Carlos M. Martinez

The objective is to propose statistical tests to compare survival analysis functions of *k* populations involving recurrent events. Recurrent events occur in many important scientific areas: *psychology*, *bioengineering*, *medicine, physics, astronomy, biology, economic, among others*. Such events are very common in the real world: *viral diseases, seizure, carcinogenic tumors, fevers, machinery and equipment failures, births, murders, rain, industrial accidents, car accidents* and son on. The idea is to generalize the weighted statistics used in classical models. The estimations of the survival functions are based on a non-parametric model proposed by **Peña** *et al*., using counting processes. **R**-*language* routines were designed to make the estimates of the new statistical tests. Some of these routines were based in packages in the same language, like *survival* and *survrec*. The **Byar** database experiment was used to measured times *(months*) of recurrence of tumors in 116 sick patients with superficial bladder cancer. These patients were randomly allocated to the following treatments: *placebo* (47 patients), *pyridoxine* (31 patients) and *thiotepa* (38 patients). The aforementioned database allowed the comparison the survival functions of the three groups using the statistical tests to determine if there were significant differences between treatments.

**Bibliography:**

**Byar D., (1980)**: “The veterans administrations study of chemoprophylaxis for recurrent stage I bladder tumors: Comparisons of placebo, pyridoxine, and topical thiotepa. *In Bladder tumor and other Topics in Urological Oncology*. New York: Plenum, 363-370.

**Martinez, C.** (**2009**), “Generalizacion de algunas pruebas clasicas de comparacion de curvas de supervivencia al caso de eventos de naturaleza recurrentes”. *Tesis doctoral UCV*. ltf87200962043. **ISBN**: 978-980-123605-04.Venezuela. Caracas.

**Martinez, C., Ramirez G., Vasquez M**. (**2009**), “Pruebas no parametricas para comparar curvas de supervivencia de dos grupos que experimentan eventos recurrentes. Propuestas”. Revista de ingenieria U.C., Vol. 16, N° 3.

**Peña E., Strawderman R., Hollander M., (2001).** “Nonparametric estimation with recurrent event data”. *Journal of the American Statistical Association* 96, 1299–1315.

**R Development Core Team** (**2010**). **R**: A language and environment for statistical computing. *R Foundation for Statistical Computing*, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.

**Keywords:** Survival analysis; Recurrent events; Statistical tests; Counting processes

**Biography:** Venezuelan, Industrial Engineer, Magister in Industrial Engineer and Doctor in Statistics, Professor Operations Research and Statistic of the University of Carabobo. Areas of investigation: Statistical Multivariate, Systems Reliability, Survival Analysis, Operations Research.