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This paper discusses the design of clinical trials where the primary endpoint is a recurrent event with the focus on the sample size calculation. For the problem, a few methods have been proposed but most of them assume a multiplicative treatment effect on the rate or mean number of recurrent events. In practice, sometimes the additive treatment effect may be preferred or more appealing because of its intuitive clinical meaning and straightforward interpretation compared to a multiplicative relationship. In this paper, new methods are presented and investigated for the sample size calculation based on the additive rates model for superiority, non‐inferiority, and equivalence trials. They allow for flexible baseline rate function, staggered entry, random dropout, and overdispersion in event numbers, and simulation studies show that the proposed methods perform well in a variety of settings. We also illustrate how to use the proposed methods to design a clinical trial based on real data. [ABSTRACT FROM AUTHOR]