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This paper presents formulae for determining the number of subjects necessary, in either a case-control or a cohort study, to estimate the odds ratio or relative risk, respectively, to within a selected percentage (epsilon) of the true population value with some specified probability. This approach differs somewhat from previous comparable work that estimated the log odds ratio within a stated fixed distance rather than as a percentage of the actual odds ratio. Comparable development for relative risk has not previously appeared in the literature. These formulae provide guidelines for determination of study size that does not depend on hypothesis testing considerations.
Lemeshow et al. (Fri,) studied this question.