Statistical inference for clinical data
Introduit| English | Sens |
|---|---|
| confidence interval/ˈkɒnfɪdəns ˈɪntəvl/ | An interval calculated from sample data using a method with a stated long-run probability of containing the population parameter. |
| p-value/piː ˈvæljuː/ | The probability, assuming the null model, of a test statistic at least as extreme as the observed one in the direction or directions tested. |
| type I error/taɪp aɪ ˈerə/ | type I error |
| type II error/taɪp ˈtuː ˈerə/ | type II error |
| statistical power | statistical power |
| Kaplan–Meier curve | Kaplan–Meier curve |
Same estimate, opposite verdicts
- Two studies both report a relative risk of 1.8. One says the drug clearly causes harm; the other says it might not. The difference is in the intervals.
- Inference is how a sample tells us about the whole population, and its two tools are often misread.
Confidence intervals
- A 95% confidence interval 置信区间 is the range of true values reasonably compatible with the data.
- It shows both size and precision. If an RR interval excludes 1, the data are not compatible with "no effect" at that level.
A study reports RR 1.5 (95% CI 0.8–2.8). What can you conclude?
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The interval includes 1.
P-values
- A p-value P值 is the probability of data at least this extreme if the null hypothesis (no effect) were true.
- It measures surprise, not size. p > 0.05 does not prove no effect; the data are just compatible with none.
A p-value of 0.30 proves the treatment has no effect.
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It only shows the data are compatible with no effect.
Two kinds of error
- A type I error I型错误 is finding an effect that is not there (false positive); its usual limit α is 0.05.
- A type II error II型错误 is missing a real effect (β). Statistical power 检验效能 = 1 − β, often planned at 80%.
A trial is planned with β = 0.2. What is its power, in %?
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Power = 1 − β = 0.8, so 80%.
Match each term to its meaning.
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α limits type I errors; power is 1 − β.
The data type chooses the test
- Counts in groups: χ² test. Two means: t-test (paired if each person is measured twice). Several means: ANOVA.
- Skewed or small samples: rank (non-parametric) tests. Two measurements on the same people: correlation.
Match each data type to a suitable test.
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The kind of data decides the test.
Survival curves
- A Kaplan–Meier curve 卡普兰-迈耶曲线 steps down at each event: S = previous S × (1 − events/number at risk).
- People lost to follow-up are censored: they leave the number at risk without counting as events. Median survival is where the curve crosses 50%.
Put the steps of a Kaplan–Meier update in order.
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Censored people leave the number at risk without counting as events.
Worked example: reading two intervals
- (Fictional) RR 1.8, 95% CI 1.2–3.1: excludes 1, so p < 0.05; the effect is imprecise but consistently above 1.
- RR 1.8, 95% CI 0.9–3.6: includes 1, so the data are compatible with no effect. Same estimate, different verdict.
Worked example: Kaplan–Meier arithmetic
- (Synthetic) 10 patients; at 6 months, 1 event among 10 at risk: S = 9/10 = 0.90.
- One patient is censored, so 8 remain; at 12 months, 1 event: S = 0.90 × 7/8 = 0.7875, about 79%.
(Synthetic) 20 at risk, 2 events, so S = 0.90. Later, 15 are at risk and 3 have events. What is the new S? Give two decimal places.
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0.90 × (1 − 3/15) = 0.90 × 0.80 = 0.72.
Three common slips
- Reading p > 0.05 as "no difference". Absence of evidence is not evidence of absence.
- Saying there is a 95% chance the truth is in this interval. The 95% describes the method across many samples.
- Choosing the test after seeing which gives p < 0.05. The data type chooses it in advance.
Recap
- CI = compatible true values, showing size and precision; p-value = P(data this extreme | no effect).
- Type I = false positive (α); type II = missed effect (β); power = 1 − β.
- χ², t, ANOVA, rank tests and correlation by data type; Kaplan–Meier multiplies (1 − events/at risk).