Recurrent event data are commonly seen in biomedical applications. This study considers a more general regression model on gap times under recurrent event data. For an analysis on gap times, we not only need to handle censored times but also need to take account of “induced dependent censoring” which happens in gap times analysis even though the censoring variable is independent of the disease process. To handle this problem, this study assumes an Archimedean copula to specify the dependent relationship. For the estimation of marginal parameters which are interested, this study applies the Cramer-von Mises type statistic to construct an estimating function. Furthermore, this study provides two model checking approaches to check two model assumptions. Via simulation studies, it shows that the finite sample performance of the proposed estimator is well. This study also uses the proposed methodology to analyze chronic granulomatous disease (CGD) data set.