5 B

- 1

APPENDIX 5 B: ADDITIONAL SENSITIVITY ANALYSES RELATED TO THE OZONE HEALTH BENEFITS ANALYSIS
Overview The benefits analysis presented in Chapter 5 of this RIA is based on our current interpretation of the scientific and economic literature. That interpretation requires judgments regarding the best available data, models, and analytical methodologies and the assumptions that are most appropriate to adopt in the face of important uncerta inties. The majority of the analytical assumptions used to develop the main estimates of benefits have been reviewed and supported by EPA’s independent Science Advisory Board (SAB). Both EPA and the SAB recognize that data and modeling limitations as well as simplifying assumptions can introduce significant uncertainty into the estimates of benefits and that alternative choices exist for some inputs to the analysis, such as the concentration

- response functions for mortality. This appendix assesses the sensi tivity of the core benefits to: (a) the potential impact of thresholds in long

- term ozone exposure
- related mortality in incidence and benefits estimates (section 5B.2), (b) alternative response functions developed through expert elicitation (EE) for long

- t erm PM 2.5 exposure - related mortality (section 5B.3), and (c) alternative assumptions regarding income elasticity on benefits derived using willingness

- to
- pay (WTP) functions (section 5 B .3). For the core analysis, we estimated incidence and dollar benefits for two scenarios: 2025 and post

- 2025 (see Chapter 5, S ection s 5.2 and 5.4.3). However, in conducting these sensitivity analyses, we use d the 2025 scenario as the basis for making our calculations, since sensitivity analysis findings for this scenario woul d generally hold for the post

- 2025 scenario. I n addition to the three sensitivity analyses covered in this appendix, we also included two sensitivity analyses that are covered in detail in C hapter 5 . The first of these are estimates of dollar benefits asso ciated with mortality resulting from long

- term exposure to ozone. As discussed in S ection 5.2, while we felt that we had sufficient confidence to include incidence estimates associated with long

- term ozone exposure (based on effect estimates obtained from Jerrett et al., 2009) in the core analysis, limitations in our ability to specify an appropriate lag for5 B

- 2

reductions in this endpoint meant that we could not include dollar benefit estimates in the core analysis. Instead, we have included those values as se nsitivity analyses, including consideration of alternative lag structures (they are presented in Tables 5

- 20 and 5

- 27, respectively for the 2025 and post

- 2025 scenarios). 1 The second of the sensitivity analyses already covered in the chapter address es alte rnative models for short

- term ozone exposure
- rela ted mortality. As discussed in S ection 5.6.3.1, in addition to the two epidemiological studies (Smith et al., 2009 and Zanobetti and Sc h wartz 2008) that provide effect estimates for the core benefits estimat es, we have also considered seven additional epidemiological studies as sensitivity analyses. These additional studies includ e a mix of multi

- city and meta

- analysis designs. Results of this sensitivity analysis are presented in Tables 5

- 19 and 5

- 20 (incide nce and benefits, respectively for the 2025 scenario) and Tables 5

- 26 and 5

- 27 (incidence and benefits, respectively for the post
- 2025 scenario). 5B.1 Threshold Sensitivity Analysis for Premature Mortality Incidence and Benefits from Long - term Exposure to Ozone In estimating long

- term ozone mortality , we employ ed a continuous non

- threshold concentration

- response ( C

- R ) function relating ozone exposure to premature death . However, as discussed in S ection 5.6.3.1, there is uncertainty regarding the potential existence and location of a threshold in the C

- R function relating mortality and long

- term ozone concentrations. Thus, we have included a sensitivity analysis exploring the impact of potential th resholds in the C

- R relationship on estimates of long

- term exposure
- related mortality that were evaluated in Jerrett et al. (2009), consistent with advice from CASAC ( Frey, 2014 ). In their memo clarifying the results of their study (Sasser, 2014), the aut hors note that in terms of goodness of fit, long

- term health risk models including ozone clearly performed better than models without ozone , indicating the improved predictions of respiratory mortality when ozone is included. In exploring different functio nal forms, the authors report that the model including a threshold at 56 ppb had the lowest log

- likelihood value of all models evaluated (i.e., linear models and models including thresholds ranging from 40

