Study designs
Introduced| English | Meaning |
|---|---|
| randomised controlled trial | randomised controlled trial |
| cohort study | cohort study |
| relative risk | The risk in the exposed group divided by the risk in the unexposed. |
| case-control study | case-control study |
| odds ratio | The odds of exposure in cases divided by the odds in controls. |
The right design for the question
- Does a new vaccine work? Did a factory chemical cause a rare cancer? You cannot answer both with the same kind of study.
- Each design answers some questions well and others not at all, and the design decides which statistic you may calculate.
Randomised controlled trial
- A randomised controlled trial 随机对照试验 assigns the exposure by chance, then follows both groups forward.
- Chance balances known and unknown differences between groups, so it is the strongest single test of a treatment. It is only possible when you can ethically assign the exposure.
Cohort study
- A cohort study 队列研究 starts with exposed and unexposed people and follows them forward to count outcomes.
- Because it samples by exposure, it measures risks directly and gives a relative risk 相对危险度: $RR = \dfrac{a/(a+b)}{c/(c+d)}$.
(Synthetic) Exposed 300 with 30 events; unexposed 300 with 10 events. What is the relative risk?
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0.10 ÷ 0.0333 = 3.0.
Case-control study
- A case-control study 病例对照研究 starts with people who have the outcome (cases) and without it (controls), then looks back at exposure.
- It suits rare diseases. Since the researcher sets the number of cases, risks cannot be found; only the odds ratio 比值比 $OR = ad/bc$ is valid.
A relative risk can be calculated directly from a case-control study.
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The researcher chose how many cases and controls to include, so only the odds ratio is valid.
(Fictional) Cases: 40 exposed, 20 unexposed. Controls: 20 exposed, 40 unexposed. What is the odds ratio?
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OR = (40 × 40) ÷ (20 × 20) = 4.0.
Cross-sectional and ecological
- A cross-sectional study takes one snapshot: exposure and outcome are measured together, so which came first is unclear.
- An ecological study compares groups, not individuals, so a link between countries may not hold for people.
Match each question to the best design.
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The question and the rarity of the outcome choose the design.
Order these designs from strongest to weakest protection against bias.
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This is the usual ladder; each step adds a source of bias.
Countries that eat more chocolate win more Nobel prizes. What is the main problem with concluding that chocolate makes people clever?
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An ecological link between groups may not hold for people.
Worked example: a synthetic cohort
- (Synthetic) Exposed 200 with 20 events; unexposed 200 with 10: risks 0.10 and 0.05, so RR = 2.0.
- Attributable fraction in the exposed = (RR − 1)/RR = 1/2 = 50%: half their events are due to the exposure, if the study is unbiased.
The relative risk is 4. What is the attributable fraction among the exposed, in %?
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(4 − 1) ÷ 4 = 0.75, so 75%.
Worked example: a case-control table
- (Fictional) 30 of 40 cases were exposed and 20 of 60 controls were exposed. So a = 30, b = 20, c = 10, d = 40.
- $OR = (30 \times 40) \div (20 \times 10) = 6.0$. When the outcome is rare, the OR is close to the RR.
Three common slips
- Computing RR from a case-control study. The researcher chose the denominators.
- Reading a cross-sectional association as cause. Exposure and outcome were measured together.
- Thinking "prospective" removes confounding. Only randomisation balances the unknowns.
Recap
- Trial (assigned by chance) → cohort (by exposure, RR) → case-control (by outcome, OR) → cross-sectional → ecological.
- $RR = \dfrac{a/(a+b)}{c/(c+d)}$; $OR = ad/bc$; rare outcome: OR ≈ RR.
- Attributable fraction in the exposed = (RR − 1)/RR.