Situation: Over 3 weeks, 46 residents from many barangays of a municipality developed acute bloody diarrhea. They had bought food from many different sources, so no list of all exposed persons exists. The public health nurse helps the municipal epidemiology and surveillance unit compare the cases with well residents (controls) on what they ate before the illness. Why should the team report an odds ratio rather than a relative risk from these data?

In a case-control study the investigator decides how many cases and controls to include (here 2 controls per case). The groups are therefore not a population followed over time, and the incidence of disease among the exposed and unexposed cannot be calculated. Relative risk needs incidence, so the odds ratio is used; it approximates the relative risk when the disease is rare.

This outbreak investigation is a case-control study. The team identified 46 residents with bloody diarrhea (cases) and then selected well residents (controls) for comparison. The defining feature of this design is that the investigator fixes the number of cases and controls before any exposure data are collected. Because the team deliberately set the case-to-control ratio, the resulting data do not represent a naturally occurring population followed forward over time.

The central statistical problem is that relative risk (RR) requires incidence. Incidence is the proportion of people who develop disease among those who were exposed, compared with the proportion who develop disease among those who were unexposed. To calculate incidence, the investigator must know the total number of exposed and unexposed persons at the start of follow-up. In this scenario, there is no list of all exposed persons, and the team chose how many controls to include, so the denominator needed for incidence is unknown. Without incidence, RR cannot be computed.

The odds ratio (OR) is used instead because it is based on the odds of exposure among cases versus controls, not on disease incidence. The OR compares how often cases were exposed to a suspected food item relative to how often controls were exposed. This calculation is valid even when the investigator has fixed the numbers of cases and controls, because the odds of exposure can be estimated from the sampled groups alone.

Feature	Case-control study	Cohort study
Starting point	Disease status (cases vs. controls)	Exposure status (exposed vs. unexposed)
Investigator control	Sets numbers of cases and controls	Follows a defined population over time
Incidence calculable	No	Yes
Appropriate measure	Odds ratio	Relative risk

Memon and colleagues explain that the choice between OR and RR depends on the study design and the ability to estimate disease incidence. In situations where the investigator selects participants based on outcome status rather than following a population forward, the RR cannot be directly computed because the underlying risk of disease in the exposed and unexposed groups is not observable. The OR remains the appropriate measure of association in this setting.

Watch out! The OR approximates the RR when the disease is rare in the population. In this outbreak, bloody diarrhea is uncommon among the general population of the municipality, so the OR will closely approximate the RR. However, the reason the team reports an OR is not because the disease is rare; it is because the case-control design prevents calculation of incidence, which RR requires.

Key point! Option 2 is incorrect because a high disease frequency would make the OR a poor approximation of the RR, but it would not prevent calculation of RR in a cohort design. Option 3 is incorrect because rarity of exposure affects the precision of both OR and RR, not the choice between them. Option 4 is incorrect because the short duration of illness affects the timing of follow-up, not the fundamental inability to compute incidence in a case-control design.