4.1. VOI ANALYTIC FRAMEWORK

Let R represent the population average risk of an adverse health effect due to exposure to a specified chemical within a given population. This risk can be defined as the fraction of the people exhibiting the adverse health effect due to chemical exposure. Let θ_tox and θ_exp denote the sets of parameters that govern the distribution of chemical toxicity and chemical exposure, respectively. Conditional on θ_tox and θ_exp, the population average risk R can be modelled as

Given R, the decision maker decides whether a chemical warrants exposure mitigation action, and if so, to what extent the level of exposure needs to be reduced. When there exists uncertainty in θ_tox and/or θ_exp, the uncertainty propagates to the population risk, which in turn leads to uncertainty in risk-based decision making. Uncertainty in toxicity may be reduced by collecting additional toxicity data, thereby reducing uncertainty in decision making.

The VOI analysis in this study aims to answer the following question: given that additional toxicity testing data may be beneficial, which toxicity testing methodology and assessment process provides the most value? The VOI framework presented in Hagiwara et al. (2022) provides a method to answer this question by explicitly considering the quality of the information provided by one of the two alternative toxicity tests considered here (i.e., two-year rodent bioassay versus five-day in vivo transcriptomic rodent assay), the cost of running such a test, and the delay in decision-making due to the additional testing and human health assessment process.

In applying the VOI framework, the associated costs and benefits of various decision-making approaches need to be defined to determine the ‘value’ of collecting additional toxicity testing data. As part of this process, an economic value is assigned to the costs associated with adverse health effects as well as exposure mitigation. The VOI is calculated over a pre-specified time horizon (which includes the pre- and post-regulation periods), as reflected by the reduction in total social cost (TSC) (which includes the health cost prior to regulation, the reduced health cost after regulation, and the control cost associated with regulation). The sum of the health costs associated with both the pre- and post-regulation periods is termed the total health cost (THC).

In the presence of uncertainty, TSC and THC are estimated using expected total social cost (ETSC) and expected total health cost (ETHC), where the expectation is taken with respect to the uncertainty distribution about population risk. Since both the ETSC and ETHC depend on the degree of uncertainty in risk, there exists a trade-off amongst the benefits of reduced uncertainty, the costs of testing, and delays in decision making.

The VOI framework quantifies the reduction in uncertainty in toxicity, and ultimately in risk, when additional toxicity tests are performed. This is achieved using Bayesian updating, in which the prior uncertainty distribution for toxicity (represented by the parameter θ_tox) is updated given the new toxicity data. This approach ultimately allows for evaluation of the reduction in ETSC/ETHC for different toxicity testing paradigms.

The time required to collect additional toxicity testing data is another important factor in VOI analysis. The delay in reaching a decision pending the collection and analysis of additional data results in a delay in implementing exposure mitigation action, with health costs accruing during this period of inaction. Earlier decisions to control chemical exposure can be advantageous since the TSC is reduced due to an earlier reduction in health costs. The benefit of an earlier decision is quantified by the economic value of this reduction.

The VOI framework integrates all the costs and consequences noted above, with consideration of the timeliness and value of new toxicity testing information collected in support of decision making and the human health assessment process. The framework can be applied to quantify the VOI of different toxicity testing strategies within multiple decision-making contexts, via consideration of context-specific goals. These goals may include the desire to minimize the TSC, to maximize a reduction in the THC, and/or to reduce uncertainty in order support an unambiguous assessment of risk relative to the regulatory objectives [See Hagiwara et al. (2022) for details].

4.2. DECISION MAKING CONTEXTS

The VOI framework requires specification of the decision rules by which the decision makers would choose regulatory action to reduce chemical exposures. These rules determine the specific circumstances under which VOI metrics associated with different testing strategies are quantified and compared. Following Hagiwara et al. (2022), two types of decision makers are considered, the BRDM and the TRDM. The BRDM makes choices to mitigate exposure when the reduction in health cost (or improvement in health benefit) outweighs the associated cost of control, as depicted in Figure 4-2. The proportionate level of exposure mitigation that minimizes the TSC is called the optimal reduction in exposure (ORE). In the presence of uncertainty, the BRDM chooses an action (or inaction) that would minimize the ETSC, with the assumption that the associated control cost monotonically increases with increasing exposure reduction. It should be noted that the BRDM is able to make a decision regardless of the degree of uncertainty in the available toxicity and exposure information. Therefore, the value of additional toxicity information is evaluated against the ETSC with the ORE based on currently available information.

Figure 4-2

Illustration of social cost (SC) as a function of increasing control cost (CC) and decreasing health cost (HC). Optimal reduction in exposure (ORE) that minimizes social cost is denoted by black solid circle.

The TRDM takes regulatory action when the average population risk exceeds a prespecified TRL. The TRDM must consider uncertainty when determining whether the risk is above or below the TRL. Specifically, the TRDM chooses to regulate a chemical if a prespecified lower quantile, q_L, of the uncertainty distribution for risk exceeds the TRL. Similarly, the TRDM would conclude that exposure mitigation is not required when a prespecified upper quantile, q_U, of the uncertainty is below the TRL. Unlike the BRDM, the TRDM cannot determine whether the chemical requires a regulatory action without collection of further evidence when the TRL lies in between the q_L and q_U A graphical representation of three types of situations, which the TRDM could encounter, is given in Figure 4-3 below.

