An Application of Gamma Generalized Linear Model for Estimation of Survival Function of Diabetic Nephropathy Patients

Authors

  • Gurprit Grover Department of Statistics, University of Delhi, Delhi, India
  • Alka Sabharwal Alka Sabharwal Department of Statistics, University of Delhi, Delhi, India
  • Juhi Mittal Department of Statistics, University of Delhi, Delhi, India

DOI:

https://doi.org/10.6000/1929-6029.2013.02.03.6

Keywords:

Akaike Information Criterion, Gamma distribution, generalized linear models, Kaplan Meier method, log link, reciprocal link, serum creatinine, survival distributions

Abstract

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.

Author Biographies

Gurprit Grover, Department of Statistics, University of Delhi, Delhi, India

Department of Statistics

Alka Sabharwal Alka Sabharwal, Department of Statistics, University of Delhi, Delhi, India

Department of Statistics

Juhi Mittal, Department of Statistics, University of Delhi, Delhi, India

Department of Statistics

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Published

2013-07-30

How to Cite

Grover, G., Alka Sabharwal, A. S., & Mittal, J. (2013). An Application of Gamma Generalized Linear Model for Estimation of Survival Function of Diabetic Nephropathy Patients. International Journal of Statistics in Medical Research, 2(3), 209–219. https://doi.org/10.6000/1929-6029.2013.02.03.6

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General Articles