A mixture cure rate model is considered for time-to-event data having a cure fraction under a competing risks scenario. It is assumed that the count of unobservable competing causes follows a Conway-Maxwell Poisson (COM-Poisson) distribution, and time-to-event follows a generalized exponential distribution. The expectation-maximization (EM) algorithm is applied for estimating the proposed model parameters under the interval-censoring. The model performance is studied by Monte Carlo simulation using Akaike information criteria (AIC) and Bayesian information criteria (BIC), for varying sample sizes, cure fractions, and model parameters. Further, the coverage probabilities and root mean square errors (RMSE) obtained from the simulation study are also analysed. Finally, the maximum likelihood estimators (MLE) and their standard errors are obtained using the proposed model for the breast cosmesis dataset.

cure rate model, EM algorithm, maximum likelihood estimates, Akaike information criteria, Bayesian information criteria.

Received: April 26, 2022; Accepted: June 21, 2022; Published: August 6, 2022

How to cite this article: Janani Amirtharaj and G. Vijayasree, COM-Poisson cure rate model with generalized exponential lifetimes under interval-censoring: an EM-based approach, JP Journal of Biostatistics 21 (2022), 29-54. http://dx.doi.org/10.17654/0973514322019

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] N. Balakrishnan and S. Pal, EM algorithm-based likelihood estimation for some cure rate models, Journal of Statistical Theory and Practice 6 (2012), 698-724.
[2] N. Balakrishnan and S. Pal, Expectation maximization-based likelihood inference for flexible cure rate models with Weibull lifetimes, Stat. Methods Med. Res. 25 (2013a), 1535-1563.
[3] N. Balakrishnan and S. Pal, Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family, Comput. Statist. Data Anal. 67 (2013b), 41-67.
[4] N. Balakrishnan and S. Pal, An EM algorithm for the estimation of parameters of a flexible cure rate model with generalized gamma lifetimes and model discrimination using likelihood and information-based methods, Comput. Statist. 30 (2014), 151-189.
[5] N. Balakrishnan and S. Pal, Likelihood inference for flexible cure rate models with gamma lifetimes, Comm. Statist. Theory Methods 44 (2015), 4007-4048.
[6] J. Berkson and R. P. Gage, Survival cure for cancer patients following treatment, J. Amer. Stat. Assoc. 47 (1952), 501-515.
[7] J. W. Boag, Maximum likelihood estimates of the proportion of patients cured by cancer therapy, Journal of the Royal Statistical Society: Series B 11 (1949), 15-53.
[8] R. W. Conway and W. L. Maxwell, A queuing model with state dependent services rates, Journal of Industrial Engineering 12 (1962), 132-136.
[9] D. Cox and D. Oakes, Analysis of Survival Data, Chapman & Hall, London, 1984.
[10] F. Daly and R. E. Gaunt, The Conway-Maxwell-Poisson distribution: distributional theory and approximation, Latin American Journal of Probability and Mathematical Statistics 13 (2016), 635-658.
[11] K. Davies, S. Pal and J. A. Siddiqua, Stochastic EM algorithm for generalized exponential cure rate model and an empirical study, J. Appl. Stat. 48 (2021), 2112-2135.
[12] V. T. Farewell, The use of mixture models for the analysis of survival data with long-term survivors, Biometrics 38 (1982), 1041-1046.
[13] R. D. Gupta and D. Kundu, Generalized exponential distribution: existing results and some recent developments, J. Statist. Plann. Inference 137 (2007), 3537-3547.
[14] J. B. Kadane, G. Shmueli, T. P. Minka, S. Borle and P. Boatwright, Conjugate analysis of the Conway-Maxwell-Poisson distribution, Bayesian Analysis 1 (2006), 363-374.
[15] N. Kannan, D. Kundu, P. Nair and R. C. Tripathi, The generalized exponential cure rate model with covariates, J. Appl. Stat. 37(9-10) (2010), 1625-1636.
[16] A. Y. C. Kuk and C. H. Chen, A mixture model combining logistic regression with proportional hazards regression, Biometrika 79 (1992), 531-541.
[17] T. A. Louis, Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society: Series B 44 (1982), 226-233.
[18] R. A. Maller and X. Zhou, Survival Analysis with Long-term Survivors, John Wiley & Sons, New York, 1996.
[19] G. J. McLachlan and T. Krishnan, The EM Algorithm and Extensions, Second ed., John Wiley & Sons, Hoboken, New Jersey, 2008.
[20] S. Pal and N. Balakrishnan, Likelihood inference based on EM algorithm for the destructive length-biased Poisson cure rate model with Weibull lifetime, Comm. Statist. Simulation Comput. 47(3) (2018), 644-660. https://doi.org/10.1080/03610918.2015.1053918.
[21] S. Pal and N. Balakrishnan, Destructive negative binomial cure rate model and EM-based likelihood inference under Weibull lifetime, Statist. Probab. Lett. 116 (2016), 9-20.
[22] S. Pal and N. Balakrishnan, Likelihood inference for COM-Poisson cure rate model with interval-censored data and Weibull lifetimes, Stat. Methods Med. Res. 26(5) (2017), 2093-2113.
[23] S. Pal and N. Balakrishnan, An EM type estimation procedure for the destructive exponentially weighted Poisson regression cure model under generalized gamma lifetime, J. Stat. Comput. Simulation 87(6) (2017a), 1107-1129.
[24] S. Pal and N. Balakrishnan, Likelihood inference for the destructive exponentially weighted Poisson cure rate model with Weibull lifetime and an application to melanoma data, Comput. Statist. 32(2) (2017b), 429-449.
[25] Y. Peng and K. B. G. Dear, A nonparametric mixture model for cure rate estimation, Biometrics 56 (2000), 237-243.
[26] Y. Peng, K. B. G. Dear and J. W. Denham, A generalized F mixture model for cure rate estimation, Stat. Med. 7 (1998), 813-830.
[27] J. Rodrigues, M. de Castro, V. G. Cancho and N. Balakrishnan, COM-Poisson cure rate survival models and an application to a cutaneous melanoma data, J. Statist. Plann. Inference 139 (2009), 3605-3611.
[28] J. Rodrigues, G. M. Coderio, V. G. Cancho and N. Balakrishnan, Relaxed Poisson cure rate model, Biom. J. 58 (2016), 397-415.
[29] G. Shmueli, T. P. Minka, J. B. Kadane, S. Borle and P. Boatwright, A useful distribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribution, Journal of the Royal Statistical Society: Series C 54 (2005), 127-142.
[30] J. M. G. Taylor, Semi-parametric estimation in failure time mixture model, Biometrics 51 (1995), 899-907.
[31] P. Wiangnak and S. Pal, Gamma lifetimes and associated inference for interval-censored cure rate model with COM-Poisson competing cause, Comm. Statist. Theory Methods 47(6) (2017), 1491-1509.
[32] A. Y. Yokovlev, B. Asselain, V. Bardou, A. Fourquet, T. Hoang, A. Rochefediere and A. Tsodkov, A simple stochastic model of tumor recurrence and its application to data on premenopausal breast cancer, Biometrics et Analyse de Donnees Spatio-Temporelles 12 (1993), 66-82.