- 60 ppb), and thus provided the

1 The sensitivity analysis

- related benefits estimates presented in these tables include (a) benefits estimates reflecting application of a zero lag model and (b) estimates reflecting application of the same 20

- year segmented lag used in modeling benefits fo r PM 2.5 , together with application of a 3% and 7% discount rate. See S ections 5.6.3 and 5.6.4 for additional discussion of lags in relation to long

- term ozone
- related mortality.5 B

- 3

best overall statis tical fit to the data. However, they also note that it is not clear whether the 56 ppb threshold model is a better predictor of respiratory mortality than when using a linear (no

threshold) model for this dataset. Using one statistical test, the model with a threshold at 56 ppb was determined to be statistically superior to the linear model. Using another, more stringent test, none of the threshold models considered were statistically superior to the linear model. Under the less stringent test, although the threshold model produces a statistically superior prediction than the linear model, there is uncertainty about the specific location of the threshold, if one exists. This is because the confidence intervals on the model predictions indicate that a thresho ld could exist anywhere from 0 to 60 ppb. The authors conclude that considerable caution should be exercised in using any specific threshold, particularly when the more stringent statistical test indicates there is no significantly improved prediction. Bas ed on this additional information from the authors, we have chosen to reflect the uncertainty about the existence and location of a potential threshold by estimating mortality attributable to long

- term ozone exposures using a range of threshold

- based effec t estimates as sensitivity analyses. Specifically, we estimate long

term ozone mortality benefits using unique risk coefficients that include a range of thresholds from 40 ppb to 60 ppb in 5 ppb increments, while also including a model with a threshold equ al to 56 ppb, which had the lowest log

- likelihood value for all models examined. 2 Table 5B

- 1 provides the results of these sensitivity analyses (based on modeling incidence) for 60 ppb, 65 ppb and 70 ppb. We note that the same pattern in terms of relative reductions across thresholds (relative to the core estimate) would hold for the dollar benefit estimates generated for this endpoint.

2 There is a separate effect estimate (and associated standard error) for each of the fitted threshold models estimated in Jerrett et al. (2009). As a result, the sensitivity of estimated mortality attributable to long

- term ozone concentrations is affected by both the assumed threshold level (below which there is no effect of ozone ) and the effect estimate applied to ozone concentrations above the threshold.5 B

- 4

Table 5B - 1. Long - term Ozone Mortality Incidence at Various Assumed Thresholds a Threshold Concentration 70 ppb 65 ppb 60 ppb No threshold (core model) 680 2,100 3,900 4 6 0 ppb 520 1,600 2,900 45 56 ppb 410 1,100 1,700 5 0 5 ppb 120 280 510 5 5 0 ppb 5.6 58 140 56 45 ppb 3.3 47 105 6 4 0 ppb <1 10 13
a All estimates rounded to two significant digits. The results of the sensitivity analysis based on the suite of threshold

- based risk coefficients suggests that threshold models can result in substantially lower estimates of ozone attributable long

- term mortality. For example, estimated incidence and dolla r benefits for long

term mortality using a model that includes a 55 ppb threshold are approximately 70% less than long

- term mortality benefits estimated using the core co

- pollutant non

- threshold model. Generally, estimated long

- term mortality benefits are progressively reduced when using models with increasing thresholds, with the highest threshold considered (60 ppb) removing virtually all of the estimated incidence reduction and associated benefits. 5B.2 Alternative Concentration - Response Functions for PM 2.5 – Related Mortality In modeling PM 2.5 cobenefits, we estimate that total dollar benefits are driven largely by reductions in mortality (see Table 5

- 22 and 5

- 29). Therefore, it is particularly important to attempt to characterize the uncertainties associated with reductions in premature mortal ity as modeled in the PM 2.5 cobenefits analysis. To better understand the concentration

- response relationship between PM 2.5 exposure and premature mortality, the EPA conducted an expert elicitation in 2006 (Roman et al., 2008; IEc, 2006). 3 In general, the results of the expert elicitation support the conclusion that the benefits of PM 2.5 control are very likely to be substantial. Alternative concentration

