6 Assessment of Risk and Benefit in Epidemiologic Studies
II Comparison of Risks in Different Study Groups
After the differences in risk are calculated by the methods outlined in detail subsequently, the level of statistical significance must be determined to ensure that any observed difference is probably real (i.e., not caused by chance). (Significance testing is discussed in detail in Chapter 10.) When the difference is statistically significant, but not clinically important, it is real but trivial. When the difference appears to be clinically important, but is not statistically significant, it may be a false-negative (beta) error if the sample size is small (see Chapter 12), or it may be a chance finding.
A Absolute Differences in Risk
Figure 6-1 provides data on age-adjusted death rates for lung cancer among adult male smokers and nonsmokers in the U.S. population in 1986 and in the United Kingdom (UK) population.1,2 For the United States in 1986, the lung cancer death rate in smokers was 191 per 100,000 population per year, whereas the rate in nonsmokers was 8.7 per 100,000 per year. Because the death rates for lung cancer in the population were low (<1% per year) in the year for which data are shown, the rate and the risk for lung cancer death would be essentially the same. The risk difference (attributable risk) in the United States can be calculated as follows:

Figure 6-1 Risk of death from lung cancer.
Comparison of the risks of death from lung cancer per 100,000 adult male population per year for smokers and nonsmokers in the United States (USA) and United Kingdom (UK).
(Data from US Centers for Disease Control: MMWR 38:501–505, 1989; and Doll R, Hill AB: BMJ 2:1071–1081, 1956.)
Similarly, the attributable risk in the UK can be calculated as follows:
B Relative Differences in Risk
1 Relative Risk (Risk Ratio)
The data on lung cancer deaths in Figure 6-1 are used to determine the attributable risk (AR). The same data can be used to calculate the RR. For men in the United States, 191/100,000 divided by 8.7/100,000 yields an RR of 22. Figure 6-2 shows the conversion from absolute to relative risks. Absolute risk is shown on the left axis and relative risk on the right axis. In relative risk terms the value of the risk for lung cancer death in the unexposed group is 1. Compared with that, the risk for lung cancer death in the exposed group is 22 times as great, and the attributable risk is the difference, which is 182.3/100,000 in absolute risk terms and 21 in relative risk terms.

Figure 6-2 Risk of death from lung cancer.
Diagram shows the risks of death from lung cancer per 100,000 adult male population per year for smokers and nonsmokers in the United States, expressed in absolute terms (left axis) and in relative terms (right axis).
(Data from US Centers for Disease Control: MMWR 38:501–505, 1989.)
2 Odds Ratio
People may be unfamiliar with the concept of odds and the difference between “risk” and “odds.” Based on the symbols used in Table 6-1, the risk of disease in the exposed group is a/(a + b), whereas the odds of disease in the exposed group is simply a/b. If a is small compared with b, the odds would be similar to the risk. If a particular disease occurs in 1 person among a group of 100 persons in a given year, the risk of that disease is 1 in 100 (0.0100), and the odds of that disease are 1 to 99 (0.0101). If the risk of the disease is relatively large (>5%), the odds ratio is not a good estimate of the risk ratio. The odds ratio can be calculated by dividing the odds of exposure in the diseased group by the odds of exposure in the nondiseased group. In the terms used in Table 6-1, the formula for the OR is as follows:
In mathematical terms, it would make no difference whether the odds ratio was calculated as (a/c)/(b/d) or as (a/b)/(c/d) because cross-multiplication in either case would yield ad/bc. In a case-control study, it makes no sense to use (a/b)/(c/d) because cells a and b come from different study groups. The fact that the odds ratio is the same whether it is developed from a horizontal analysis of the table or from a vertical analysis proves to be valuable, however, for analyzing data from case-control studies. Although a risk or a risk ratio cannot be calculated from a case-control study, an odds ratio can be calculated. Under most real-world circumstances, the odds ratio from a carefully performed case-control study is a good estimate of the risk ratio that would have been obtained from a more costly and time-consuming prospective cohort study. The odds ratio may be used as an estimate of the risk ratio if the risk of disease in the population is low. (It can be used if the risk ratio is <1%, and probably if <5%.) The odds ratio also is used in logistic methods of statistical analysis (logistic regression, log-linear models, Cox regression analyses), discussed briefly in Chapter 13.
3 Which Side Is Up in the Risk Ratio and Odds Ratio?

Figure 6-3 Possible risk ratios plotted on logarithmic scale.
Scale shows that reciprocal risks are equidistant from the neutral point, where the risk ratio is equal to 1.0.
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