1. Air quality standards –a statistician’s perspective Peter Guttorp Northwest Research Center for Statistics and the Environment peter@stat.washington.edu www.stat.washington.edu/peter

2. Clean Air Act First federal air pollution laws 1955 Clean Air Act 1970 EPA formed to enforce CAA Requires EPA to set National Ambient Air Quality Standards (1970) primary: public health secondary: public welfare States are responsible for meeting standards State Implementation Plan must be approved by EPA

3. Exposure issues for particulate matter (PM) Personal exposures vs. outdoor and central measurements Composition of PM (size and sources) PM vs. co-pollutants (gases/vapors) Susceptible vs. general population

4. Phoenix particulate matter and respiratory deaths Main question: Are respiratory deaths among elderly caused by particulate matter air pollution? Data: Single site PM 10,PM 2.5 5/95 – 6/98 Mortality Meteorology (temperature, specific humidity) Incl. baseline, lags 0-3, quadratic functions of met, total of 29 variables

5. Bayesian model averaging BIC(m) = deviance(m) + dim(m) log(n) K a priori equally likely models

6. BMA, cont. Uses all models considered, rather than the best model Often several models are nearly equally good Can use prior information about models Leaps and bounds algorithm to find best models of each size

8. temp humpm

9. .54.09.33.51

10. Is PM a pollutant? The same concentration of PM has had different health effects in Boston and Seattle Some evidence that sulphates better predictor of health effects PM is probably many pollutants –Size –Chemical composition –Co-pollutants Classification due to measurement technique?

11. Health effects of ozone 64 million people live in areas with ozone exceeding 0.12 ppm

12. Biological effects of ozone Adversely affects the ability of plants to produce and store food Leaf loss Severe forest dieback Precursors part of acid rain

13. Ozone standard In each region the expected number of daily maximum 1-hr ozone concentrations in excess of 0.12 ppm shall be no higher than one per year Implementation: A region is in violation if 0.12 ppm is exceeded at any monitoring site in the region more than 3 times in 3 years

14. A hypothesis testing framework The EPA is required to protect human health. Hence the more serious error is to declare a region in compliance when it is not. The correct null hypothesis therefore is that the region is violating the standard.

15. Optimal test One station, observe Y 3 = # exceedances in 3 years Let  = E(Y 1 ) H 0 :  > 1 vs. H A :  ≤ 1 When  = 1, approximately Y 3 ~ Bin(3365,1/365) ≈ Po(3) so a UMP test rejects for small Y 3. For Y 3 = 0  = 0.05 In other words, no exceedances should be allowed.

16. How does the EPA perform the test? EPA wants Y 3 ≤ 3, so  = 0.647 The argument is that  ≈ Y 3 / 3 (Law of large numbers applied to n=3) Using Y 3 / 3 as test statistic, equate the critical value to the boundary between the hypotheses (!). This implementation of the standard does not offer adequate protection for the health of individuals.

17. More than one station Consider K independent stations. EPA uses T = max i≤K Y 3 i ; sufficiency argues use of S =  i≤K Y 3 i P(T ≤ 3) = P K (Y 3 ≤ 3) = 0.647 K If K=7, P(T ≤ 3) = 0.048 S ~ Po(3K), so for K=7 rejecting when S ≤ 13 is a level 0.05 test (size 0.043) P(T≤3 | S=13) = 0.36

18. Statistical comparisons Let. For Houston, TX,  =0.235 (0.059 ppm) and  =0.064. The station exceeds 0.12 ppm with probability 0.041, for an expected number of exceedances of 15 (18 were observed in 1999) At level 0.18 ppm (severe violation) the exceedance probability is 0.0016, corresponding to 0.6 violations per year (1 observed in 1999) 

19. More comparisons For South Coast,CA,  =0.245 (0.065 ppm) and  =0.065. In order for a single station to exceed 0.12 ppm with probability 1/365, we need  =0.165, or 0.031 ppm. For the observed mean, the exceedance probability of.12 ppm is 0.059 (about 21 expected exceedances per year). For mean level 0.15 (0.18) ppm the probability is 0.735 (0.884)

20. The Barnett-O’Hagan setup Ideal standard: bound on level of pollutant in an area over a time period Realizable standard: a standard for which one can determine without uncertainty where it is satisfied Statistically verifiable standard: ideal standard augmented with operational procedure for assessing compliance

21. Consequences for hypothesis tests One option: set values of  and  at the design level and a “safe” level, respectively. For example, the “safe” level could be the highest level for which the relative risk of health effects on some susceptible population is not significantly different from one

22. A new ozone standard Summer 1997: 8-hour averages instead of 1-hour Limit 0. 08 ppm instead of 0.12 increases non-attainment counties from 104 to 394 Instead of expected number of exceedances, limit is put on a 3-year average of fourth-highest ozone concentration change from ideal to realizable standard

23. Legal challenges of the new air quality standards The new 8-hr standard for ozone was challenged to the Supreme Court. The US Court of Appeals directed EPA to consider potential positive health effects of ground-level ozone. The EPA has not found any.

24. Spatial and temporal dependence Daily maxima of ozone show some temporal structure There is substantial spatial correlation between daily maxima at different monitors in a region Simulations indicate that 10 sites in the Chicago area behaves similar to 2 independent sites

25. Network bias Many health effects studies use air quality data from compliance networks health outcome data from hospital records Compliance networks aim at finding large values of pollution Actual exposure may be lower than network values

26. A calculation

27. Special cases CaseBias negligible

29. A more complete picture? Health effects studies need actual exposure. Standards can only be set on ambient air. PNW PM Center studies personal exposure in elderly Much of personal exposure, especially in elderly, comes from indoor sources. Only about 5% of variability due to ambient sources. Most of ambient variability due to time (not space).

30. A conditional calculation Given an observation of.120 ppm in the Houston region, what is the probability that an individual in the region is subjected to more that.120 ppm? Need to calculate supremum of Gaussian process (after transformation) over a region that is highly correlated with measurement site, taking into account measurement error.

31. One-dimensional case M(T)=max(X(t),0≤t≤T), X stationary N T (u)=# upcrossings of u by X in [0,T] P(M(T)>u) = P(X(0)>u)+P(N T (u)≥1,X(0)≤u) ≤ P(X(0)>u) +EN T (u) u X‘(t)

32. Two dimensions

33. A lower bound Choose N points in S: S N

34. Probability of exceeding level u

35. Level of standard to protect against 0.18 ppm

36. General setup Given measurements of a Gaussian field observed with error, find c [t] such that where [t] denotes season and the mean of equals the  -quantile of the estimated health effects distribution.

37. Other approches to setting standards Standard relative to natural variability Areal average standards Multi-pollutant standards All require substantial statistical input.

38. A risk based approach Mike Holland, EMRC End point cancer cases per million people PollutantConcRiskExp cases Benzene5 0.07 0.36 PAHs0.001 1243 1.24 Arsenic0.02 21 0.43 Cadmium0.005 26 0.13 Nickel0.03 1.43 0.04 Total 2.20

39. Some difficulties with the risk based approach Are risks additive? There can be more than one endpoint Uncertainties in risk estimates and in concentrations need to propagate through the analysis Cost-benefit analysis not necessarily politically appropriate

40. What do we mean by trends in extreme values?

41. Multiple variables Extreme in one, not extreme in others? Interesting scenario: Medium temperature, about 0C Large snowfall Extreme winds

42. What to do? “Standard” extreme value asymptotics works for values high in all variables Heffernan approach: Model:for x large, where Z comes from extreme value theory.