Sample Size Determination

Definition, purpose & why it matters

• Definition — Sample size determination is the formal, pre-study estimation of the number of subjects a planned study needs so that it has a high probability of detecting a pre-specified, clinically worthwhile effect if it truly exists, at a chosen significance level. It is an iterative process (ball-park → refined justification), not a single look-up from a table.
• The two failure modes it exists to avoid — An under-powered study (too few subjects) cannot distinguish a real, worthwhile benefit from chance, so a true effect is missed and wrongly reported as "no significant difference" — a misuse of time. An over-powered study (too large) wastes resources and exposes excess subjects on the inferior arm unnecessarily.
• Why it matters — three imperatives — Scientific/peer-review (the BMJ checklist asks "Was a pre-study calculation of study size reported?"); resource/cost (sponsors and grant bodies need a justified projected size and reassurance of an unequivocal result); and regulatory (FDA, CPMP and ICH E9 require a stated, justified study size).
• The ethical dimension (cuts both ways) — A trial too small to detect a useful difference is unfair to every subject exposed to its risks to answer a question it cannot answer; a trial too large means more subjects than necessary received the (later-known) inferior treatment. Both under- and over-recruitment are ethical failings — a scientifically sound, adequately-powered n is a precondition for ethics-committee approval.