Bivariate Basu-Dhar geometric model for survival data with a cure fraction
DOI:
https://doi.org/10.1285/i20705948v11n2p655Keywords:
Basu-Dhar distribution, cure fraction, discrete distributions, MCMC methods, lifetime dataAbstract
Under a context of survival lifetime analysis, we introduce in this paper Bayesian and maximum likelihood approaches for the bivariate Basu-Dhar geometric model in the presence of covariates and a cure fraction. This distribution is useful to model bivariate discrete lifetime data. In the Bayesian estimation, posterior summaries of interest were obtained using standard Markov Chain Monte Carlo methods in the OpenBUGS software. Maximum likelihood estimates for the parameters of interest were computed using the \textquotedblleft maxLik" package of the R software. Illustrations of the proposed approaches are given for two real data sets.References
Achcar, J. A., Coelho-Barros, E. A. and Mazucheli, J. (2013). Block and Basu bivariate lifetime distribution in the presence of cure fraction. Journal of Applied Statistics,
(9):1864-1874.
Achcar, J. A., Davarzani, N. and Souza, R. M. (2016). Basu-Dhar bivariate geometric distribution in the presence of covariates and censored data: a Bayesian approach.
Journal of Applied Statistics, 43(9):1636-1648.
Almalki, S. J. and Nadarajah, S. (2014). A new discrete modified Weibull distribution. IEEE Transactions on Reliability, 63(1):68-80.
Arnold, B. (1975). A characterization of the exponential distribution by multivariate geometric compounding. Sankhya: The Indian Journal of Statistics, Series A,
(1):164-173.
Basu, A. P. and Dhar, S. (1995). Bivariate geometric distribution. Journal of Applied Statistical Science, 2(1):33-44.
Block, H. W. and Basu, A. P. (1974). A continuous bivariate exponential extension. Journal of the American Statistical Association, 69(348):1031-1037.
Boag, J. W. (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal Statistical Society. Series B (Methodological),
(1):15-53.
Brenna, S. M., Silva, I. D., Zeferino, L. C., Pereira, J. S., Martinez, E. Z. and Syrjanen, K. J. (2004). Prognostic value of P53 codon 72 polymorphism in invasive cervical
cancer in Brazil. Gynecologic Oncology, 93(2):374-380.
Davarzani, N., Achcar, J. A., Simirnov, E. N. and Peeters, R. (2015). Bivariate lifetime geometric distribution in presence of cure fraction. Journal of Data Science, 13(4):755-
Dewan, I., Sudheesh, K. K. and Anisha, P. (2016). Proportional hazards model for discrete data: some new developments. Communications in Statistics - Theory and
Methods, 45(21):6481-6493.
Freund, J. E. (1961). A bivariate extension of the exponential distribution. Journal of the American Statistical Association, 56(296):971-977.
Geisser, S. and Eddy, W. (1979). A predictive approach to model selection. Journal of the American Statistical Association, 74(365):153-160.
Gupta, R. D. and Kundu, D. (1999). Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2):173-188.
Hawkes, A. G. (1972). A bivariate exponential distribution with applications to reliability. Journal of the Royal Statistical Society. Series B (Methodological), 34(1):129-131.
Henningsen, A. and Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3):443-458.
Herzog, W., Schellberg, D. and Deter, H. C. (1997). First recovery in anorexia nervosa patients in the long-term course: a discrete-time survival analysis. Journal of
Consulting and Clinical Psychology, 65(1):169-177.
Huster, W. J., Brookmeyer, R. and Self, S. G. (1989). Modelling paired survival data with covariates. Biometrics, 45(1):145-156.
Kulasekera, K. B. and Tonkyn, D. W. (1992). A new discrete distribution, with applications to survival, dispersal and dispersion. Communications in Statistics-Simulation
and Computation, 21(2):499-518.
Lambert, P. C., Thompson, J. R., Weston, C. L. and Dickman, P. W. (2007). Estimating and modeling the cure fraction in population-based cancer survival analysis.
Biostatistics, 8(3):576-594.
Marshall, A. W. and Olkin, I. (1967). A generalized bivariate exponential distribution. Journal of Applied Probability, 4(2):291-302.
Martinez, E. Z. and Achcar J. A. (2014). Bayesian bivariate generalized Lindley model for survival data with a cure fraction. Computer Methods and Programs in Biomedicine 117(2):145-157.
Martinez, E. Z., Achcar, J. A., Jacome, A. A. and Santos, J. S. (2013). Mixture and non-mixture cure fraction models based on the generalized modied Weibull distribution
with an application to gastric cancer data. Computer Methods and Programs in Biomedicine, 112(3):343-355.
Nakagawa, T. and Osaki, S. (1975). The discrete Weibull distribution. IEEE Transactions on Reliability, 24(5):300-301.
Roy, D. (2004) Discrete Rayleigh distribution. IEEE Transactions on Reliability, 53(2):255-260.
Sarkar, S. K. (1987) A continuous bivariate exponential distribution. Journal of the American Statistical Association, 82(398):667-675.
Scheike, T. H. and Jensen, T. K. (1997). A discrete survival model with random effects: an application to time to pregnancy. Biometrics, 53(1):318-329.
Singer, J. D. and Willett, J. B. (1993). It's about time: Using discrete-time survival analysis to study duration and the timing of events. Journal of Educational and
Behavioral Statistics, 18(2):155-195.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2014). The deviance information criterion: 12 years on (with discussion). Journal of the Royal
Statistical Society: Series B (Statistical Methodology), 76(3):485-493.
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