Original Article

Identifying Influential Prognostic Factors of Death Hazard Rates in Patients with Chronic Kidney Disease (CKD) Using Weibull Model with Non-Constant Shape Parameter


Introduction: Chronic Kidney Disease (CKD) is a disease in which damaged kidneys could not remove waste material from the blood which could result in other health problems. The aim of this analysis was to identify significant laboratory prognostic factors on death hazard due to CKD.

Methods: There were 109 patients with end-stage renal disease (ESRD) treated at Helal pharmaceutical and clinical complex. The survival time was set as the time interval from starting dialysis until death due to CKD. Age, gender and factors such as creatinine, cholesterol, uric acid, SGOT, SGPT, bilirubin, hemoglobin, potassium, ALP, HbA1C, ferritin, calcium, phosphorus, PTH and albumin were employed in this study. Weibull Distribution with non-Constant Shape Parameter versus constant Shape Parameter for the analysis were used.

Results: Death due to CKD occurred in 29 (26.6%) of the patients. Sixty-seven (61.5%) had uric acid higher than 6.8 (mg/dl) and 39(35%) had phosphorus higher than 4.7 (mg/dl) which were poor prognoses. The incidence of death was 48.4%. Calcium<8.5 (mg/dl) (p=0.002), Calcium > 9.5 (mg/dl) (p=0.003), Albumin 4-6.3 (g/dl) (p=0.034), Phosphorus (p=0.022), hemoglobin<10 (g/dl) (p=0.043), hemoglobin>12.5 (g/dl) (p=0.006) and iPTH (p<0.001) were significant variables which had an effect on death hazard rates.

Conclusion: The Weibull model with Non-Constant shape parameter was suggested to be more accurate for identifying risk factors, leading to more precise results, compared to constant shape parameter. Investigators mostly emphasize on the importance of Calcium, Albumin, Phosphorus, hemoglobin and iPTH for reducing hazard rates in CKD patients.

