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Difficulty: HardMeasures of Disease Frequency and Association

An epidemiology research board is reviewing statistical data from four distinct clinical studies. Based on the study design and the provided data, match each clinical research scenario with its most appropriate epidemiological measure of association and its correctly calculated value.

  • A retrospective investigation identifies 200 patients with a rare autoimmune disease and 200 healthy volunteers. Upon interview, 100 of the affected patients and 50 of the healthy volunteers report a history of specific occupational solvent exposure.Odds Ratio = 3.0
  • A prospective investigation follows 1,000 individuals who consume a high-sodium diet and 1,000 individuals who consume a normal-sodium diet. Over ten years, 200 individuals in the high-sodium group and 40 in the normal-sodium group develop chronic kidney disease.Relative Risk = 5.0
  • A multi-center, double-blind trial randomizes 500 heart failure patients to a novel beta-blocker and 500 to placebo. Over five years, 20 patients in the treatment group and 70 in the placebo group die from cardiovascular causes.Number Needed to Treat = 10
  • A post-marketing surveillance trial observes 1,000 patients prescribed a new antiepileptic drug and 1,000 patients on standard therapy. After one year, 50 patients on the new drug and 10 on the standard therapy report developing severe drug-induced tremor.Number Needed to Harm = 25

Answer

The retrospective study pairs with Odds Ratio = 3.0. The prospective study pairs with Relative Risk = 5.0. The trial evaluating death reduction pairs with Number Needed to Treat = 10. The trial tracking drug-induced tremors pairs with Number Needed to Harm = 25.
Each study design fundamentally dictates the appropriate measure of association. Case-control studies necessitate the Odds Ratio. Prospective cohort studies are ideal for Relative Risk calculations. Interventional trials report Number Needed to Treat when the intervention reduces disease, and Number Needed to Harm when evaluating side effects. The arithmetic matches the definitions precisely.

Step-by-Step Solution

1
Identify the study design for each scenario to determine the correct statistical metric.
Scenario 1 is a case-control study (requires Odds Ratio). Scenario 2 is a cohort study (requires Relative Risk). Scenarios 3 and 4 are trials evaluating absolute differences in outcomes (require NNT and NNH).
You cannot calculate incidence (and therefore Relative Risk) in a standard case-control study. Likewise, NNT applies to interventions that prevent events, whereas NNH applies to exposures that cause adverse events.
2
Calculate the metric for the case-control study.
OR=100×150100×50=3.0OR = \frac{100 \times 150}{100 \times 50} = 3.0.
OR is the cross-product ratio: (Exposed Cases * Unexposed Controls) / (Unexposed Cases * Exposed Controls).
3
Calculate the metric for the prospective cohort study.
RR=200/100040/1000=5.0RR = \frac{200/1000}{40/1000} = 5.0.
RR compares the incidence of disease in the exposed population to the incidence in the unexposed population.
4
Calculate the Number Needed to Treat (NNT) for the trial showing cardiovascular benefit.
ARR=0.14−0.04=0.10ARR = 0.14 - 0.04 = 0.10. NNT=10.10=10NNT = \frac{1}{0.10} = 10.
NNT represents the number of patients who must be treated to prevent one additional adverse outcome.
5
Calculate the Number Needed to Harm (NNH) for the trial showing medication adverse effects.
ARI=0.05−0.01=0.04ARI = 0.05 - 0.01 = 0.04. NNH=10.04=25NNH = \frac{1}{0.04} = 25.
NNH represents the number of patients who must be exposed to an intervention to cause one additional adverse event.

Key Concept

Selection of epidemiological metrics based on study design, specifically differentiating when to calculate OR vs. RR, and NNT vs. NNH.
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Topics

Measures of Disease Frequency and Association

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