Question

Difficulty: HardMeasures of Disease Frequency and Association

Public health officials investigate a cluster of an unusual neurological syndrome in a rural county. They identify 120 patients diagnosed with the syndrome over the past year. They also recruit 240 healthy individuals from the same county, matched for age and sex, to serve as a comparison group. All participants complete detailed questionnaires regarding their dietary habits, occupational exposures, and residential history over the previous 5 years.

The data regarding the frequent consumption of unpasteurized dairy products are summarized in the table below:

Neurological SyndromeHealthy Individuals
Consumed unpasteurized dairy9060
Did not consume unpasteurized dairy30180

Based on the design of this investigation, which of the following is the most appropriate measure of association, and what is its calculated value?

  1. Odds ratio of 9.0Answer
  2. B
    Relative risk of 4.2
  3. C
    Odds ratio of 3.0
  4. D
    Relative risk of 9.0
  5. E
    Odds ratio of 0.11

Answer

The most appropriate measure of association is an odds ratio of 9.0.
The scenario describes an investigation where subjects are selected based on whether they have a specific outcome (neurological syndrome) or not (healthy matched individuals), and then their prior exposures (unpasteurized dairy) are assessed. This methodology defines a case-control study. Because the ratio of cases to controls is artificially determined by the investigators, the true incidence of the disease in the population cannot be measured. Consequently, relative risk cannot be calculated. The appropriate measure of association is the odds ratio, which compares the odds of exposure among cases to the odds of exposure among controls. Using the data provided: Odds of exposure in cases = 90/30=3.090 / 30 = 3.0. Odds of exposure in controls = 60/180=0.33360 / 180 = 0.333. Odds Ratio = 3.0/0.333=9.03.0 / 0.333 = 9.0. (Alternatively, using the cross-product formula: OR=90×18060×30=9.0OR = \frac{90 \times 180}{60 \times 30} = 9.0).

Step-by-Step Solution

1
Identify the study design from the scenario.
The study selected participants based on their disease status (syndrome vs. healthy) and looked back at their past exposure. This is a case-control study.
Study design dictates which statistical measure of association is valid.
2
Determine the appropriate measure of association.
Case-control studies use the odds ratio (OR).
Because researchers artificially fix the number of cases and controls, true incidence cannot be measured, making relative risk an invalid metric.
3
Extract values from the 2x2 contingency table.
Exposed cases (a) = 90. Unexposed cases (c) = 30. Exposed controls (b) = 60. Unexposed controls (d) = 180.
These variables populate the OR formula.
4
Calculate the odds ratio.
OR = 9.0
OR=a×db×c=90×18060×30=162001800=9.0OR = \frac{a \times d}{b \times c} = \frac{90 \times 180}{60 \times 30} = \frac{16200}{1800} = 9.0

Key Concept

Case-control studies select patients based on disease status and use the odds ratio to estimate the strength of association between an exposure and an outcome, as they cannot directly measure disease incidence required for relative risk.
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