1. Levey AS, Becker C, Inker LA. Glomerular filtration rate and albuminuria for detection and staging of acute and chronic kidney disease in adults: A systematic review. JAMA - J Am Med Assoc [Internet] 2015 [cited 2020 Oct 31];313(8):837–46. Available from: https://jamanetwork.com/journals/jama/fullarticle/2130322.
2. Ozieh MN, Bishu KG, Dismuke CE, Egede LE. Trends in healthcare expenditure in United States adults with chronic kidney disease: 2002-2011. BMC Health Serv Res [Internet] 2017 [cited 2020 Oct 18];17(1):1–9. Available from: https://link.springer.com/articles/10.1186/ s12913-017-2303-3.
3. Chen TK, Knicely DH, Grams ME. Chronic Kidney Disease Diagnosis and Management: A Review [Internet]. JAMA J. Am. Med. Assoc.2019 [cited 2020 Oct 18];322(13):1294–304. Available from: https://jamanetwork.com/journals/jama/ fullarticle/2752067.
4. Ketteler M, Block GA, Evenepoel P, Fukagawa M, Herzog CA, McCann L, et al. Diagnosis, evaluation, prevention, and treatment of chronic kidney disease-mineral and bone disorder: Synopsis of the kidney disease: Improving global outcomes 2017 clinical practice guideline update [Internet]. Ann. Intern. Med.2018 [cited 2020 Oct 31];168(6):422–30. Available from: http://annals.org/article.aspx?doi=10.7326/M17- 2640
5. Coresh J, Astor BC, Greene T, Eknoyan G, Levey AS. Prevalence of chronic kidney disease and decreased kidney function in the adult US population: Third National Health and Nutrition Examination Survey. Am J Kidney Dis 2003;41(1):1–12.
6. Stanifer JW, Muiru A, Jafar TH, Patel UD. Chronic kidney disease in low- and middleincome countries [Internet]. Nephrol. Dial. Transplant.2016 [cited 2020 Oct 18];31(6):868–74. Available from: https://academic.oup.com/ ndt/article/31/6/868/1752179.
7. Xie Y, Bowe B, Mokdad AH, Xian H, Yan Y, Li T, et al. Analysis of the Global Burden of Disease study highlights the global, regional, and national trends of chronic kidney disease epidemiology from 1990 to 2016. Kidney Int [Internet] 2018 [cited 2020 Oct 19];94(3):567– 81. Available from: https://www.sciencedirect. com/science/article/pii/S0085253818303181.
8. Tohidi M, Hasheminia M, Mohebi R, Khalili D, Hosseinpanah F, Yazdani B, et al. Incidence of Chronic Kidney Disease and Its Risk Factors, Results of Over 10 Year Follow Up in an Iranian Cohort. PLoS One [Internet] 2012 [cited 2020 Oct 18];7(9):e45304. Available from: https://dx.plos.org/10.1371/journal.pone.0045304.
9. Bouya S, Balouchi A, Rafiemanesh H, Hesaraki M. Prevalence of Chronic Kidney Disease in Iranian General Population: A Meta-Analysis and Systematic Review. Ther Apher Dial [Internet] 2018 [cited 2020 Oct 18];22(6):594–9. Available from: http://doi. wiley.com/10.1111/1744-9987.12716.
10. Naghavi M, Wang H, Lozano R, Davis A, Liang X, Zhou M, et al. Global, regional, and national age–sex specific all-cause and causespecific mortality for 240 causes of death, 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013. Lancet [Internet] 2015 [cited 2020 Oct 18];385(9963):117–71. Available from: https://linkinghub.elsevier. com/retrieve/pii/S0140673614616822.
11. Vos T, Barber RM, Bell B, BertozziVilla A, Biryukov S, Bolliger I, et al. Global, regional, and national incidence, prevalence, and years lived with disability for 301 acute and chronic diseases and injuries in 188 countries, 1990-2013: A systematic analysis for the Global Burden of Disease Study 2013. Lancet 2015;386(9995):743–800.
12. Neovius M, Jacobson SH, Eriksson JK, Elinder CG, Hylander B. Mortality in chronic kidney disease and renal replacement therapy: A population-based cohort study. BMJ Open [Internet] 2014 [cited 2020 Oct 19];4(2):4251. Available from: http://bmjopen.bmj.com/.
13. Abecassis M, Bartlett ST, Collins AJ, Davis CL, Delmonico FL, Friedewald JJ, et al. Kidney transplantation as primary therapy for end-stage renal disease: A National Kidney Foundation/Kidney Disease Outcomes Quality Initiative (NKF/KDOQITM) conference. Clin J Am Soc Nephrol [Internet] 2008 [cited 2020 Oct 19];3(2):471–80. Available from: www. cjasn.org.
14. Neild GH. Chronic renal failure [Internet]. In: The Scientific Basis of Urology, Second Edition. CRC Press; 2004 [cited 2020 Oct 19]. page 257–64.Available from: https:// www.ncbi.nlm.nih.gov/books/NBK535404/.
15. Van Eeghen EE, Bakker SD, van Bochove A, Loffeld RJLF. Impact of age and comorbidity on survival in colorectal cancer. J Gastrointest Oncol [Internet] 2015 [cited 2020 Oct 31];6(6):605–12. Available from: /pmc/ articles/PMC4671847/?report=abstract.
16. Balakrishnan N, Ling MH. Expectation maximization algorithm for one shot device accelerated life testing with weibull lifetimes, and variable parameters over stress. IEEE Trans Reliab 2013;62(2):537–51.
17. Wang W, Kececioglu DB. Fitting the Weibull log-linear model to accelerated life-test data. IEEE Trans Reliab 2000;49(2):217–23.
