A New Long-Term Survival Distribution for Cancer Data

Abstract

1 1 Universidade Federal de S~ao Carlos and 2 Universidade de S~ao Paulo Abstract: In this paper we propose a new three-parameters lifetime distribu- tion with decreasing hazard function, the long-term exponential geometric distribution. The new distribution arises on latent competing risks scenarios, where the lifetime associated with a particular risk is not observable, rather we observe only the minimum lifetime value among all risks, and there is presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its survival and hazard functions, order statistics, Bonferroni function and the Lorenz curve. The parameter estimation is based on the usual maximum likelihood approach. We compare the new distribution with its particular case, the long-term exponential distribution, as well as with the long-term Weibull distribution on two real datasets, observing its poten- tial and competitiveness in comparison with an usual lifetime distribution.