The risk ratio is calculated as the ratio of the attack rates or risks, i.e., 65.4% divided by 11.4%, which equals 5.7. This risk ratio indicates that persons who ate the beef were 5.7 times more likely to become ill than those who did not eat the beef.
Considering the third criterion listed earlier, notice that almost all (53 out of 57) of the cases could be accounted for by the beef. Some investigators use a more quantitative approach and calculate a population attributable risk percent for each food. The population attributable risk percent describes the proportion of illness in the entire study population that could be attributable to a given exposure, assuming that those who became ill in the unexposed group and a similar proportion in the exposed group must be attributable to something else. The population attributable risk percent may actually be an underestimate in many outbreaks, since it does not take into account such common occurrences as cross-contamination of foods or sampling of a spouse’s dish. The population attributable risk percent for beef was 76.7% (see Table 6.8), much higher than that for any other food.
Statistical significance testing. When an exposure is found to have a relative risk different from 1.0, many investigators calculate a chi-square or other test of statistical significance to determine the likelihood of finding an association as large or larger on the basis of chance alone. A detailed description of statistical testing is beyond the scope of this lesson, but the following text presents some key features and formulas.
To test an association for statistical significance, assume first that the exposure is not related to disease, i.e., the relative risk (RR) equals 1.0. This assumption is known as the null hypothesis. The alternative hypothesis, which will be adopted if the null hypothesis proves to be implausible, is that exposure is associated with disease. Next, compute a measure of association, such as a risk ratio or odds ratio. Then calculate a chi-square or other statistical test. This test indicates the probability of finding an association as strong as or stronger than the one you have observed if the null hypothesis were really true, that is, if in reality the exposure being tested was not related to the disease. This probability is called the p-value. A very small p-value means that the observed association occurs only rarely if the null hypothesis is true. If the p-value is smaller than some cutoff that has been specified in advance, commonly 0.05 or 5%, you discard or reject the null hypothesis in favor of the alternative hypothesis.