  We derive the sample size formulae for comparing two negative binomial rates
based on both the relative and absolute rate difference metrics in
noninferiority and equivalence trials with unequal follow-up times, and
establish an approximate relationship between the sample sizes required for the
treatment comparison based on the two treatment effect metrics. The proposed
method allows the dispersion parameter to vary by treatment groups. The
accuracy of these methods is assessed by simulations. It is demonstrated that
ignoring the between-subject variation in the follow-up time by setting the
follow-up time for all individuals to be the mean follow-up time may greatly
underestimate the required size, resulting in underpowered studies. Methods are
provided for back-calculating the dispersion parameter based on the published
summary results.