Figure 4-3

Illustration of three types of scenarios that the TRDM may encounter. (A) The TRL is in between the 5^th and 95^th percentiles of the uncertainty distribution about risk and therefore TRDM cannot make decision whether to implement exposure mitigation action (more...)

4.3. VOI CONCEPTS AND METRICS

As noted in Section 4.1, the TSC is a sum of the THC, which reflects costs accrued prior to regulation and reduced costs after the implementation of regulation, and the total control cost (TCC) over a given time horizon [see Hagiwara et al. (2022), Eq. (10)]. The THC is a function of both the risk and the economic valuation of the adverse health effect(s) of interest, in addition to the time required to implement regulation, while the TCC is the cost of exposure mitigation once such action is implemented. The THC is reduced when exposure mitigation action is taken (and reduced more when action is taken earlier); however, the TCC increases as the reduction in exposure increases. When the time required to implement the regulation is fixed, there exists an ORE that minimizes the TSC.

In the presence of uncertainty, the ETSC is the objective function that the BRDM seeks to optimize when performing VOI analysis. In contrast, the TRDM uses the ETHC to calculate VOI. Both the ETSC and ETHC are the expected values of TSC and THC, respectively, for a given time horizon and decision-making paradigm. To assess the value of new information, a baseline expected value of current information, denoted as EV|CI, is calculated for each decision-making context. For the BRDM, EV|CI is the minimal value of the ETSC based on ORE obtained using the current level of uncertainty about the population average risk [see Hagiwara et al. (2022), Eq. (18)]. For the TRDM, EV|CI is the ETHC when uncertainty about toxicity and exposure is sufficiently great to preclude a regulatory decision, in which case no exposure mitigation action is taken based on the current level of uncertainty.

The expected value of immediate partial perfect information (EVIPPI) is the expected reduction in ETSC or ETHC (compared to the EV|CI case) achieved through immediate perfect information about one or more of the parameters that govern the population risk. In the present report, the term 'partial perfect information' is used to refer to an elimination of uncertainty about μ_tox, as toxicity testing can only reduce uncertainty about μ_tox, and not uncertainty about exposure. Thus, EVIPPI can serve as an upper limit on the VOI for any alternative toxicity-testing strategy that may be contemplated.

In practice, it is impossible to eliminate uncertainty completely. The expected value of immediate sample information (EVISI) measures the reduction in ETSC or ETHC achieved by a toxicity test that reduces uncertainty in μ_tox by a known degree or proportion. This VOI metric does not consider the delay in decision-making due to testing and human health assessment process. Therefore, it serves as an upper limit on the VOI for the specific toxicity-testing method under consideration.

The expected value of delayed sample information (EVDSI) differs from the EVISI in that it acknowledges that both the ETSC and ETHC are impacted by the delay in decision-making due to toxicity testing and human health assessment process. A positive EVDSI value implies that the reduction in uncertainty due to testing is beneficial after taking this delay into account. The difference between the EVISI and EVDSI, which is the loss in value solely due to the delay component, is referred to as the cost of delay (COD).

The cost of toxicity testing needs to be considered when determining the VOI. The expected net benefit of sampling (ENBS), defined as the difference between the EVDSI and the cost of testing (COT), reflects these costs. Finally, the return on investment (ROI), defined as the ratio between ENBS and COT, reflects the economic benefits per dollar spent in testing.

In practice, implementing VOI analyses requires careful consideration of the health endpoint or endpoints to be included in the analysis and the methods used to evaluate each of these endpoints in economic terms. With multiple health endpoints, consideration will also need to be given to the nature of the dose-response relationship for each endpoint. The BRDM and TRDM may also be subject to different constraints in real-world decision making, which may need to be considered in conducting VOI analyses in specific circumstances.

It should be noted that additional toxicity testing has value when the information obtained through testing results in a posterior decision that differs from the prior decision that would have been taken in the absence of collecting additional toxicity data. By reducing uncertainty about the toxicity of the chemical of interest, it is possible to make a better decision on the need for regulatory action, within the context of the decision-making paradigm being used. For the BRDM, if the additional information results in a posterior ORE that is different from the prior ORE, the additional toxicity testing data has provided value by virtue of the reduction in uncertainty. For the TRDM, the value of uncertainty reduction is realized when the additional toxicity testing information leads to a decision to regulate the chemical of interest, resulting in a concomitant socio-economic benefit expressed as a reduction in health cost. In other words, if additional toxicity testing information cannot alter the decision under either of our two decision rules (benefit-risk or target-risk), such information does not provide value under the VOI framework used here.

The key concepts in VOI analysis are summarized in Table 4-1. Precise mathematical definitions of these concepts can be found in Hagiwara et al. (2022). A visual illustration of the quantitative relationships among the output parameters discussed in this section is provided in Figure 4-4.

Figure 4-4

Illustration of the decision contexts and VOI metrics used in the current case study to compare ETAP and THHA.