A penalized algorithm for event-specific rate models for recurrent events

We introduce a covariate-specific total variation penalty in two semiparametric models for the rate function of recurrent event process. The two models are a stratified Cox model, introduced in Prentice and others (1981. On the regression analysis of multivariate failure time data. Biometrika 68: , 373-379.), and a stratified Aalen's additive model. We show the consistency and asymptotic normality of our penalized estimators. We demonstrate, through a simulation study, that our estimators outperform classical estimators for small-to-moderate sample sizes. Finally, an application to the bladder tumor data of Byar (1980. The veterans administration study of chemoprophylaxis for recurrent stage 1 bladder tumors: comparison of placebo, pyridoxine, and topical thiotepa. In Pavone-Macaluso, M. Smith, P. H. and F. Edsmyn (editors), Bladder Tumors and Others Topics in Urological Oncology, pp. 363-370.) is presented.