Theory 21/Clinical Trials Methodology
Power Is an Effect-to-Noise Ratio
The claim
Trial power is set by the ratio of effect size to outcome measurement noise rather than by sample size, so improving measurement can raise power more cheaply than recruiting more patients.
01The mechanism
Detectability depends on signal against noise. Adding patients reduces sampling variance but leaves measurement variance untouched, while a better instrument reduces both the numerator's error and the denominator.
That makes measurement quality the cheaper lever, which is often overlooked in planning.
02What this is not
Sample-size planning
That treats noise as fixed. This treats it as a design variable, which changes the cost of power.
03Predictions
- P1Power should improve more from measurement than from equivalent-cost recruitment.
- P2Studies with better instruments should need fewer patients.
04Refutation
Power insensitive to measurement quality would favour sample-size-only planning.