Journal of Biostatistics and Epidemiology 2016. 2(2):52-59.

Cure mixture model based on hazard modeling non-proportional, application to esophageal cancer
Mahboubeh Rasouli, Mahmoodreza Ghadimi, Masoomeh Shohani, Asieh Ashouri, Samaneh Hosseinzadeh, Kazem Mohammad, Mahmood Mahmoodi


Background & Aim: Esophageal cancer is one of the main common causes of death. The high prevalence of esophageal cancer in northern Iran is an important public health problem. The main aim of this paper was to assess the factors affecting survival of  atients with esophageal cancer in neighbor provinces around the Caspian Sea using Weibull mixture cure model and mixture cure model based on a non-proportional hazard.
Methods & Materials: This prospective study was designed to gather data of esophageal cancer from the Babol cancer registry, Iran, registered during 1990 to 1991. The study cases were also followed for a period of 15 years up to 2006. Mixture cure model via non-proportional hazard modeling was used to calculate cure fraction and investigate the factors responsible for the cure probability of patients. Estimates were obtained by maximization of the likelihood via SAS proc NLMIXED.
Results: The median survival time was about 9 months and survival probability in 1, 3, and 5 years following diagnosis were 23%, 15% and 13%, respectively. The family history affected the cured fraction independently of its effect on the early outcome  In addition, it had significant effect on the probability of uncured state in the both models.
Conclusion: The results demonstrated the great potential in cure modeling survival data via nonproportional hazard model compared to Weibull mixture cure model.


Long-term survival; Esophageal cancer; Non-Proportional hazard model; Mixture cure model

Full Text:



Yazdanbod A, Naseri Moghadam S, Malekzadeh R. Upper gastrointestinal cancer in Ardabil, north-west of Iran: A review. Arch Iran Med 2004; 7(3): 173-7.

Ferlay J, Bray F, Pisani P, Parkin DM. Globocan 2002: Cancer incidence. Mortality and prevalence worldwide. IARC CancerBase No. 5, version 2.0. Lyon, France: IARC Press; 2004.

American Cancer Society. Cancer Facts and Figures 2007. Atlanta, GA: American Cancer Society; 2007.

Lu S, Lin P, Wang G, Luo X, Wu M. Comprehensive prevention and treatment for esophageal cancer. Chin Med J (Engl) 1999; 112(10): 918-23.

Ghavamzadeh A, Moussavi A, Jahani M, Rastegarpanah M, Iravani M. Esophageal cancer in Iran. Semin Oncol 2001; 28(2): 153-7.

Naghavi M. Death report from 10 provinces in Iran. Tehran, Iran: Ministry of Health and Medical Education; 2000.

Dusek L, Muzk J, Koptikova J, Brabec P, Zaloudik J, Vyzula R, et al. The nationam web portal for cancer epidemiology in the Czech Republic. Brno, Czech Republic: Masaryk University; 2000.

Whelan SL, Parkin DM, Masuyer E. Trends in cancer incidence and mortality. Lyon, France: IARC scientific publication; 1993. p. 102.

Bollschweiler E, Wolfgarten E, Nowroth T, Rosendahl U, Monig SP, Holscher AH. Vitamin intake and risk of subtypes of esophageal cancer in Germany. J Cancer Res Clin Oncol 2002; 128(10): 575-80.

Eloubeidi MA, Desmond R, Arguedas MR, Reed CE, Wilcox CM. Prognostic factors for the survival of patients with esophageal carcinoma in the U.S.: the importance of tumor length and lymph node status. Cancer 2002; 95(7): 1434-43.

Enzinger PC, Mayer RJ. Esophageal cancer. N Engl J Med 2003; 349(23): 2241-52.

Glade MJ. Food, nutrition, and the prevention of cancer: a global perspective. American Institute for Cancer Research/World Cancer Research Fund, American Institute for Cancer Research, 1997. Nutrition 1999; 15(6): 523-6.

Medvec BR. Esophageal cancer: treatment and nursing interventions. Semin Oncol Nurs 1988; 4(4): 246-56.

Tsottles ND, Reedy AM. Esophageal cancer. In: Yarbro CH, Frogge MH, Goodman M, Editors. Cancer Nursing: Principles and Practice. Burlington, MA: Jones & Bartlett Learning; 2005.

Corley DA, Buffler PA. Oesophageal and gastric cardia adenocarcinomas: analysis of regional variation using the Cancer Incidence in Five Continents database. Int J Epidemiol 2001; 30(6): 1415-25.

Mohebbi M, Mahmoodi M, Wolfe R, Nourijelyani K, Mohammad K, Zeraati H, et al. Geographical spread of gastrointestinal tract cancer incidence in the Caspian Sea region of Iran: spatial analysis of cancer registry data. BMC Cancer 2008; 8: 137.

Nyren O, Adami HO, Hunter D. Esophageal Cancer. In: Adami HO, Hunter DJ, Trichopoulos D, Editors. Textbook of cancer epidemiology. Oxford, UK: Oxford University Press; 2002. p. 137-61.

Stein HJ, von Rahden BH, Siewert JR. Survival after oesophagectomy for cancer of the oesophagus. Langenbecks Arch Surg 2005; 390(4): 280-5.

Zendehdel K. Risk indicators for esophageal cancer: some medical conditions and tobaccorelated indicators [Thesis]. Tehran, Iran: Tehran University of Medical Sciences; 2007. [In Persian].

Cox DR. Regression Models and Life-Tables. J R Stat Soc Series B Stat 1972; 34(2): 187-220.

Perperoglou A, Keramopoullos A, van Houwelingen HC. Approaches in modeling long-term survival: an application to breast cancer. Stat Med 2007; 26(13): 2666-85.

