Odds ratios. In most case-control studies, the population is not well defined, and the total number of people exposed (or unexposed) to a suspected vehicle or source is not known. Without a proper denominator, attack rates cannot be calculated. In the example above, since the investigators did not know how many community residents did or did not shop at Grocery Store A, they could not calculate attack rates or a risk ratio. For a case-control study, the measure of association of choice is the odds ratio. Fortunately, for a rare disease such as legionellosis and most other outbreak-associated diseases, the odds ratio from a case-control study approximates the relative risk that would have been found if a cohort study had been feasible.
The odds ratio for Grocery Store A is calculated as:
25 x 26 / 28 x 2 = 11.6
An odds ratio of 11 is quite large, indicating that shopping at Grocery Store A was strongly associated with developing legionellosis. These data would seem to indicate that persons exposed to Grocery Store A had 11.6 times the odds of developing legionellosis than persons not exposed to that store.
To test the statistical significance of this finding, a chi-square test can be computed using the formula shown earlier.