The Modelling Survival Times for Diabetes Patient Using Exponential, Weibull and Rayleigh-Lomax Distribution

Manda Lisa Usvita; Arisman Adnan; Rado Yendra

doi:https://doi.org/10.14445/22315373/IJMTT-V67I5P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 5 | Year 2021 | Article Id. IJMTT-V67I5P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I5P513

The Modelling Survival Times for Diabetes Patient Using Exponential, Weibull and Rayleigh-Lomax Distribution

Manda Lisa Usvita, Arisman Adnan, Rado Yendra

Citation :

Manda Lisa Usvita, Arisman Adnan, Rado Yendra, "The Modelling Survival Times for Diabetes Patient Using Exponential, Weibull and Rayleigh-Lomax Distribution," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 5, pp. 109-112, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I5P513

Abstract

Diabetes is a complex, slowly progressive silent killer disease. This destroys multiple organs by damaging and clogging the small capillaries – micro vascular system. Survival functions (probability density function) of diabetes patients are estimated in this paper. Conclusions about the occurrence probability distribution of diabetes patient in the Mandau Regional General Hospital (RSUD), Bengkalis Regency, Riau Province will be easier to use statistical models. For this purpose, three kinds of distribution, namely Exponential (E), Weibull (W), and Rayleigh-Lomax (RL) were applied to survival times of diabetes patients. Method of Moments was used to obtain the estimated parameter. Based on the smallest Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC) values, and graphical inspection (probability density function (pdf)) to survival times of diabetes patients, the study has shown that RL is the best fit distribution in modeling survival times for diabetes patients in the Mandau RSUD, Bengkalis Regency, Riau Province.

Keywords

Diabetes, exponential distribution, Rayleigh-Lomax distribution, survival times, Weibull distribution.

References

[1] D. Collet, Modeling survival data in medical research, 2nd ed., Chapman and Hall/CRC, London, (2003).
[2] D. G. Kleinbaum and M. Klein, Survival Analysis, A Self-Learning Text 3rd Ed, Springer, New York, (2012).
[3] E. T. Lee and J.W. Wang, Statistical methods for survival data analysis, Third Ed., Johns Wiley and Sons, New Jersey, (2003).
[4] G. Casela and R. L. Berger, Statistical Inference, 2nd ed., Duxbury, New York, (2002).
[5] G. Gurpit, S. Alka, and M. Juhi, An Application of Gamma Generalized Linear Model for Estimation of Survival Function of Diabetic Nephropathy Patiens, International Journal of Statistics in Medical Research, 2(2013), 209-219.
[6] H. Bozdogan, Akaike’s information criterion and recent developments in information complexity, Journal of Mathematical Psychology, 44 (2000), 62-91.
[7] International Diabetes Federation, International Diabetes Federation 9th ed., Brusseles,( 2019).
[8] Juli, Kencing Manis dan Hipertensi Masuk 10 Pola Penyakit Utama di Bengkalis, 3 November 2019, http ://infopublik.id/ kategori/ nusantara/ 384135, accessed 11 januari 2020.
[9] K. Atkinson and W. Han, Elementary Numerical Analysis, 3rd ed., John Wiley and Sons, New Jersey, (2004).
[10] K. Fatima, U. Jan, and S. P. Ahmad, Statistical Properties of Rayleigh Lomax Distribution with Applications in Survival Analysis, Journal of Data Science, 3(2018), 531-548.
[11] S. K. Marvasti, S.Rimaz, J. Abolghasemi, and I. Heydari, Comparing of Cox model and parametric models in analysis of effective factors on event time of neuropathy in patients with type 2 diabetes, Journal of Research in Medical Science, (2017).
[12] S. Alka dan G. Gurprit, A Parametric Approach to Estimate Survival Time of Diabetic Nephropathy with Left Truncated and Right Censored Data, International Journal of Statistics and Probability, 1(1) (2012) 128-137.
[13] V. Lusiana, Menkes sebut diabetes paling banyak ”serang” warga Riau ini sebabnya, 25 Maret 2019, https://riau.antaranews.com/berita/112025, accessed 8 juni 2019.