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In this paper, a new long term survival model called Nadarajah-Haghighi model for survival data with long term survivors was proposed. The model is used in fitting data where the population of interest is a mixture of individuals that are susceptible to the event of interest and individuals that are not susceptible to the event of interest. The statistical properties of the proposed model including quantile function, moments, mean and variance were provided. Maximum likelihood estimation procedure was used to estimate the parameters of the model assuming right censoring. Furthermore, Bayesian method of estimation was also employed in estimating the parameters of the model assuming right censoring. Simulations study was performed in order to ascertain the performances of the MLE estimators. Random samples of different sample sizes were generated from the model with some arbitrary values for the parameters for 5%, 1:3% and 1:5% cure fraction values. Bias, standard error and mean square error were used as discrimination criteria. Additionally, we compared the performance of the proposed model with some competing models. The results of the applications indicates that the proposed model is more efficient than the models compared with. Finally, we fitted some models considering type of treatment as a covariate. It was observed that the covariate have effect on the shape parameter of the proposed model.
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Berkson, J. and Gage, R. P. (1952). Survival curve for cancer patients following treatment. Journal of the American
Statistical Association, 47(259):501–515.
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), 11(1):15–53.
Cancho, V. G., Rodrigues, J., and de Castro, M. (2011). A flexible model for survival data with a cure rate: a bayesian
approach. Journal of Applied Statistics, 38(1):57–70.
Cantor, A. B. and Shuster, J. J. (1992). Parametric versus non-parametric methods for estimating cure rates based on
censored survival data. Statistics in Medicine, 11(7):931–937.
Coelho-Barros, E. A., Achcar, J. A., and Mazucheli, J. (2017). Cure rate models considering the burr xii distribution
in presence of covariate. Journal of Statistical Theory and Applications, 16(2):150–164.
Farewell, V. T. (1986). Mixture models in survival analysis: Are they worth the risk? Canadian Journal of Statistics,
Gamel, J. W., McLean, I. W., and Rosenberg, S. H. (1990). Proportion cured and mean log survival time as functions
of tumour size. Statistics in Medicine, 9(8):999–1006.
Gieser, P. W., Chang, M. N., Rao, P., Shuster, J. J., and Pullen, J. (1998). Modelling cure rates using the gompertz
model with covariate information. Statistics in medicine, 17(8):831–839.
Kannan, N., Kundu, D., Nair, P., and Tripathi, R. C. (2010). The generalized exponential cure rate model with
covariates. Journal of Applied Statistics, 37(10):1625–1636.
Kersey, J. H., Weisdorf, D., Nesbit, M. E., LeBien, T. W., Woods, W. G., McGlave, P. B., Kim, T., Vallera, D. A.,
Goldman, A. I., Bostrom, B., et al. (1987). Comparison of autologous and allogeneic bone marrow transplantation
for treatment of high-risk refractory acute lymphoblastic leukemia. New England Journal of Medicine, 317(8):461–
Kutal, D. and Qian, L. (2018). A non-mixture cure model for right-censored data with frechet distribution. ´ Stats,
Maller, R. A. and Zhou, X. (1996). Survival analysis with long-term survivors. Wiley New York.
Meeker, W. Q. (1987). Limited failure population life tests: application to integrated circuit reliability. Technometrics,
Nadarajah, S. and Haghighi, F. (2011). An extension of the exponential distribution. Statistics, 45(6):543–558.
Nelsen, R. B. (2007). An introduction to copulas. Springer Science & Business Media.
Ng, S. and McLachlan, G. (1998). On modifications to the long-term survival mixture model in the presence of
competing risks. Journal of Statistical Computation and Simulation, 61(1-2):77–96.
Peng, Y., Dear, K. B., and Denham, J. (1998). A generalized f mixture model for cure rate estimation. Statistics in
Shao, Q. and Zhou, X. (2004). A new parametric model for survival data with long-term survivors. Statistics in
Sy, J. P. and Taylor, J. M. (2000). Estimation in a cox proportional hazards cure model. Biometrics, 56(1):227–236.