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COM-Poisson cure rate survival models and an application to cutaneous melanoma data. (English) Zbl 1173.62074
Summary: We develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow the R. W. Conway and W. L. Maxwell Poisson distribution [J. Indust. Eng. XII, No. 2, 132–136 (1961)]. This model includes as special cases some of the well-known cure rate models discussed in the literature. Next, we discuss the maximum likelihood estimation of the parameters of this cure rate survival model. Finally, we illustrate the usefulness of this model by applying it to real cutaneous melanoma data.

MSC:
62N02 Estimation in survival analysis and censored data
62P10 Applications of statistics to biology and medical sciences; meta analysis
Software:
GAMLSS; SPLIDA; R
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[1] Berkson, J.; Gage, R.P., Survival cure for cancer patients following treatment, Journal of the American statistical association, 47, 259, 501-515, (1952)
[2] Boag, J.W., Maximum likelihood estimates of the proportion of patients cured by cancer therapy, Journal of the royal statistical society B, 11, 1, 15-53, (1949) · Zbl 0034.08001
[3] Chen, M.-H.; Ibrahim, J.G.; Sinha, D., A new Bayesian model for survival data with a surviving fraction, Journal of the American statistical association, 94, 447, 909-919, (1999) · Zbl 0996.62019
[4] Claeskens, G.; Nguti, R.; Janssen, P., One-sided tests in shared frailty models, Test, 17, 1, 69-82, (2008) · Zbl 1148.62086
[5] Conway, R.W.; Maxwell, W.L., A queuing model with state dependent services rates, The journal of industrial engineering, XII, 2, 132-136, (1961)
[6] Cox, D.; Oakes, D., Analysis of survival data, (1984), Chapman & Hall London
[7] Hoggart, C.J.; Griffin, J.E., A Bayesian partition model for customer attrition, (), 61-70
[8] Ibrahim, J.G.; Chen, M.-H.; Sinha, D., Bayesian survival analysis, (2001), Springer New York · Zbl 0978.62091
[9] Johnson, N.L.; Kemp, A.W.; Kotz, S., Univariate discrete distribution, (2005), Hoboken New Jersey
[10] Kadane, J.B.; Shmueli, G.; Minka, T.P.; Borle, S.; Boatwright, P., Conjugate analysis of the conway – maxwell – poisson distribution, Bayesian analysis, 1, 2, 363-374, (2006) · Zbl 1331.62086
[11] Kirkwood, J.M.; Ibrahim, J.G.; Sondak, V.K.; Richards, J.; Flaherty, L.E.; Ernstoff, M.S.; Smith, T.J.; Rao, U.; Steele, M.; Blum, R.H., High- and low-dose interferon alfa-2b in high-risk melanoma: first analysis of intergroup trial E1690/S9111/C9190, Journal of clinical oncology, 18, 12, 2444-2458, (2000)
[12] Kokonendji, C.C.; Mizère, D.; Balakrishnan, N., Connections of the Poisson weight function to overdispersion and underdispersion, Journal of statistical planning and inference, 138, 5, 1287-1296, (2008) · Zbl 1133.62007
[13] Meeker, W.Q., Escobar, L.A., 1998. Statistical Methods for Reliability Data. New York. · Zbl 0949.62086
[14] R: A language and environment for statistical computing, (2008), R Foundation for Statistical Computing Vienna, Austria
[15] Rigby, R.A.; Stasinopoulos, D.M., Generalized additive models for location, scale and shape (with discussion), Applied statistics, 54, 3, 507-554, (2005) · Zbl 05188697
[16] Rodrigues, J.; Cancho, V.G.; de Castro, M.; Louzada-Neto, F., On the unification of the long-term survival models, Statistics and probability letters, 79, 753-759, (2009) · Zbl 1349.62485
[17] Self, S.G.; Liang, K.-Y., Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions, Journal of the American statistical association, 82, 398, 605-610, (1987) · Zbl 0639.62020
[18] Shmueli, G.; Minka, T.P.; Kadane, J.B.; Borle, S.; Boatwright, P., A useful distribution for Fitting discrete data: revival of the conway – maxwell – poisson distribution, Journal of the royal statistical society C, 54, 1, 127-142, (2005) · Zbl 05188676
[19] Stasinopoulos, D.M.; Rigby, R.A., Generalized additive models for location, scale and shape (GAMLSS) in R, Journal of statistical software, 23, 7, 1-46, (2007)
[20] Tsodikov, A.D.; Ibrahim, J.G.; Yakovlev, A.Y., Estimating cure rates from survival data: an alternative to two-component mixture models, Journal of the American statistical association, 98, 464, 1063-1078, (2003)
[21] Yakovlev, A.Y., Parametric versus nonparametric methods for estimating cure rates based on censored survival-data, Statistics in medicine, 13, 9, 983-985, (1994)
[22] Yakovlev, A.Y.; Tsodikov, A.D., Stochastic models of tumor latency and their biostatistical applications, (1996), World Scientific Singapore · Zbl 0919.92024
[23] Yakovlev, A.Y.; Tsodikov, A.D.; Bass, L., A stochastic-model of hormesis, Mathematical biosciences, 116, 2, 197-219, (1993) · Zbl 0777.92010
[24] Yin, G.; Ibrahim, J.G., Cure rate models: a unified approach, The Canadian journal of statistics, 33, 4, 559-570, (2005) · Zbl 1098.62127
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