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(The "unexposed" group actually contains those with background exposure plus those truly unexposed.) Several studies are available that could be used for the purpose of estimating Z. Jarvis and coworkers (1985) studied 569 nonsmoking schoolchildren ages 11 to 16 in Great Britain. The investigators reported that, when compared with salivary cotinine levels in children of nonsmoking parents (N = 269), mean levels of salivary cotinine were 3.0 times as high in children whose father smoked (N = 96), 4.4 times as high in children whose mother smoked, and 7.7 times as high in children whose parents were both smokers. Pattishall and coworkers (1985) reported that children from homes with smokers (N = 20) had 4.1 times as high mean levels of serum cotinine as children from nonsmoking families. Black children in the same study, however, had lower values of Z (2.8) than did white children. Coultas and coworkers (1987) found that, among 600 U.S. children up to age 17 years, mean salivary cotinine levels were between 1.3 and 2.6 times as high among subjects exposed to one cigarette smoker at home as among unexposed subjects, and between 2.9 and 3.5 times as high among subjects exposed to two or more smokers at home as among subjects not exposed to cigarette smokers at home. Strachan and coworkers (1989) reported separate results for 61/2 to 71/2-year-old Scottish children belonging to families living in their own homes and for those belonging to families living in rented homes. In the former, geometric mean salivary cotinine was 6 times as high among subjects exposed to one cigarette smoker at home as among unexposed subjects and 16 to 17 times as high among subjects exposed to two or more smokers at home as among unexposed subjects. For children belonging to families living in rented homes, the same ratios were 3 to 5.5 times and 4 to 7 times, respectively. While these studies show consistent relationships between mean body cotinine levels in children and home smoker occupancy, there is also a wide variability in the estimated Z ratios, ranging from 1+ to 17. These different estimates may have very important effects on the background exposure adjustment and, thus, on the calculation of adjusted relative risks for different studies (see also Chapter 6). For example, for a study in which the observed relative risk (RR) is 2.0 but for which the Z ratio is 3, equation 81 can be solved for dN, which is the estimated increase in relative risk for the group called "unexposed" but who in fact have been exposed to some recent ETS. Solving, dN = 1. Thus, the adjusted RR for the group identified as "unexposed" would be 2, and the adjusted RR for an "exposed" group compared with a truly unexposed group would be 1 + (3*1) = 4, i.e., twice the observed risk. For a similar example (observed RR = 2) but with Z = 5, dN = 0.3, the RR for a group identified as "unexposed" in this case would be 1.3, and the adjusted RR for an "exposed" to a truly unexposed group would be 2.67. Finally, if the observed RR is still 2 but Z = 17, dN = 0.07, RR for "unexposed" would be 1.07 and the adjusted RR for exposed children would be 2.13. These results are shown in Table 81. These calculations show that when use of parental questionnaires significantly underestimates their children's exposures to other sources of ETS (other than via the parental ETS) and values of Z are lower (as found in black children by Pattishall and coworkers [1985], and in children of lower socioeconomic status by Strachan and coworkers [1989]), the "true" RR of children exposed to ETS may be considerably underestimated. But perhaps the most important conclusion that may be derived from the above analysis is that exposure to ETS from sources other than smoking parents may be high enough to constitute a significant risk for their health. This may be particularly consequential for children of lower socioeconomic levels, whose nutritional status, crowded conditions at home, and opportunity for contact with biological agents of disease make them a part of the population that is particularly susceptible to respiratory illnesses during infancy and childhood. Available data show that ETS exposure via nonhousehold members in these children, as measured by cotinine levels in body fluids, may be as much as one-third that of children exposed to one smoking parent (Z = 3). In the example presented above (observed RR=2), the estimate of the adjusted relative risk is 4 for children of smoking parents to the truly unexposed children. However, using the same assumptions, children of nonsmoking parents who are exposed to ETS (at background levels found in some of the studies) would have twice as high a risk of developing the illness under study as children truly unexposed to ETS. A cautionary note about the model is appropriate. Table 81 shows that, for observed RR= 2 and Z = 3, the adjusted relative risk is 4. However, as the observed RR and Z get closer together, the behavior of the model becomes erratic. This is shown in Table 82. In fact, the model (equation 81) becomes undefined if Z is less than or equal to the observed RR, and it reaches some stability only as Z becomes at least 30% to 50% greater than the RR.  X X` hp x (#%'0*,.8135@8:x8`?c ,  Table 83. Range of estimates of adjusted relative risk and attributable risk for asthma induction in children based on both threshold and nonthreshold models, and different values for Z. ddx  ddx  .EEE EEEEUEEE EEEEU. L L L vvv Threshold model1d ENonthreshold model2ă.P P .Observed relative risk1.752.251.752.251.752.002.25.  .Z = Cotinine ratio (exposed/unexposed)ܩܩ1010333.P P .Adjusted relative risk3ܩܩ1.9142.6242.8054.0056.005.P P .ARE6 0.430.560.480.620.640.750.83.P P .ART7 (PI8=0.17)0.070.09ܩܩܩܩܩ.P P .ART (PI9=0.26)ܩܩ0.120.160.170.200.22.              .ETSattributable population impact108,000 to 20,000 10,000 to 26,00013,000 to 34,00018,000 to 45,00019,000 to 46,00022,000 to 54,00024,000 to 60,000Xp` hp x (#%'0*,.8135@8: 10 cig./day) is required to induce new cases.  2Nonthreshold model assumes that all ETS exposure can produce some new cases of asthma.  3Equation 81 for the nonthreshold model; no adjustment for the threshold model.  4Ratio of mean body cotinine levels: Z = 10. 5Ratio of mean body cotinine levels: Z = 3.  6Attributable risk fraction for the exposed population.  7Attributable risk fraction for the total (mixed) population.  8Proportion of women of reproductive age who smoke at least 10 cigarettes per day (0.26 ' 0.65).  9Proportion of women of reproductive age who smoke cigarettes. 10Range based on 2 million to 5 million asthmatic children under 18 years old in the United States, and assumes that the number of ETSattributable new cases at each age is constant. 3' Xp` hp x (#%'0*,.8135@8: