Sample size requirements for stratified prospective studies with null hypothesis of non‐unity relative risk using the score test

The standard test of the null hypothesis of unity of the relative risk seeks to determine if two treatments differ. It does not apply when the requirement is either to establish the equivalence of two treatments or to determine whether the relative risk is less than a specified value other than one. This paper presents the asymptotic power function of the score test for the null hypothesis of a specified value of a common relative risk for stratified prospective studies and proposes an approximate formula for the sample size required for a specific power of the test. One can obtain a sample size formula for stratified studies with the standard null hypothesis of unity relative risk as a special case of this formula.