For the analysis with recurrent events, we propose a generalization of the accelerated failure time model to allow for evolving covariate effects. These so-called accelerated recurrence time models postulate that the time to expected recurrence frequency, upon transformation, is a linear function of covariates with frequency-dependent coefficients. This modelling strategy shares the same spirit as quantile regression. An estimation and inference procedure is developed by generalizing the celebrated Powell's ("J. Econometrics" 25, 1984, 303; "J. Econometrics" 32, 1986, 143) estimator for censored quantile regression. Consistency and asymptotic normality of the proposed estimator are established. An algorithm is devised to attain good computational efficiency. Simulations demonstrate that this proposal performs well under practical settings. This methodology is illustrated in an application to the well-known bladder cancer study. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.
