Application of Gamma Frailty Model in Survival of Liver Cirrhosis Patients
Goals and Objectives: A typical analysis of survival data involves the modeling of time-to-event data, such as the time till death. A frailty model is a random effect model for time-to-event data, where the random effect has a multiplicative influence on the baseline hazard function. This article aims to investigate the use of gamma frailty model with concomitant variable in order to individualize the prognostic factors that influence the liver cirrhosis patients’ survival times. Methods: During the one-year study period (May 2008-May 2009), data have been used from the recorded information of patients with liver cirrhosis who were scheduled for liver transplantation and were followed up for at least seven years in Imam Khomeini Hospital in Iran. In order to determine the effective factors for cirrhotic patients’ survival in the presence of latent variables, the gamma frailty distribution has been applied. In this article, it was considering the parametric model, such as Exponential and Weibull distributions for survival time. Data analysis is performed using R software, and the error level of 0.05 was considered for all tests. Results: 305 patients with liver cirrhosis including 180 (59%) men and 125 (41%) women were studied. The age average of patients was 39.8 years. At the end of the study, 82 (26%) patients died, among them 48 (58%) were men and 34 (42%) women. The main cause of liver cirrhosis was found hepatitis 'B' with 23%, followed by cryptogenic with 22.6% were identified as the second factor. Generally, 7-year’s survival was 28.44 months, for dead patients and for censoring was 19.33 and 31.79 months, respectively. Using multi-parametric survival models of progressive and regressive, Exponential and Weibull models with regard to the gamma frailty distribution were fitted to the cirrhosis data. In both models, factors including, age, bilirubin serum, albumin serum, and encephalopathy had a significant effect on survival time of cirrhotic patients. Conclusion: To investigate the effective factors for the time of patients’ death with liver cirrhosis in the presence of latent variables, gamma frailty model with parametric distributions seems desirable.
[1] Alavian M. Comprehensive guide to public cirrhosis: Kosar; 1392.
[2] O'Shea RS, Dasarathy S, McCullough AJ. Alcoholic liver disease. Hepatology. 2010;51(1):307-28.
[3] Komova A, Maevskaya M, Ivashkin V. Prevalence of Liver Disease in Russia’s Largest City: A Population-based Study. American Journal of Clinical Medicine Research. 2014;2(5):99-102.
[4] Khademolhosseini F, Malekhosseini S, Salahi H, Nikeghbalian S, Bahador A, Lankarani KB, et al. Outcome and characteristics of patients on the liver transplant waiting list: Shiraz experience. Middle East Journal of Digestive Diseases (MEJDD). 2009;1(2):63-7.
[5] Goodarzi Z, Jazayeri SM. Hepatitis B virus preS variant and hepatocellular carcinoma. Hepatitis Monthly. 2008;8(2):129-33.
[6] Poustchi H, Sepanlou SG, Esmaeili S, Mehrabi M, Ansarymoghadam A. Hepatocellular carcinoma in the world and the middle East. Middle East Journal of Digestive Diseases (MEJDD). 2010;2(1):31-41.
[7] Grattagliano I, Ubaldi E, Bonfrate L, Portincasa P. Management of liver cirrhosis between primary care and specialists. World J Gastroenterol. 2011;17(18):2273-82.
[8] Daniels D, Grytdal S, Wasley A, Control CfD, Prevention. surveillance for acute viral hepatitis, United States, 2007: Department of Health and Human Services, Centers for Disease Control and Prevention; 2009.
[9] Hougaard P. Frailty models for survival data. Lifetime data analysis. 1995;1(3):255-73.
[10] Gutierrez RG. Parametric frailty and shared frailty survival models. Stata Journal. 2002;2(1):22-44.
[11] McGilchrist C, Aisbett C. Regression with frailty in survival analysis. Biometrics. 1991:461-6.
[12] Zokaei M, Maghsoudi M. Paper: Reconstruction Of Frailty-Based Mortality Models By A Generalisation Of Gompertz Distribution.
[13] Pourhoseingholi MA, Hajizadeh E, Moghimi Dehkordi B, Safaee A, Abadi A, Zali MR. Comparing Cox regression and parametric models for survival of patients with gastric carcinoma. Asian Pacific Journal of Cancer Prevention. 2007;8(3):412.
[14] Oakes D. Bivariate survival models induced by frailties. Journal of the American Statistical Association. 1989;84(406):487-93.
[15] Oakes D. Biometrika centenary: survival analysis. Biometrika. 2001;88(1):99-142.
