Sample Size Determination

Sample Size Determination

1. Definition, purpose & why it matters

• Sample size determination is the formal, pre-study estimation of the number of subjects required so that a planned study has a high probability of detecting a pre-specified, clinically worthwhile effect if it truly exists, at a chosen significance level (Machin 3e Ch.1, pp.1–2).
• The statistical objective of any study is to estimate, from a sample, the value of a population parameter — e.g. recording the weight of n babies to estimate the population mean birth weight ω_Pop; sample size determines how precisely that estimate is pinned down (Machin 3e Ch.1, pp.2–3).
• Providing a sample size is not a single look-up from a table — it is a several-stage, iterative process: preliminary "ball-park" figures decide whether to start detailed planning; later stages refine the supporting evidence into a persuasive case for the final patient number that is justified in the protocol (Machin 3e Ch.1, p.2).
• Three quantities drive the required number of patients in the motivating two-group binary-endpoint trial (Machin 3e Ch.1, p.3):
  • the anticipated clinical difference between treatments (effect size);
  • the significance level α;
  • the chance of detecting the anticipated difference, the power 1 − β.
• Scientific-credibility / peer-review imperative: major medical journals demand a detailed justification of study size in any submission. The BMJ General Statistical Checklist explicitly asks: "Was a pre-study calculation of study size reported?" (Machin 3e Ch.1, p.1).
• Resource / "cost" imperative: investigators, grant-awarding bodies and pharmaceutical developers all want to know how much a study will "cost" in time, resource and money — projected study size is a key component — and want reassurance the resource will be well spent (likelihood of an unequivocal result) (Machin 3e Ch.1, p.1).
• Regulatory imperative: the FDA (USA, 1988 NDA guidelines) and the Committee for Proprietary Medicinal Products (CPMP, EU, 1995), encapsulated in ICH Topic E9 (1998), Statistical Principles for Clinical Trials, require information on planned study size (Machin 3e Ch.1, pp.1–2).
• The two failure modes the calculation exists to avoid (Machin 3e Ch.1, p.2):
  • Under-powered (too few subjects): a misuse of time — realistic medical differences cannot be distinguished from chance variation, so a true and worthwhile benefit may be missed and reported as "no significant difference" (a Type II error of the study as a whole).
  • Over-powered (too large): a waste of important resources; if a treatment could have been "proven" superior with fewer patients, the excess subjects on the inferior arm are unnecessary.