an example throughout the text to illustrate various methodologies in finding the critical dose.

Table 3 Dose Response Dataset II

Observation	Concentration (PPM)	# on test	# exhibiting the adverse response
1	0	10	0
2	10	10	0
3	20	10	3
4	40	10	4
5	80	10	6

Hypothetical dichotomous data set used as an example for Benchmark Dose estimation where there is significant model uncertainty when estimating the dose response.

Table 4 BMD Model Estimates

	BMD	BMDL	X^2 GOF P-Value	AIC	MA Weights^A	AIC^A
Probit	21.2	16.4	0.77	68.21	0.44	68.21
Multistage	21.9	12.1	0.76	68.49	0.14	70.49
Weibull	26.4	14.1	0.56	70.13	0.17	70.13
Gamma	25.4	13.5	0.48	70.72	0.13	70.72
Log Probit	25.4	14.3	0.40	71.31	0.09	71.31
Quantal Linear	10.9	7.2	0.19	73.54	0.03	73.54
MA Average Dose	22.8	14.5	NA	NA	NA	NA
MA Average Model	23.0	12.3	0.50	NA	NA	NA
Semiparametric	18.6	9.2	NA	NA	NA	NA

Computed benchmark doses across various estimation methodologies where the BMR = 10%, This is done using seven models available in the EPA BMDS model suite for dichotomous data described in Table II as well as the semiparametric method of Wheeler and Bailer.^{(30) A} The weights are computed using the AIC calculation method of Wheeler and Bailer⁽²⁷⁾ and not the BMDS software.

Table 5 BMD Model Estimates

	BMD	BMDL	X^2 GOF P-Value	AIC	MA Weights^A	AIC^A
Quantal Linear	8.7	5.8	0.78	43.97	0.341	45.97
Log Probit	13.0	3.3	0.66	45.30	0.176	47.38
Gamma	11.6	5.9	0.59	45.80	0.137	47.80
Weibull	11.0	5.9	0.59	45.85	0.133	47.85
Multistage	9.4	5.8	0.61	45.96	0.126	47.96
Probit	22.1	16.2	0.22	48.72	0.087	48.72
MA Average Dose	11.5	6.3	NA	NA	NA	NA
MA Average Model	11.1	5.3	0.40	NA	NA	NA
Semiparametric	15.1	8.5	NA	NA	NA	NA

Computed benchmark doses across various estimation methodologies where the BMR = 10%. This is done using seven models available in the EPA BMDS model suite for dichotomous data described in Table III as well as the semiparametric method of Wheeler and Bailer.^{(30) A} The weights are computed using the AIC calculation method of Wheeler and Bailer⁽²⁷⁾ and not the BMDS software.

Table 6 OEL Flowchart Showing Step-by-Step Process for Calculating the POD Using the BMD and a Suite of Models

	BMD Step	Action
1	Choice of models to be fit	Before the analysis develop a modeling approach that takes into account possible curvature that might be realistic. Models should be chosen on the basis of some a priori scientific rational (e.g., biologically relevant for carcinogenesis).
2	Fit models and estimate the BMD/BMDL using a prespecified BMR.	Given the model suite fit all models chosen and estimate the BMD/ BMDL at a prespecified BMR and confidence limit (typically taken to be BMR = 10% and confidence limit = 95%).
3	Select the best model given the data.	Using a statistical test (typically the Pearson chi-squared goodness of fit statistic) determine if the model adequately fits the data using some significance level (often.1) chosen prior to the analysis. Then from the remaining models use some predefined criterion (e.g., AIC) to pick the model to estimate the BMD/BMDL.
4	Calculate the POD from the BMD/BMDL.	With the best model chosen, use the BMD/BMDL to calculate the POD.

Table 7 OEL Estimation Methods

Method	Data Requirements	Considerations for use	Epidemiological Considerations	Caveats
NOAEL	Minimal data requirements	Use if no other method is appropriate or available.	Location and number of dose groups/exposure-strata is important.	Does not model the dose response curve and suffers from experimental design (dose-spacing) issues.
Traditional BMD	A minimum of two non-background responses with one partial response (i.e., not 100%)	Use if following current standard of exposure-response modeling.	Requires more sophistication on the modeler's part.	Overly optimistic inference poor coverage when true model is not known
Average Dose MA BMD	Same as traditional BMD	Use if output from standard exposure-response software allows this approach.	Potentiality for a large number of models to be averaged	Simple to implement with existing software but the method has poor coverage.
Average Model MA BMD	Same as traditional BMD	Use if computational resources allow for its implementation	Presently not extended for observational studies	Near nominal coverage for most situations. Requires non-standard (though readily available) software to implement.
Semiparametric BMD	Same as traditional BMD	Use if computational resources allow for its implementation.	Presently not extended for observational studies	Requires sophisticated software to implement.
Biologically Based Methods	Depends on the model more than empirical models.	Sufficient information exists on mode of action.	Sufficient info on biological features of model available in humans.	May allow better characterization of endpoint but requires knowledge of the mode of action. Still requires specification of which biological component is impacted by exposure.

List of the methods that can be used to develop an OEL; these methods are arranged in order of complexity as well as ability to account for model uncertainty. Here the NOAEL/LOAEL approach is the least complex and least able to account for uncertainty in the model form and the semiparametric methods are the most complex and most able to account for model uncertainty.

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