A flexible bimodal model with long-term survivors and different regression structures. (English) Zbl 1489.62353
Summary: The cure fraction models are useful to model lifetime data with long-term survivors. In this paper, we introduce a flexible cure rate survival model where the model parameters are related to covariates in different regression structures. The regression model allows to model jointly the location, scale and shape effects. The maximum likelihood method is employed to estimate the model parameters. We provide Monte Carlo simulation experiments to verify the performance of the maximum likelihood estimates for different sample sizes and cure rate percentages. Furthermore, some diagnostic measures to assess departures from model assumptions as well as to detect outlying observations are also considered. Finally, applications to real data are presented to show the usefulness of the new cure rate model.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62N02 | Estimation in survival analysis and censored data |
| 62N05 | Reliability and life testing |
Keywords:
bi-modality; cure rate models; parametric inference; residual analysis; sensitivity analysisReferences:
| [1] | Alizadeh, M.; Ramires, T. G.; MirMostafaee, S. M. T. K.; Samizadeh, M.; Ortega, E. M. M., A new useful four-parameter extension of the Gumbel distribution: Properties, regression model and applications using the GAMLSS framework, Communications in Statistics - Simulation and Computation (2018) · Zbl 1491.62014 · doi:10.1080/03610918.2018.1423691 |
| [2] | Balakrishnan, N.; Koutras, M. V.; Milienos, F.; Pal, S., Piecewise linear approximations for cure rate models and associated inferential issues, Methodology and Computing in Applied Probability, 18, 4, 937-66 (2016) · Zbl 1373.62481 |
| [3] | Balakrishnan, N.; Pal, S., An EM algorithm for the estimation of flexible cure rate model parameters with generalized gamma lifetime and model discrimination using likelihood- and information-based methods, Computational Statistics, 30, 1, 151-89 (2015) · Zbl 1342.65019 |
| [4] | Berkson, J.; Gage, R. P., Survival curve for cancer patients following treatment, Journal of the American Statistical Association, 47, 259, 501-15 (1952) |
| [5] | Boag, J. W., Maximum likelihood estimates of the proportion of patients cured by cancer therapy, Journal of the Royal Statistical Society B, 11, 15-53 (1949) · Zbl 0034.08001 |
| [6] | Cancho, V. G.; Bandyopadhyay, D.; Louzada, F.; Yiqi, B., The destructive negative binomial cure rate model with a latent activation scheme, Statistical Methodology, 13, 48-68 (2013) · Zbl 1365.62410 |
| [7] | Cook, R. D.; Weisberg, S., Residuals and influence in regression (1982), New York, NY: Chapman and Hall, New York, NY · Zbl 0564.62054 |
| [8] | Cooray, K., Exponentiated sinh Cauchy distribution with applications, Communications in Statistics - Theory and Methods, 42, 21, 3838-52 (2013) · Zbl 1466.62248 |
| [9] | Cox, D. R.; Hinkley, D. V., Theoretical statistics (1974), London, UK: Chapman and Hall, London, UK · Zbl 0334.62003 |
| [10] | Dunn, P. K.; Smyth, G. K., Randomized quantile residuals, Journal of Computational and Graphical Statistics, 5, 3, 236-44 (1996) |
| [11] | Farewell, V. T., The use of mixture models for the analysis of survival data with long-term survivors, Biometrics, 38, 4, 1041-6 (1982) |
| [12] | Gendoo, D. M. A.; Ratanasirigulchai, N.; Schroder, M.; Pare, L.; Parker, J. S.; Prat, A.; Haibe-Kains, B. (2015) |
| [13] | Haque, R.; Ahmed, S. A.; Inzhakova, G.; Shi, J.; Avila, C.; Polikoff, J.; Bernstein, L.; Enger, M. S.; Press, M. F., Impact of breast cancer subtypes and treatment on survival: An analysis spanning two decades, Cancer Epidemiology Biomarkers & Prevention, 21, 10, 1848-55 (2012) |