Sposto R. Cure model analysis in cancer: an application to data from the Children's Cancer Group. Stat Med 2002; 21(2): 293-312.

Mackenzie G. Regression Models for Survival Data: The Generalized Time-Dependent Logistic Family. J R Stat Soc Series D 1996; 45(1): 21-34.

Mackenzie G. On a non-proportional hazards regression model for repeated medical random counts. Stat Med 1997; 16(16): 1831-43.

Al-Tawarah Y. On the generalized time dependent logistic family of survival models [PhD Thesis]. Keele, England: Keele University; 2004.

Rasouli M, Ghadimi MR, Mahmoodi M, Mohammad K, Zeraati H, Hosseini M. Survival analysis of patients with esophageal cancer using parametric cure model. Asian Pac J Cancer Prev 2011; 12(9): 2359-63.

Bagheri M. Study of risk factors of GI cancer in Mazandaran Provience [PhD Thesis]. Tehran, Iran: School of Public Health and Institute of Public Health Research, Tehran University of Medical Sciences; 1997. [In Persian].

Pour P, Ghadirian P. Familial cancer of the esophagus in Iran. Cancer 1974; 33(6): 1649-52.

Ghadirian P. Familial history of esophageal cancer. Cancer 1985; 56(8): 2112-6.

Shafieizadeh T, Holakaiee K, Fotohi A, Mahmody M, Drakhshandeh P. Familial esophageal cancer in Babol [MSc Thesis]. Tehran, Iran: School of Public Health, Tehran University of Medical Sciences; 2005. [In Persian].

Akbari MR, Malekzadeh R, Nasrollahzadeh D, Amanian D, Sun P, Islami F, et al. Familial risks of esophageal cancer among the Turkmen population of the Caspian littoral of Iran. Int J Cancer 2006; 119(5): 1047-51.

Ghadirian P, Stein GF, Gorodetzky C, Roberfroid MB, Mahon GA, Bartsch H, et al. Oesophageal cancer studies in the Caspian littoral of Iran: some residual results, including opium use as a risk factor. Int J Cancer 85; 35(5): 593-7.

Wang YP, Han XY, Su W, Wang YL, Zhu YW, Sasaba T, et al. Esophageal cancer in Shanxi Province, People's Republic of China: a case-control study in high and moderate risk areas. Cancer Causes Control 1992; 3(2): 107-13.

Vaughan TL, Davis S, Kristal A, Thomas DB. Obesity, alcohol, and tobacco as risk factors for cancers of the esophagus and gastric cardia: adenocarcinoma versus squamous cell carcinoma. Cancer Epidemiol Biomarkers Prev 1995; 4(2): 85-92.

Brown LM, Silverman DT, Pottern LM, Schoenberg JB, Greenberg RS, Swanson GM, et al. Adenocarcinoma of the esophagus and esophagogastric junction in white men in the United States: alcohol, tobacco, and socioeconomic factors. Cancer Causes Control 1994; 5(4): 333-40.

Kabat GC, Ng SK, Wynder EL. Tobacco, alcohol intake, and diet in relation to adenocarcinoma of the esophagus and gastric cardia. Cancer Causes Control 1993; 4(2): 123-32.

Zhang ZF, Kurtz RC, Sun M, Karpeh M Jr, Yu GP, Gargon N, et al. Adenocarcinomas of the esophagus and gastric cardia: medical conditions, tobacco, alcohol, and socioeconomic factors. Cancer Epidemiol Biomarkers Prev 1996; 5(10): 761-8.

Wu-Williams AH, Yu MC, Mack TM. Lifestyle, workplace, and stomach cancer by subsite in young men of Los Angeles County. Cancer Res 1990; 50(9): 2569-76.

Li JY, Ershow AG, Chen ZJ, Wacholder S, Li GY, Guo W, et al. A case-control study of cancer of the esophagus and gastric cardia in Linxian. Int J Cancer 1989; 43(5): 755-61.

Jedrychowski W, Boeing H, Wahrendorf J, Popiela T, Tobiasz-Adamczyk B, Kulig J. Vodka consumption, tobacco smoking and risk of gastric cancer in Poland. Int J Epidemiol 1993; 22(4): 606-13.

Palli D, Bianchi S, Decarli A, Cipriani F, Avellini C, Cocco P, et al. A case-control study of cancers of the gastric cardia in Italy. Br J Cancer 1992; 65(2): 263-6.

Gonzalez CA, Agudo A, Montes J, Riboli E, Sanz JM. Tobacco and alcohol intake in relation to adenocarcinoma of the gastric cardia in Spain. Cancer Causes Control 1994; 5(1): 88-9.

Gao YT, McLaughlin JK, Gridley G, Blot WJ, Ji BT, Dai Q, et al. Risk factors for esophageal cancer in Shanghai, China. II. Role of diet and nutrients. Int J Cancer 1994; 58(2): 197-202.

Levi F, Ollyo JB, La Vecchia C, Boyle P, Monnier P, Savary M. The consumption of tobacco, alcohol and the risk of adenocarcinoma in Barrett's oesophagus. Int J Cancer 1990; 45(5): 852-4.

Altman DG, De Stavola BL, Love SB, Stepniewska KA. Review of survival analyses published in cancer journals. Br J Cancer 1995; 72(2): 511-8.

Blagojevic M. Extending the model. Undergraduate logistic survival generalized time-dependent summer project [Thesis]. Keele, UK: Keele University; 2001.


  • There are currently no refbacks.

Creative Commons Attribution-NonCommercial 3.0

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License which allows users to read, copy, distribute and make derivative works for non-commercial purposes from the material, as long as the author of the original work is cited properly.