- response functions are useful for assessing uncertainty beyond random statistical error, including unc ertainty in the functional form of the model or alternative study design. In this analysis, we present the results derived from the expert elicitation as

3 Expert elicitation is a formal, highly

- structured and well

- documented process whereby expert judgments, usually of multiple experts, are obtained (Ayyub, 2002).5 B

- 5

indicative of the uncertainty associated with a major component of the health impact functions, and we provide the independent estimates derived from each of the twelve experts to better characterize the degree of variability in the expert responses. In previous RIAs, the EPA presented benefits estimates using concentration

- response functions derived from the PM 2.5 Expert Elicitation (Roman et al., 2008) as a range from the lowest expert value (Expert K) to the highest expert value (Expert E). However, this approach did not indicate the A gency’s judgment on what the best estimate of PM 2.5 benefits may be, a nd the EPA’s independent SAB recommended refinements to the way EPA presented the results of the elicitation (U.S. EPA

- SAB, 2008). Therefore, we began to present the cohort

- based studies (Krewski et al., 2009; Laden et al., 2006) 4 as our core estimates in the proposal RIA for the Portland Cement NESHAP (U.S. EPA, 2009a). Using alternate relationships between PM 2.5 and premature mortality supplied by experts, higher and lower benefits estimates are plausible, but most of the expert

- based estimates of the mea n PM 2.5 effect on mortality fall between the two epidemiology

- based estimates (Roman et al., 2008). In addition to these studies, we have included a discussion o f other recent multi

- state cohort studies conducted in North America, but we have not estimated benefits using the effect coefficients from these studies (see Appendix 5D). Please note that the benefits estimates results presented are not the direct results from the studies or expert elicitation; rather, the estimates are based in part on the effect coefficients provided in those studies or by experts. In addition, because we are using a dollar

- per - ton approach in modeling PM 2.5 cobenefits in this RIA, we cannot generate confidence intervals reflecting the statistical fit characterized in the expert elicitation

- based functions. Even these multiple characterizations based on application of the range of expert elicitation

- based effect estimates omit the contribution to overall uncertainty from uncertainty in air quality changes, baseline incidence rates , and populations exposed. Furthermore, the approach presented here does not yet include methods for addressing correlation between input parameters and the identification of reasonable upper and lower bounds for input distributions characterizing uncertai nty in additional model elements.

4 We have since updated the Harvard Six Cities cohort study from Laden et al. (2006) to use the most recent follow

up publication of this cohort (Lepeule et al, 2012). This study is reflected in the dollar

- per - ton values used in this RIA.5 B

- 6

The PM 2.5 expert elicitation and the derivation of effect estimates from the expert elicitation results (used in generating these alternative dollar

- per - ton estimates) are described in detail in the 2006 PM 2.5 NAAQS RIA ( U.S. EPA, 2006 ), the elicitation summary report (IEc, 2006) and Roman et al. (2008), and consequently, we do not present those effect estimates (and associated functional forms) here. Table 5B

- 2 presents the results of this sensitivity analysis as complete d for the 2025 scenario (overall conclusions generated from this analysis are transferable to the post

- 2025 scenario). The alternative mortality estimates presented in Table 5B

- 2 were generated similar to the core cobenefits PM 2.5 mortality estimates, but applying dollar

- per - ton values (for each expert elicitation

- based effect estimate) to the sector

- level estimates of NOx reductions associated with the 2025 scenario. We have also included the core cobenefits estimates for each alternative standard to facil itate comparison against these alternative sensitivity analysis estimates. Because application of these effect estimates (using a dollar

- per - ton approach) represents a linear calculation, results in terms of the relative ranking of the core estimates compa red with expert elicitation estimates will remain the same for all alternative standards evaluated. Therefore, we only present estimates for the 70 ppb alternative standard, observing that observations drawn from this sensitivity analysis would hold for ot her alternative standards considered (and for the post
- 2025 scenario

– for all alternative standards

– as well). Table 5B - 2. Application of Alternative (Expert Elicitation - Based Effect Estimates) to the

Modeling of PM 2.5 Co - benefit Estimates for PM 2.5 (avo ided incidence)

