[The subscriptein RReindicates that we are calculating the relative risk
(RR) forex-smokers.]
(b) For current smokers,RRcF38 = 2
81 = 56
¼
ð 38 Þð 56 Þ
ð 81 Þð 2 Þ
¼ 13 : 14[The subscriptcin RRcindicates that we are calculating the relative risk
(RR) for current smokers.]In these calculations, the nonsmokers (who never smoke) are used as
references. These values indicate that the risk of having pancreatitis for
current smokers is approximately 13.14 times the risk for people who
never smoke. The e¤ect for ex-smokers is smaller (4.55 times) but is still
very high (compared to 1.0, the no-e¤ect baseline for relative risks and
odds ratios). In other words, if the smokers were to quit smoking, they
would reduce their own risk (from 13.14 times to 4.55 times) butnotto
the normal level for people who never smoke.1.3.3 Generalized Odds for Ordered 2DkTables
In this section we provide an interesting generalization of the concept of odds
ratios to ordinal outcomes which is sometime used in biomedical research.
Readers, especially beginners, may decide to skip it without loss of continuity;
if so, corresponding exercises should be skipped accordingly: 1.24(b), 1.25(c),
1.26(b), 1.27(b,c), 1.35(c), 1.38(c), and 1.45(b).
We can see this possible generalization by noting that an odds ratio can be
interpreted as an odds for a di¤erent event. For example, consider again the
same 22 table as used in Section 1.3.2 (Table 1.11). The number of case–
control pairs with di¤erent exposure histories isðADþBCÞ; among them,AD
pairs with an exposed case andBCpairs with an exposed control. Therefore
AD=BC, the odds ratio of Section 1.3.2, can be seen as the odds of finding a
pair with an exposed case among discordant pairs (adiscordant pairis a case–
control pair withdi¤erentexposure histories).
TABLE 1.12
Use of Cigarettes Cases Controls
Never 2 56
Ex-smokers 13 80
Current smokers 38 81
Total 53 21722 DESCRIPTIVE METHODS FOR CATEGORICAL DATA