The number of patients required in a clinical trial

The clinician who wishes to test two alternative treatment methods may reasonably expect a statistician to tell him whether the number of patients available from his own or collaborating hospitals is likely to be adequate to give a statistically significant result in a reasonable time. The answer he receives, however, will depend upon the model his statistical consultant adopts, and it should be said at once that statisticians are not unanimous upon what is the “correct” way to answer his question. Two widely different estimates of patient numbers to be found in recent radiological literature (Boag, 1960; B.I.R. Working Party, 1963) reflect these different approaches to the question and an attempt is made below to explain how these differences arise. Briefly, the varying estimates arise because they may be answers to two different questions, either of which could reasonably be asked in preparation for a clinical trial. The first is: Given particular success rates for two groups treated in different ways, how large must the groups be in order that the difference shall be judged significant? Clearly, with small numbers of patients quite large apparent differences could arise purely by chance.