< when : reaches order rejection hypothesis better control therapy. method different gested Cornell (1986), formula for posterior probability. probability treatment therapy. corresponding probability ECMO. Under hypothesis, Under alternative hypothesis, definitions consistent those given earlier terms probability under inferior treatments. Similarly, refer numbers balls added tively. design considered provides modification decision

doi:10.1201/9781482277128-37

Chapter

ABSTRACT

As before, the integer assigned to the design parameter r is the minimum value for which the power is greater than a specified value. The formula used for power is the same as that for PCS given earlier, calculated with 'YJ and an alternative value of 'Y > 'YJ, except for one modification. The upper limit for the summation is t instead of r - 1, since the null hypothesis is rejected only if s ~ t. Thus the power, denoted by 1 - {3, is given by

1 - {3 = E II1;rb b=O

where II1;rb denotes IIrb calculated under HI with'Y > 'YJ. Equation (5) gives the value of a for a one-sided test. For a given t, the

sum in equation (5) should be doubled for a two-sided test. Another term, equal to E~=oIIl;a" should be added to the sum in equation (6) to calculate 1 - (3 for a two-sided test. Moreover, a two-sided test also requires that the stopping rule be modified so that r balls of either type may be added provided that not more than t balls of both types are added. A one-sided test is appropriate for our ECMO example. Therefore, to avoid complexity, the rest of the formulas presented will be for one-sided tests only.