Binary data

Examples of binary data include anything with a yes/no outcome such as response, hence binary data from a group of patients will provide an estimate of the proportion responding. There are several ways in which proportions can be compared. A simple significance test is to use the Pearson chi-square test on data displayed in a contingency table (see Section 9.3.1); alternative methods which lead more naturally to estimates and confidence intervals as well as tests of significance are to compare differences in proportions, or the ratios of proportions (relative risk) or, where appropriate, the odds ratio (the ratio of success to failure in one group divided by the ratio of success to failure in the other).

For the purposes of sample size calculation, we will consider the situation where proportions are to be compared. We define a, ¡3 as before and here S is the difference in proportions, for example p2 — pi.

An approximate formula for the number of patients required in each group (assuming equal numbers are to be randomized to each group) can be given in a similar form to that for continuous data, namely:

at (Z1— a/2 + Z1—3 )2(p1(1 — pQ + p2 (1 — p2))

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