Attack Rate

The attack rate is the workhorse of outbreak investigation: of the people exposed, what share fell ill? It is computed for the group as a whole and then again for each suspected exposure, and the food-specific attack rate table — attack rate among those who ate the dish, against those who did not — is the tool that has solved more foodborne outbreaks than any laboratory.

The name is wrong, and the CDC says so itself. Its Principles of Epidemiology in Public Health Practice lists the attack rate among the measures that are "commonly called rates" but are in fact proportions: there is no time in the denominator, so nothing is being measured per unit of time. It is an incidence proportion over the outbreak window. The correct term is attack proportion and nobody uses it, which is a reasonable thing to know and an unreasonable hill to die on — but it explains why an attack rate cannot be compared with an incidence rate, and that error is not merely terminological.

Reading the food-specific table has one rule that catches people out. The dish to suspect is not the one with the highest attack rate among those who ate it; it is the one with the largest difference between eaters and non-eaters. A popular dish eaten by nearly everybody at the supper will show a high attack rate simply because nearly everybody there got ill, and the give-away is a low attack rate among the handful who avoided it.

Two limits worth carrying. The secondary attack rate — cases among household contacts of a primary case — measures transmissibility rather than a common exposure, and it uses the same arithmetic on a completely different question. And the whole method rests on a defined, enumerable exposed population, which is why it works beautifully for a wedding reception and poorly for a city.