[16] Zhang Y, Chen M-H, Ibrahim JG, Zeng D, Chen Q, Pan Z, et al. Bayesian gamma frailty models for survival data with semi-competing risks and treatment switching. Lifetime data analysis. 2014;20(1):76-105.
[17] Abolghasemi J, Asadi Lari M, Mohammadi M, Salehi M. Effective factors in the appearance of metastasis in patients with breast cancer using frailty model. Arak Medical University Journal. 2013;15(8):85-94.
[18] Velázquez RF, Rodriguez M, Navascues CA, Linares A, Perez R, Sotorríos NG, et al. Prospective analysis of risk factors for hepatocellular carcinoma in patients with liver cirrhosis. Hepatology. 2003;37(3):520-7.
[19] Sabet B, Rajaee-fard A, Nikeghbalian S, Malek-Hosseini SA. Six Years Liver Transplants Outcome in Shiraz Transplant Center. Journal of Isfahan Medical School, 2009; 27. (99).
[20] Hui AY, Chan HL-Y, Wong VW-S, Liew C-T, Chim AM-L, Chan FK-L, et al. Identification of chronic hepatitis B patients without significant liver fibrosis by a simple noninvasive predictive model. The American journal of gastroenterology. 2005;100(3):616-23.
[21] Fazeli, Pour FB, Abadi, Pourhoseingholi, Taghinejad. Studying of liver cancer mortality and morbidity burden in Iran.
[22] Khameneh ME, Sepehri MM, Saberifiroozi M. Using Data Mining for Identify Patients at High Risk to Hepatocellular Carcinoma in the Cirrhosis Liver: Preliminary Report. Govaresh. 2014;19(4):265-74.
[23] Saberifiroozi M, Serati AR, Malekhosseini SA, Salahi H, Bahador A, Lankarani KB, et al. Analysis of patients listed for liver transplantation in Shiraz, Iran. Indian Journal of Gastroenterology. 2006;25(1):11.
[24] Malek-Hosseini S, Mehdizadeh A, Salahi H, Saberi-Firouzi M, Bagheri-Lankarani K, Bahador A, et al., editors. Results of liver transplantation: analysis of 140 cases at a single center. Transplantation proceedings; 2005: Elsevier.
[25] Hajiani E, Seyedian M. Evaluation of cardiac echocardiography in patients with liver cirrhosis. 2008;13(3).
[26] Bustamante J, Rimola A, Ventura P-J, Navasa M, Cirera I, Reggiardo V, et al. Prognostic significance of hepatic encephalopathy in patients with cirrhosis. Journal of hepatology. 1999;30(5):890-5.
[27] Attallah AM, Shiha GE, Omran MM, Zalata KR. A discriminant score based on four routine laboratory blood tests for accurate diagnosis of severe fibrosis and/or liver cirrhosis in Egyptian patients with chronic hepatitis C. Hepatology research. 2006;34(3):163-9.
[28] Solerio E, Isaia G, Innarella R, Di Stefano M, Farina M, Borghesio E, et al. Osteoporosis: still a typical complication of primary biliary cirrhosis? Digestive and liver disease. 2003;35(5):339-46.
[29] Boulton‐Jones J, Fenn R, West J, Logan R, Ryder S. Fracture risk of women with primary biliary cirrhosis: no increase compared with general population controls. Alimentary pharmacology & therapeutics. 2004;20(5):551-7.
[30] Alavian S-M. Immunization: An Important Strategy to Control Hepatitis B. Hepatitis monthly. 2006;6(1):5-3.
[31] Maynard JE, Kane MA, Hadler SC. Global control of hepatitis B through vaccination: role of hepatitis B vaccine in the Expanded Programme on Immunization. Review of Infectious Diseases. 1989;11(Supplement 3):S574-S8.
[32] Polido Jr WT, Lee K-H, Tay K-H, Wong S-Y, Singh R, Leong S-O, et al. Adult living donor liver transplantation in Singapore: the Asian centre for liver diseases and transplantation experience. strategies. 2007;9:11.
[33] Féray C, Caccamo L, Alexander GJ, Ducot B, Gugenheim J, Casanovas T, et al. European collaborative study on factors influencing outcome after liver transplantation for hepatitis C. Gastroenterology. 1999;117(3):619-25.
[1] Alavian M. Comprehensive guide to public cirrhosis: Kosar; 1392.
[2] O'Shea RS, Dasarathy S, McCullough AJ. Alcoholic liver disease. Hepatology. 2010;51(1):307-28.