| [14] | Hashimoto, E. M.; Ortega, E. M. M.; Cordeiro, G. M.; Cancho, V. G., The Poisson Birnbaum-Saunders model with long-term survivors, Statistics, 48, 6, 1394-413 (2014) · Zbl 1306.62231 |
| [15] | Jácome, A. A. A.; Wohnrath, D. R.; Neto, C. S.; Fregnani, J. H. T. G.; Quinto, A. L.; Oliveira, A. T. T.; Vazquez, V. L.; Fava, G.; Martinez, E. Z.; Santos, J. S., Effect of adjuvant chemoradiotherapy on overall survival of gastric cancer patients submitted to D2 lymphadenectomy, Gastric Cancer, 16, 2, 233-8 (2013) |
| [16] | Johnson, N. L.; Kotz, S.; Balakrishnan, N., Continuous univariate distributions (1994), New York, NY: Wiley, New York, NY · Zbl 0811.62001 |
| [17] | Maller, R. A.; Zhou, X., Survival analysis with long-term survivors (1996), New York, NY: Wiley, New York, NY · Zbl 1151.62350 |
| [18] | Martinez, E. Z.; Achcar, J. A.; Jácome, A. A. A.; Santos, J. S., Mixture and non-mixture cure fraction models based on the generalized modified Weibull distribution with an application to gastric cancer data, Computer Methods and Programs in Biomedicine, 112, 3, 343-55 (2013) |
| [19] | Ortega, E. M. M.; Cancho, V. G.; Paula, G. A., Generalized log-gamma regression models with cure fraction, Lifetime Data Analysis, 15, 1, 79-106 (2009) · Zbl 1302.62236 |
| [20] | Ortega, E. M. M.; Cordeiro, G. M.; Campelo, A. K.; Kattan, M. W.; Cancho, V. G., A power series beta Weibull regression model for predicting breast carcinoma, Statistics in Medicine, 34, 8, 1366-88 (2015) |
| [21] | Ortega, E. M. M.; Cordeiro, G. M.; Hashimoto, E. M.; Suzuki, A. K., Regression models generated by gamma random variables with long-term survivors, Communications for Statistical Applications and Methods, 24, 1, 43-65 (2017) |
| [22] | R Core Team, R: A language and environment for statistical computing (2016), Vienna, Austria: R Foundation for Statistical Computing, Vienna, Austria |
| [23] | Ramires, T. G.; Ortega, E. M. M.; Cordeiro, G. M.; Hens, N., A bimodal flexible distribution for lifetime data, Journal of Statistical Computation and Simulation, 86, 12, 2450-70 (2016) · Zbl 1510.62402 |
| [24] | Ramires, T. G.; Ortega, E. M.; Cordeiro, G. M.; Paula, G. A.; Hens, N., New regression model with four regression structures and computational aspects, Communications in Statistics - Simulation and Computation, 47, 7, 1940-62 (2017) · Zbl 07550078 · doi:10.1080/03610918.2017.1332212 |
| [25] | Rigby, R. A.; Stasinopoulos, D. M., Generalized additive models for location, scale and shape, Journal of the Royal Statistical Society: Series C (Applied Statistics), 54, 3, 507-54 (2005) · Zbl 1490.62201 |
| [26] | Rodrigues, J.; de Castro, M.; Cancho, V. G.; Balakrishnan, N., COM-Poisson cure rate survival models and an application to a cutaneous melanoma data, Journal of Statistical Planning and Inference, 139, 10, 3605-11 (2009) · Zbl 1173.62074 |
| [27] | Rodrigues, J.; Cordeiro, G. M.; Cancho, V. G.; Balakrishnan, N., Relaxed Poisson cure rate models, Biometrical Journal. Biometrische Zeitschrift, 58, 2, 397-415 (2016) · Zbl 1381.62281 |
| [28] | Talacko, J., Perks’ distributions and their role in the theory of Wiener’s stochastic variables, Trabajos de Estadística, 7, 2, 159-74 (1956) · Zbl 0074.12804 |
| [29] | Voudouris, V.; Gilchrist, R.; Rigby, R.; Sedgwick, J.; Stasinopoulos, D., Modelling skewness and kurtosis with the BCPE density in GAMLSS, Journal of Applied Statistics, 39, 6, 1279-93 (2012) · Zbl 1514.62333 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
