Matched Pairs in Sequential Trials for Significance of a Difference between Proportions

are they economical in use but also keep the effectiveness of a given method of treatment under continuous review. Yet sequential methods, though firmly established in various other experimental fields, have not often been used in medical research. One of the reasons for the limited use of these methods is that the success of the treatment and its length are frequently related to such individual characteristics of the patient as age, sex and severity of condition at entering the trial. The chance of contracting a particular disease may also vary with such environmental conditions as housing, dietary habits and occupation. For such reasons, medical research workers may insist on having experimental and control cases similar with respect to characteristics which they regard as important in a given case. From the statistician's point of view this approach implies single or multiple stratification and a certain degree of correlation in response to treatment between members of the same pair. Stratification means a more complicated sampling machinery than would be necessary for unrestricted pairing, and correlation raises the question of the applicability of the usual sequential formulae to a matched-pair trial. The usual test based on unrestricted pairing will show, with required probabilities, whether the new treatment is or is not significantly better (or worse) than the standard, without involving us in any difficulties of selection or theoretical problems. At first glance, therefore, it might seem that the introduction of matched pairs is an unnecessary complication unless it can be shown to result in a sizeable reduction in the average amount of testing required to reach a decision. Even if there is little or no reduction in the average sample size,