BiostatisticsTier 1Medical Sciences concept

Statistical power - definition and determinants

Core concept

	H0 true	H0 false
Reject H0	Type I error (alpha) - false positive	Correct (power)
Do not reject H0	Correct	Type II error (beta) - false negative

Power = 1 - beta = probability of detecting an effect that is really there
- Conventionally set at 80% or 90%; alpha at 0.05 (two-sided)
Type II error = missing a real effect -> "no significant difference" is not "no difference"
A negative trial is uninterpretable until you know it was powered and look at the confidence interval

The four determinants

```

n proportional to (Zalpha/2 + Zbeta)^2 x variance / delta^2

```

Raise power by	Direction
Sample size (n)	inc n -> inc power (the only one usually under your control)
Effect size (delta)	larger true effect -> easier to detect
Variance / SD	dec variance -> inc power (homogeneous population, precise measurement, paired design)
Alpha	inc alpha (0.05 -> 0.10) -> inc power, at the cost of more false positives

Effect size is in the denominator and squared: halving the effect you wish to detect quadruples n
For a binary outcome, what drives n is the number of events, not the number of patients -> event-driven trials, enrichment with high-risk patients
Zalpha/2 = 1.96 at alpha 0.05; Zbeta = 0.84 at 80% power, 1.28 at 90%
Multiple comparisons inflate alpha: familywise error = 1 - (1 - 0.05)^k; 20 tests -> 64% chance of at least one false positive
- Bonferroni: alpha/k; alpha-spending in interim analyses

Post-hoc power calculation is invalid - once the result is in, the CI carries all the information; a "power" computed from the observed effect is just a restatement of the p-value
Underpowered subgroups are why forest-plot subgroup effects are usually noise
Non-inferiority trials invert the logic: the margin must be pre-specified and clinically justified, and per-protocol analysis is the conservative one (ITT biases toward non-inferiority)
Rare adverse events: rule of three - if 0 events in n patients, the upper 95% bound of the true rate is 3/n
- 0/300 -> could still be as high as 1%
Interim analyses and early stopping for benefit overestimate the effect size

3 more sections, plus exam facts

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