[3] Komova A, Maevskaya M, Ivashkin V. Prevalence of Liver Disease in Russia’s Largest City: A Population-based Study. American Journal of Clinical Medicine Research. 2014;2(5):99-102.
[4] Khademolhosseini F, Malekhosseini S, Salahi H, Nikeghbalian S, Bahador A, Lankarani KB, et al. Outcome and characteristics of patients on the liver transplant waiting list: Shiraz experience. Middle East Journal of Digestive Diseases (MEJDD). 2009;1(2):63-7.
[5] Goodarzi Z, Jazayeri SM. Hepatitis B virus preS variant and hepatocellular carcinoma. Hepatitis Monthly. 2008;8(2):129-33.
[6] Poustchi H, Sepanlou SG, Esmaeili S, Mehrabi M, Ansarymoghadam A. Hepatocellular carcinoma in the world and the middle East. Middle East Journal of Digestive Diseases (MEJDD). 2010;2(1):31-41.
[7] Grattagliano I, Ubaldi E, Bonfrate L, Portincasa P. Management of liver cirrhosis between primary care and specialists. World J Gastroenterol. 2011;17(18):2273-82.
[8] Daniels D, Grytdal S, Wasley A, Control CfD, Prevention. surveillance for acute viral hepatitis, United States, 2007: Department of Health and Human Services, Centers for Disease Control and Prevention; 2009.
[9] Hougaard P. Frailty models for survival data. Lifetime data analysis. 1995;1(3):255-73.
[10] Gutierrez RG. Parametric frailty and shared frailty survival models. Stata Journal. 2002;2(1):22-44.
[11] McGilchrist C, Aisbett C. Regression with frailty in survival analysis. Biometrics. 1991:461-6.
[12] Zokaei M, Maghsoudi M. Paper: Reconstruction Of Frailty-Based Mortality Models By A Generalisation Of Gompertz Distribution.
[13] Pourhoseingholi MA, Hajizadeh E, Moghimi Dehkordi B, Safaee A, Abadi A, Zali MR. Comparing Cox regression and parametric models for survival of patients with gastric carcinoma. Asian Pacific Journal of Cancer Prevention. 2007;8(3):412.
[14] Oakes D. Bivariate survival models induced by frailties. Journal of the American Statistical Association. 1989;84(406):487-93.
[15] Oakes D. Biometrika centenary: survival analysis. Biometrika. 2001;88(1):99-142.
[16] Zhang Y, Chen M-H, Ibrahim JG, Zeng D, Chen Q, Pan Z, et al. Bayesian gamma frailty models for survival data with semi-competing risks and treatment switching. Lifetime data analysis. 2014;20(1):76-105.
[17] Abolghasemi J, Asadi Lari M, Mohammadi M, Salehi M. Effective factors in the appearance of metastasis in patients with breast cancer using frailty model. Arak Medical University Journal. 2013;15(8):85-94.
[18] Velázquez RF, Rodriguez M, Navascues CA, Linares A, Perez R, Sotorríos NG, et al. Prospective analysis of risk factors for hepatocellular carcinoma in patients with liver cirrhosis. Hepatology. 2003;37(3):520-7.
[19] Sabet B, Rajaee-fard A, Nikeghbalian S, Malek-Hosseini SA. Six Years Liver Transplants Outcome in Shiraz Transplant Center. Journal of Isfahan Medical School, 2009; 27. (99).
[20] Hui AY, Chan HL-Y, Wong VW-S, Liew C-T, Chim AM-L, Chan FK-L, et al. Identification of chronic hepatitis B patients without significant liver fibrosis by a simple noninvasive predictive model. The American journal of gastroenterology. 2005;100(3):616-23.
[21] Fazeli, Pour FB, Abadi, Pourhoseingholi, Taghinejad. Studying of liver cancer mortality and morbidity burden in Iran.
[22] Khameneh ME, Sepehri MM, Saberifiroozi M. Using Data Mining for Identify Patients at High Risk to Hepatocellular Carcinoma in the Cirrhosis Liver: Preliminary Report. Govaresh. 2014;19(4):265-74.
[23] Saberifiroozi M, Serati AR, Malekhosseini SA, Salahi H, Bahador A, Lankarani KB, et al. Analysis of patients listed for liver transplantation in Shiraz, Iran. Indian Journal of Gastroenterology. 2006;25(1):11.
