An Application of Gamma Generalized Linear Model for Estimation of Survival Function of Diabetic Nephropathy Patients
DOI:
https://doi.org/10.6000/1929-6029.2013.02.03.6Keywords:
Akaike Information Criterion, Gamma distribution, generalized linear models, Kaplan Meier method, log link, reciprocal link, serum creatinine, survival distributionsAbstract
Diabetic nephropathy (DN) is a generic term referring to deleterious effect on renal structure and/or function caused by diabetes mellitus. World Health Organization estimates that diabetes affects more than 170 million people worldwide and this number may rise to 370 million by 2030. The rate of rise in Serum Creatinine (SrCr) is a well-accepted marker for the progression of Diabetic Nephropathy (DN). In this paper, survival functions of type 2 diabetic patients with renal complication are estimated. Firstly, most appropriate distribution for duration of diabetes is selected through minimum Akaike Information Criterion value, Gamma distribution is found to be an appropriate model. Secondly, the parameters estimates of the selected distribution are obtained by fitting a Generalized Linear Model (GLM), with duration of diabetes as the response variable and predictors as SrCr and number of successes (number of times SrCr values exceed its normal range (1.4 mg/dl)). These covariates are linked with the response variable using two different link functions namely log and reciprocal links. Using the estimates of parameters obtained from generalized linear regression analysis, survival functions for different durations under both the links are estimated. Further we compared the estimated survival functions under both the links with Kaplan Meier (KM) estimates graphically. Findings suggested that the Kaplan Meier estimate and Gamma distribution under both links provided a close estimate of survival functions. Median survival time is 16.3 years and 16.8 years obtained from KM method and Gamma GLM respectively.
References
King H, Aubert RE, Herman WH. Global burden of diabetes, 1995-2025: prevalence, numerical estimates, and projections. Diabetes Care 1998; 21: 1414-31. http://dx.doi.org/10.2337/diacare.21.9.1414 DOI: https://doi.org/10.2337/diacare.21.9.1414
Amos AF, McCarty DJ, Zimmet P. The rising global burden of diabetes and its complications: estimates and projections to the year 2010. Diabet Med 1997; 14(5): S1-S85. doi:10.1002/(SICI)1096-9136(199712)14:5+3.0.CO;2-R. DOI: https://doi.org/10.1002/(SICI)1096-9136(199712)14:5+<S7::AID-DIA522>3.0.CO;2-R
Campbell RC, Ruggenenti P, Remuzzi G. Proteinuria in diabetic nephropathy: treatment and evolution. Current Diabetic Report 2007; 3(6): 497-504. http://dx.doi.org/10.1007/s11892-003-0014-0 DOI: https://doi.org/10.1007/s11892-003-0014-0
Craig KJ, Donovan K, Munnery M, Owens DR, Williams JD, Phillips AO. Identification and management of diabetic nephropathy in the diabetes clinic. Diabetes Care 2003; 26(6): 1806-11. http://dx.doi.org/10.2337/diacare.26.6.1806 DOI: https://doi.org/10.2337/diacare.26.6.1806
Mazze, Strock, Simonson, Bergenstal. Staged-diabetes management: A systematic approach. 2nd ed. John Wiley & Sons; 2005 DOI: https://doi.org/10.1002/9780470061701
Adler AI, Stevens RJ, Manley SE, Bilous RW, Cull CA, Holman RR. Development and Progression of nephropathy in type 2 diabetes: Observation and modeling from the United Kingdom Prospective Diabetes Study. Kidney Int 2003; 63: 225-32. http://dx.doi.org/10.1046/j.1523-1755.2003.00712.x DOI: https://doi.org/10.1046/j.1523-1755.2003.00712.x
Dabla PK. Renal function in diabetic nephropathy. World J Diabetes 2010; 1(2): 48-56. http://dx.doi.org/10.4239/wjd.v1.i2.48 DOI: https://doi.org/10.4239/wjd.v1.i2.48
Akaike H. Information theory and an extension of the maximum likelihood principle. Proceeding of 2nd International Symposium on information theory. Petrov BN, Caski F, Eds., Akademia Kiado, Budapest 1973; pp. 267-81.
