Confidence interval estimation for number of patient-years needed to treat

The number of patient-years needed to treat (NPY NT), also called the event-based number needed to treat, to avoid one additional exacerbation has been reported in recently published respiratory trials, but the confidence intervals are not routinely reported. The challenge of constructing confidence intervals for NPY NT is due to the fact that exacerbation data or count data in general are usually analyzed using Poisson-based models such as Poisson or negative binomial regression and the rate ratio is the natural metric for between-treatment comparison, while NPY NT is based on rate difference, which is not usually calculated for those models. Therefore, the variance estimates from these analysis models are directly related to the rate ratio rather than the rate difference. In this paper, we propose several methods to construct confidence intervals for the NPY NT, assuming that the event rates are estimated using Poisson or negative binomial regression models. The coverage property of the confidence intervals constructed with these methods is assessed by simulations.