[24] Malek-Hosseini S, Mehdizadeh A, Salahi H, Saberi-Firouzi M, Bagheri-Lankarani K, Bahador A, et al., editors. Results of liver transplantation: analysis of 140 cases at a single center. Transplantation proceedings; 2005: Elsevier.
[25] Hajiani E, Seyedian M. Evaluation of cardiac echocardiography in patients with liver cirrhosis. 2008;13(3).
[26] Bustamante J, Rimola A, Ventura P-J, Navasa M, Cirera I, Reggiardo V, et al. Prognostic significance of hepatic encephalopathy in patients with cirrhosis. Journal of hepatology. 1999;30(5):890-5.
[27] Attallah AM, Shiha GE, Omran MM, Zalata KR. A discriminant score based on four routine laboratory blood tests for accurate diagnosis of severe fibrosis and/or liver cirrhosis in Egyptian patients with chronic hepatitis C. Hepatology research. 2006;34(3):163-9.
[28] Solerio E, Isaia G, Innarella R, Di Stefano M, Farina M, Borghesio E, et al. Osteoporosis: still a typical complication of primary biliary cirrhosis? Digestive and liver disease. 2003;35(5):339-46.
[29] Boulton‐Jones J, Fenn R, West J, Logan R, Ryder S. Fracture risk of women with primary biliary cirrhosis: no increase compared with general population controls. Alimentary pharmacology & therapeutics. 2004;20(5):551-7.
[30] Alavian S-M. Immunization: An Important Strategy to Control Hepatitis B. Hepatitis monthly. 2006;6(1):5-3.
[31] Maynard JE, Kane MA, Hadler SC. Global control of hepatitis B through vaccination: role of hepatitis B vaccine in the Expanded Programme on Immunization. Review of Infectious Diseases. 1989;11(Supplement 3):S574-S8.
[32] Polido Jr WT, Lee K-H, Tay K-H, Wong S-Y, Singh R, Leong S-O, et al. Adult living donor liver transplantation in Singapore: the Asian centre for liver diseases and transplantation experience. strategies. 2007;9:11.
[33] Féray C, Caccamo L, Alexander GJ, Ducot B, Gugenheim J, Casanovas T, et al. European collaborative study on factors influencing outcome after liver transplantation for hepatitis C. Gastroenterology. 1999;117(3):619-25.
@article{"International Journal of Medical, Medicine and Health Sciences:75594", author = "Elnaz Saeedi and Jamileh Abolaghasemi and Mohsen Nasiri Tousi and Saeedeh Khosravi", title = "Application of Gamma Frailty Model in Survival of Liver Cirrhosis Patients", abstract = "Goals and Objectives: A typical analysis of survival data involves the modeling of time-to-event data, such as the time till death. A frailty model is a random effect model for time-to-event data, where the random effect has a multiplicative influence on the baseline hazard function. This article aims to investigate the use of gamma frailty model with concomitant variable in order to individualize the prognostic factors that influence the liver cirrhosis patients’ survival times. Methods: During the one-year study period (May 2008-May 2009), data have been used from the recorded information of patients with liver cirrhosis who were scheduled for liver transplantation and were followed up for at least seven years in Imam Khomeini Hospital in Iran. In order to determine the effective factors for cirrhotic patients’ survival in the presence of latent variables, the gamma frailty distribution has been applied. In this article, it was considering the parametric model, such as Exponential and Weibull distributions for survival time. Data analysis is performed using R software, and the error level of 0.05 was considered for all tests. Results: 305 patients with liver cirrhosis including 180 (59%) men and 125 (41%) women were studied. The age average of patients was 39.8 years. At the end of the study, 82 (26%) patients died, among them 48 (58%) were men and 34 (42%) women. The main cause of liver cirrhosis was found hepatitis 'B' with 23%, followed by cryptogenic with 22.6% were identified as the second factor. Generally, 7-year’s survival was 28.44 months, for dead patients and for censoring was 19.33 and 31.79 months, respectively. Using multi-parametric survival models of progressive and regressive, Exponential and Weibull models with regard to the gamma frailty distribution were fitted to the cirrhosis data. In both models, factors including, age, bilirubin serum, albumin serum, and encephalopathy had a significant effect on survival time of cirrhotic patients. Conclusion: To investigate the effective factors for the time of patients’ death with liver cirrhosis in the presence of latent variables, gamma frailty model with parametric distributions seems desirable.
", keywords = "Frailty model, latent variables, liver cirrhosis, parametric distribution.", volume = "11", number = "5", pages = "282-4", }
