# 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?

> source: MyMerci (mymerci.kr)  
> url: https://mymerci.kr/pages/nclex_q.php?qn_id=627202  
> language: ko  
> subject: Nursing Practice I — Community Health Nursing

## 문제

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?

## 보기

1. The team set the numbers of cases and controls, so incidence is unknown **✔ 정답**
2. The illness is common here, so a relative risk would overstate the effect
3. The exposure is rare here, so a relative risk would be too unstable
4. The illness lasted only days, so risk cannot be followed forward in time

**정답: 1**

## 해설

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.

## 심화 해설

Why the odds ratio, not the relative risk, in a case-control study

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.

## 임상 시나리오

Case-Control Study: Why Odds Ratio, Not Relative RiskOutbreak investigation with fixed case and control numbers
In a case-control study, the investigator decides how many cases and controls to include (e.g., 2 controls per case). The groups are not a population followed forward over time.

Relative risk requires incidence, which needs 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, so incidence cannot be calculated.

The odds ratio is used instead because it is based on the odds of exposure among cases versus controls, not on disease incidence. It approximates relative risk when the disease is rare.

CautionNever report relative risk from case-control data. The fixed case-to-control ratio means the data do not represent a natural population, so incidence is unknown and RR cannot be validly computed.

## 핵심 개념

- **Case-control study** — An observational design in which the investigator selects participants based on disease status (cases and controls) and then compares past exposure history; the investigator fixes the numbers of cases and controls.
- **Odds ratio** — A measure of association comparing the odds of exposure among cases to the odds of exposure among controls; it can be calculated in case-control studies and approximates relative risk when the disease is rare.
- **Relative risk** — The ratio of disease incidence among exposed persons to disease incidence among unexposed persons; it requires incidence data and therefore cannot be directly calculated from case-control data.
- **Incidence** — The proportion of people who develop disease among those at risk over a specified period; it requires knowing the total number of exposed and unexposed persons at the start of follow-up.

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