Klein JP, Moeschberger ML. Survival analysis techniques for censored and truncated data. Springer Verlag, New York, USA; 2003. DOI: https://doi.org/10.1007/b97377
Hayat EA, Suner A, Uyar B, Dursan O, Orman MN, Kitapcioglu G. Comparison of five survival models: breast cancer registry data from Ege university cancer research center. Turkiye Klinikeri J Med Sci 2010; 30(5): 1665-74. http://dx.doi.org/10.5336/medsci.2009-16200 DOI: https://doi.org/10.5336/medsci.2009-16200
Hakulinen T, Tenkanen L. Regression analysis of relative survival rates. Appl Statist 1987; 36: 309-317. http://dx.doi.org/10.2307/2347789 DOI: https://doi.org/10.2307/2347789
Karmen A. Application of the generalized linear model to the prediction of lung cancer survival. 2006; 1-18. http://analytics. ncsu.edu/sesug/2006/ST09_06.PDF
Yuan X, Hong D, Shyr Y. Survival model and estimation for lung cancer patients 2007; 201-22. http://capone.mtsu.edu/ dhong/YuanHongShyr07.pdf DOI: https://doi.org/10.1142/9789812772121_0010
Akram M, Ullah MA, Taj R. Survival analysis of cancer patients using parametric and non-parametric approaches. Pakistan Vet J 2007; 27(4): 194-98. http://www.pvj.com.pk/ pdf-files/27_4/194-198.pdf
Exponential families. http://www.math.siu.edu/olive/ich3.pdf
Lee ET, Go OT. Survival analysis in public health research. Annu Rev Public Health 1997; 18: 105-134. http://dx.doi.org/10.1146/annurev.publhealth.18.1.105 DOI: https://doi.org/10.1146/annurev.publhealth.18.1.105
Lindsey JK, Jones B. Choosing among generalized linear models applied to medical data. Statist Med 1998; 17: 59-68. http://dx.doi.org/10.1002/(SICI)1097-0258(19980115)17:1<59::AID-SIM733>3.0.CO;2-7 DOI: https://doi.org/10.1002/(SICI)1097-0258(19980115)17:1<59::AID-SIM733>3.0.CO;2-7
Acquah H de-Graft. Comparison of Akaike information criterion (AIC) and Bayesian information criterion (BIC) in selection of an asymmetric price relationship. J Develop Agric Econom 2010; 2(1): 1-6. http://www.academicjournals. org/JDAE
Bradburn MJ, Clark TG, Love SB, Altman DG. Survival analysis part III: Multivariate data analysis-choosing a model and assessing its adequacy and fit. Br J Cancer 2003; 89: 605-11. http://dx.doi.org/10.1038/sj.bjc.6601120 DOI: https://doi.org/10.1038/sj.bjc.6601120
Myers RH, Montgomery DC, Vining GG. Generalized Linear Models: With Application in Engineering and the SciencesJohn Wiley and Sons, New York 2002.
Huettmann F, Linke J. Assessment of different link functions for modeling binary data to derive sound inferences and predictions. Springer-Verlag Berlin Heidelberg 2003; 43-48. http://individual.utoronto.ca/julialinke/ICCSA2003_HuettmannandLinke.pdf. DOI: https://doi.org/10.1007/3-540-44842-X_5
Grover G, Gadpayle AK, Sabharwal A. Identifying patients with diabetic nephropathy based on serum creatinine under zero truncated model. Electron J Appl Statist Anal 2010; 3(1): 28-43. http://siba-ese.unile.it/index.php/ejasa/article/view/ i20705948v3n1p28/3029.
Mohan V, Pradeepa R. Epidemiology of diabetes in different regions of India. Health Administrator 2009; 22(1,2): 1- 18.
American Diabetes Association: Position statement: Diabetic nephropathy. Diabetes Care 1999; 22 (Supp 1): S66-69.
Gross JL, Azevedo MJD, Silveiro SP, Canani LH, Caramori ML, Zelmanovitz T. Diabetic nephropathy: Diagnosis, prevention, and treatment. Diabetes Care 2005; 28: 176-88. http://dx.doi.org/10.2337/diacare.28.1.164 DOI: https://doi.org/10.2337/diacare.28.1.164
Grover G, Sabharwal A, Mittal J. A Bayesian approach for estimating onset time of nephropathy for type 2 diabetic patients under various health conditions. IJSP 2013; 2(2): 89-101. http://dx.doi.org/10.5539/ijsp.v2n2p89 DOI: https://doi.org/10.5539/ijsp.v2n2p89
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