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Additional info for Sample size tables for clinical studies
In most practical situations π1 and π2 are not going to differ by so much as to make unequal allocation worthwhile. For a clinical trial any advantage is at the expense of greater complexity at the randomisation stage. For observational studies, such as case-control studies however, there may be a limited number of cases available, and so collecting more controls is a suitable method of increasing the power of the study. 3 One proportion known In some situations one may know, with a fair degree of certainty, the proportion of successes in one of the groups.
Thus the small sample leads, for given α, to a wider conﬁdence interval. 42 but on only m = 16 rather than the 98 actually weighed. 105 kg and df = 16 − 1 = 15. 53 kg. qxd 24 9/8/08 10:20 Page 24 Chapter 2 Binomial Confidence interval for a proportion If r is the number of patients who respond out of m recruited to a trial, then the response proportion p = r/m is the estimate of the true response rate πPop. 13 as p − [z1−α /2 × SE(p)] to p + [z1−α /2 × SE(p)]. 9600. 3 where, as m gets larger, the shape of the Binomial distribution comes closer and closer to that of the Normal distribution until they are almost indistinguishable.
In this situation, if we are then given a plausible value of (say) π1, then the value of π2 is obtained from π2 = ORPlanπ1 . 1 to obtain the anticipated π2, after which the anticipated value for δPlan can be obtained. Such a situation may arise if a previous study had used logistic regression for analysis (see Campbell, Machin and Walters 2007) and had quoted an OR that might then be regarded as a possible effect size for the study under design. 2) where Y = (π1 + ϕπ2) / (1 + ϕ). 2. The required sample size for Group 2 is n = ϕm.