Statistical Tests To Compare k Survival Analysis Functions Involving Recurrent Events
Carlos M. Martinez1, Guillermo Ramirez2, Maura L. Vasquez2
1Engineering Faculty, University of Carabobo (UC), Bárbula-Naguanagua, Carabobo, Venezuela; 2FACES, Central University of Venezuela (UCV), Caracas, Distrito Federal, Venezuela

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.


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

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.