# 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. The team interviewed all 46 cases and 92 controls about eating flavored ice sold by street vendors: Cases: 36 ate the ice, 10 did not Controls: 23 ate the ice, 69 did not What is the odds ratio? Round off to one decimal place.

> source: MyMerci (mymerci.kr)  
> url: https://mymerci.kr/pages/nclex_q.php?qn_id=627201  
> 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.

The team interviewed all 46 cases and 92 controls about eating flavored ice sold by street vendors:
Cases: 36 ate the ice, 10 did not
Controls: 23 ate the ice, 69 did not
What is the odds ratio? Round off to one decimal place.

## 보기

1. 0.1
2. 3.1
3. 4.8
4. 10.8 **✔ 정답**

**정답: 4**

## 해설

Odds ratio = (a × d) ÷ (b × c), where a = exposed cases (36), b = exposed controls (23), c = unexposed cases (10), d = unexposed controls (69). OR = (36 × 69) ÷ (23 × 10) = 2,484 ÷ 230 = 10.8. Check: odds of exposure in cases 36 ÷ 10 = 3.6; in controls 23 ÷ 69 = 0.333; 3.6 ÷ 0.333 = 10.8. The odds of having eaten the ice were about 11 times higher among cases.

## 심화 해설

Case–control design and the 2×2 table

This outbreak investigation is a case–control study because the team started with people who already had the outcome — the 46 cases of acute bloody diarrhea — and compared them with 92 well controls who did not develop illness. There was no complete list of everyone exposed, so a cohort study was not possible. In this design, the measure of association is the odds ratio (OR), not the relative risk.

The data are arranged as follows:

| Exposure (flavored ice) | Cases (diarrhea) | Controls (well) | Total |
| --- | --- | --- | --- |
| Ate the ice | 36 (a) | 23 (b) | 59 |
| Did not eat the ice | 10 (c) | 69 (d) | 79 |
| Total | 46 | 92 | 138 |

Calculating the odds ratio

The odds ratio compares the odds of exposure among cases with the odds of exposure among controls. The formula is:

OR = (a × d) ÷ (b × c)

Substituting the values:

- a × d = 36 × 69 = 2,484

- b × c = 23 × 10 = 230

- OR = 2,484 ÷ 230 = 10.8

The same result is obtained by comparing the odds directly. Among cases, the odds of having eaten the ice were 36 ÷ 10 = 3.6. Among controls, the odds were 23 ÷ 69 = 0.333. Dividing the two odds gives 3.6 ÷ 0.333 = 10.8.

Interpreting the odds ratio

The odds of having eaten the flavored ice were about 11 times higher among cases than among controls. This strongly suggests that the street-vended flavored ice was associated with the outbreak of bloody diarrhea.

An OR of 1.0 would mean no association. An OR greater than 1.0 indicates that exposure is more common among cases, supporting a possible causal link. An OR less than 1.0 would suggest a protective effect.

Key point! In a case–control study, the odds ratio is the correct measure of association because the investigator fixes the number of cases and controls. The relative risk cannot be validly calculated from this design because the true incidence of disease in the exposed and unexposed populations is unknown.

Why the odds ratio is used here

Simon (2001) explains that some study designs permit only the calculation of the odds ratio, not the relative risk. A case–control study is the classic example. The relative risk requires knowing the incidence of disease in exposed and unexposed groups, which requires following a defined cohort forward in time. In this outbreak, there was no complete roster of everyone who bought food from the many different sources, so a cohort could not be assembled. The investigators therefore worked backward from identified cases and used the odds ratio to estimate the strength of the association.

The odds ratio also has the advantage of being invariant to the labeling of the outcome. Whether the analysis treats “diarrhea” or “no diarrhea” as the outcome of interest, the magnitude of the odds ratio remains the same, which reduces ambiguity in interpretation [1].

Common calculation errors to avoid

A frequent mistake is misplacing the cells in the 2×2 table. The formula OR = (a × d) ÷ (b × c) depends on correct labeling: a and b must both represent the exposed group, while c and d represent the unexposed group. Reversing cases and controls would invert the result.

Another error is confusing the odds ratio with the relative risk. Watch out! The relative risk is easier to interpret intuitively, but it cannot be computed from a case–control study. Using the odds ratio formula with case–control data is appropriate; using a relative risk formula would produce a meaningless number [1].

Rounding to one decimal place, the odds ratio is 10.8, which corresponds to option 4.References (research sources)

- [1]Understanding the odds ratio and the relative risk.Research articleSimon SD (2001)

## 임상 시나리오

Case-Control OR in OutbreakStreet-vended ice and bloody diarrhea
When no complete list of exposed persons exists, use a case-control design and calculate the odds ratio. Build a 2x2 table: a=exposed cases (36), b=exposed controls (23), c=unexposed cases (10), d=unexposed controls (69).

OR = (a×d)/(b×c) = (36×69)/(23×10) = 10.8. The odds of having eaten the flavored ice were about 11 times higher among cases than controls.

CautionDo not confuse the odds of exposure in cases (3.6) with the OR. An OR of 1.0 means no association; values above 1.0 indicate higher exposure among cases.

## 핵심 개념

- **Odds ratio** — Measure of association in case-control studies; (a×d)/(b×c), comparing odds of exposure in cases versus controls.
- **Case-control study** — Study design that starts with outcome (cases) and compares past exposure with controls; used when no complete exposure list exists.
- **2x2 table** — Standard layout for exposure-outcome data: a=exposed cases, b=exposed controls, c=unexposed cases, d=unexposed controls.
- **Outbreak investigation** — Systematic process to identify source and control disease spread when cases exceed expected numbers.
- **Foodborne disease** — Illness caused by consuming contaminated food or drink, often presenting as acute diarrhea.

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