1. Environmental standards A statistical approach Peter Guttorp National Research Center for Statistics and the Environment

2. Outline Some examples of environmental standards Statistical frameworks EPA rules vs. statistical rules Assumptions Network design bias

3. Storm sewer standard Combined sewer overflows –heavy rain –raw sewage dumped Washington state law requires “the greatest reasonable reduction of combined sewer overflows at the earliest possible date” Municipalities with CSOs must –have approved CSO reduction plans –monitor discharge volume & frequency –sample discharge

4. What is the problem? Hard to monitor discharges Easy to monitor rainfall Rainfall is related to discharge Look at frequency of rainfall events vs. frequency of CSO events What is a rainfall event? WA Dept of Ecology: need 48 hrs between CSO events (based on having independent rainfall events) BUT—in some places only one event per winter!

5. Drinking water standard Maximum microbiological contaminant levels: 1. Arithmetic mean coliform count of all standard samples examined per month shall not exceed 1/100 ml 2. The number of coliform bacteria shall not exceed 4/100 ml in (a) more than one sample when less than 20 are examined (b) more than 5% of the sample if at least 20 are examined

6. A statistical setup N i = #coliforms per 100 ml in sample I Y i =1(N i > 4) The criteria are then (a) (b) If n < 20 If n ≥ 20 Let

7. If we assume N~LN( ,  2 ) (Carbonez et al., 1999) a large n calculation yields (a)  +  2 /2 ≤ 0 (b)  + 1.64  ≤ 1.39 Thus, the second condition is irrelevant under these assumptions.

8. Clean Air Act 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

9. Health effects of ozone Scarring lung tissue Accelerated aging of lungs Increased hospitalization for respiratory causes (e.g., asthma) Children particularly at risk 64 million people live in areas with ozone exceeding 120 ppb

10. 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

11. Ozone standard In each region the expected number of daily maximum 1-hr ozone concentrations in excess of 120 ppb shall be no higher than one per year Implementation: A region is in violation if 120 ppb is exceeded at any monitoring site in the region more than 3 times in 3 years

12. A hypothesis testing framework The EPA is required to protect human health in the first instance. 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.

13. 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.

14. How does the EPA perform the test? EPA wants Y 3 ≤ 3, so  = 0.647 The argument is that  ≈ Y 3 / 3, so 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.

15. 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)

16. Statistical comparisons Let. For South Coast,CA,  =0.245 (0.060 ppm) and  =0.065. In order for a single station to exceed 0.120 ppm with probability 1/365, we need  =0.165, or 0.028 ppm. For the observed mean, the exceedance probability is 0.059. For level 150 (180) ppb the probability is 0.735 (0.884) 

17. 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

18. 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

19. A new ozone standard Summer 1997: 8-hour averages instead of 1-hour Limit 80 ppb instead of 120 increases non-attainment counties from 104 to 394 Instead of number of exceedances, limit is put on a 3-year average of fourth-highest ozone concentration

20. Legal challenges of the new air quality standards The new 8-hr standard for ozone, and a new standard for particulate matter, was struck down by by the US Court of Appeals, in effect declaring the Clean Air Act unconstitutional Although the 8-hr standard was left in place, it was declared “unenforcable” The court directed EPA to consider potential health effects of ground- level ozone

21. 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

22. Network design bias Data from compliance monitoring networks are often used for health effect studies Compliance monitoring looks for large values Health effects need ambient air quality where affected people are

23. A simplistic analysis Suppose X t =  X t-1 +  t is a stationary vector time series, mean , with  t ~ N(0,  ) and  ij = , i≠j E(X 1,t |X 1,t-1 > X 2,t-1 ) =  1 E(X 1,t-1 | X 1,t-1 > X 2,t-1 ) =  1 +  1 provided  1 =  2 Consequences for health effect estimation?

24. A more complete picture? Threshold model—dose-response –Often from simpler animal models –Low dose extrapolation –Uncertainty “Acceptable” dose (“Unacceptable” dose) Separate anthropogenic influence from natural variability Achievable limit