C - R Function (and effect estimate) b 70 ppb Krewski et al., (2012) (core model) 45 Lepeule et al., (2012) (core model) 100

Expert K 10 Expert G 54 Expert L 63 Expert D 65 Expert H 67 Expert J 75 Expert F 88 Expert C 92 Expert I 92 Expert B 95 Expert A 120 Expert E 150
a All estimates rounded to two significant digits.5 B

- 7 b Expert elicitation

- based values ordered by magnitude of incidence reduction The values presented in Table 5B

- 2 suggest that the two core incidence estimate fall within the range of alternative C

- R function based estimates obtained through expert elicitation. This increases overall confidence in the core estimates with regard to th e form of the functions and magnitude of the effect estimates. We would expect the relationship between the core estimates and the expert

- derived estimates to remain constant for the remaining scenarios as well
. 5B .3 Income Elasticity of Willingness - to - Pay As discussed in Chapter 5, our estimates of monetized benefits account for growth in real GDP per capita by adjusting the WTP for individual endpoints based on the central estimate of the adjustment factor for each of the categories (minor health effects, severe and chronic health effects, premature mortality, and visibility). We examined how sensitive the estimate of total benefits is to alternative estimates of the income elasticities. Income growth projections are only currently available in BenMAP thro ugh 2024, so both the 2025 and post

- 2025 scenario estimates use income growth only through 2024 and are therefore likely underestimates. Table 5 B

- 3 lists the ranges of elasticity values used to calculate the income adjustment factors, while Table 5 B

- 4 lis ts the ranges of corresponding adjustment factors. The results of this sensitivity analysis, giving the monetized benefit subtotals for the four benefit categories, are presented in Table 5 B

- 5
.
Table 5 B - 3. Ranges of Elasticity Values Used to Account for Projected Real Income

Growth a Benefit Category Lower Sensitivity Bound Upper Sensitivity Bound Minor Health Effect b 0.04 0.30 Premature Mortality 0.08 1.00
a Derivation of these ranges can be found in Kleckner and Neumann (1999). COI estimates are assigned an adjustment factor of 1.0. b Minor health effects included in this RIA and valued using WTP

- based functions include: upper and lower respiratory symptoms, asthma exacerbations, minor restricted activity days, and acute bronchitis.5 B

- 8

Table 5 B - 4. Ranges of Adjustment Factors Used to Account for Projected Real Income

Growth to 2024 a

Benefit Category Lower Sensitivity Bound Upper Sensitivity Bound Minor Health Effect b 1.021 1.170 Premature Mortality 1.043 1.705
a Based on elasticity values reported in Table C

- 4, U.S. Census population projections, and projections of real GDP per capita. b Minor health effects included in this RIA and valued using WTP

- based functions include: upper and lower respiratory symptoms, asthma exacerbations, minor restricted activity days, and acute bronchitis.
Table 5 B - 5. Sensitivity of Monetized Ozone Benefits to Alternative Income Elasticities in

2025 (Millions of 2011$) a Bene fit Category No adjustment Lower Sensitivity Bound Upper Sensitivity Bound 70 ppb 65 ppb 70 ppb 65 ppb 70 ppb 65 ppb Minor Health Effect b $66 $200 $67 $210 $77 $240 Premature Mortality c $2,000 $6,400 $2,100 $6,600 $3,500 $11,000
a All estimates rounded to two significant digits. Only reflects income growth to 2024. b For purposes of completing this sensitivity analysis, we have included minor restricted activity days (MRADS) based resulting from short

- term ozone exposure as the min or health effect evaluated here. c Using short

- term mortality effect estimate from Smith et al. (2009) and 3% discount rate. Results using other short

term mortality studies and a 7% discount rate would show the same proportional range. Consistent with th e impact of mortality on total benefits, the adjustment factor for mortality has the largest impact on total benefits. The value of mortality in 2025 ranges from 86% to 133% of the main estimate for mortality based on the lower and upper sensitivity bounds on the mortality income adjustment factor. The effect on the value of minor health effects is much less pronounced, ranging from 96% to 108% of the main estimate for minor effects. These observations (in terms of relative impact from alternative elasticit ies) hold for all three of the alternative standard levels evaluated under both the 2025 and post

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