18. Mazucheli J, Louzada F. Lifetime models with nonconstant shape parameters Bias correction View project Applying HD-tDCS for tinnitus patients View project [Internet]. [cited 2020 Oct 31]. Available from: https://www. researchgate.net/publication/254352005.
19. Aghamolaey H, Baghestani AR, Zayeri F. Application of the Weibull distribution with a non-constant shape parameter for identifying risk factors in pharyngeal cancer patients. Asian Pacific J Cancer Prev [Internet] 2017 [cited 2020 Oct 31];18(6):1537–42. Available from: pmc/articles/PMC5697453/?report=abstract.
20. Chan CK. Temperature-Dependent Standard Deviation of Log(Failure Time) Distributions. IEEE Trans Reliab 1991;40(2):157–60.
21. Pham M. Survival Analysis - Breast Cancer. Undergrad J Math Model One + Two 2014;6(1).
22. Bastani P, Ahmad Kiadaliri A. Healthrelated quality of life after chemotherapy cycle in breast cancer in Iran. Med Oncol [Internet] 2011 [cited 2020 Nov 9];28(SUPPL. 1):70–4. Available from: https://link.springer.com/article/10.1007/s12032-010-9714-x.
23. Lv S, Niu Z, Qu L, He S, He Z. Reliability modeling of accelerated life tests with both random effects and nonconstant shape parameters. Qual Eng [Internet] 2015 cited 2020 Nov 9];27(3):329–40. Available
from: https://www.tandfonline.com/doi/abs/10 1080/08982112.2015.1037393.
24. Baghestani AR, Moghaddam SS, Majd HA, Akbari ME, Nafissi N, Gohari K. Survival analysis of patients with breast cancer using weibull parametric model. Asian Pacific J Cancer Prev 2016;16(18):8567–71.
25. Floege J, Kim J, Ireland E, Chazot C, Drueke T, De Francisco A, et al. Serum iPTH, calcium and phosphate, and the risk of mortality in a European haemodialysis population. Nephrol Dial Transplant [Internet] 2011 [cited 2020 Nov 9];26(6):1948–55. Available from: https://academic.oup.com/ndt/ article/26/6/1948/1931465.
26. Naves-Daz M, Passlick-Deetjen J, Guinsburg A, Marelli C, Fernndez-Martn JL, Rodrguez-Puyol D, et al. Calcium, phosphorus, PTH and death rates in a large sample of dialysis patients from Latin America. the CORES Study. Nephrol Dial Transplant [Internet] 2011 [cited 2020 Nov 8];26(6):1938–47. Available from: https://academic.oup.com/ndt/ article/26/6/1938/1931635.
27. Tentori F, Blayney MJ, Albert JM, Gillespie BW, Kerr PG, Bommer J, et al. Mortality Risk for Dialysis Patients With Different Levels of Serum Calcium, Phosphorus, and PTH: The Dialysis Outcomes and Practice Patterns Study (DOPPS). Am J Kidney Dis 2008;52(3):519–30.
28. Young EW, Albert JM, Satayathum S, Goodkin DA, Pisoni RL, Akiba T, et al. Predictors and consequences of altered mineral metabolism: The Dialysis Outcomes and Practice Patterns Study. Kidney Int 2005;67(3):1179–87.
29. Block GA, Klassen PS, Lazarus JM, Ofsthun N, Lowrie EG, Chertow GM. Mineral metabolism, mortality, and morbidity in maintenance hemodialysis. J Am Soc Nephrol [Internet] 2004 [cited 2020 Nov 10];15(8):2208–18. Available from: https://jasn.asnjournals.org/content/15/8/2208.
30. Kalantar-Zadeh K, Kuwae N, Regidor DL, Kovesdy CP, Kilpatrick RD, Shinaberger CS, et al. Survival predictability of time-varying indicators of bone disease in maintenance hemodialysis patients. Kidney Int 2006;70(4):771–80.
31. Reindl-Schwaighofer R, Kainz A, Kammer M, Dumfarth A, Oberbauer R. Survival analysis of conservative vs. dialysis treatment of elderly patients with CKD stage 5. PLoS One [Internet] 2017 [cited 2020 Nov 9];12(7):e0181345. Available from: https://dx.plos.org/10.1371/journal.pone.0181345.
32. Melamed ML, Eustace JA, Plantinga L, Jaar BG, Fink NE, Coresh J, et al. Changes in serum calcium, phosphate, and PTH and the risk of death in incident dialysis patients: A longitudinal study. Kidney Int 2006;70(2):351–7.
33. Covic A, Kothawala P, Bernal M, Robbins S, Chalian A, Goldsmith D. Systematic review of the evidence underlying the association between mineral metabolism disturbances and risk of all-cause mortality, cardiovascular mortality and cardiovascular events in chronic kidney disease [Internet]. Nephrol. Dial. Transplant.2009 [cited 2020 Nov 11];24(5):1506–23. Available from: https://academic.oup.com/ndt/ article/24/5/1506/1881102.
34. Riggs JE. Neurologic manifestations of electrolyte disturbances [Internet]. Neurol. Clin.2002 [cited 2020 Nov 11];20(1):227– 39. Available from: http://www.neurologic. the clinics.com/article/S0733861903000604/fulltext.
35. Iyemere VP, Proudfoot D, Weissberg PL, Shanahan CM. Vascular smooth muscle cell phenotypic plasticity and the regulation of vascular calcification [Internet]. J. Intern. Med.2006 [cited 2020 Nov 11];260(3):192–210. Available from: https://onlinelibrary. wiley.com/doi/full/10.1111/j.1365-2796.2006.01692.x.
36. Giachelli CM. Vascular calcification mechanisms [Internet]. J. Am. Soc. Nephrol.2004 [cited 2020 Nov
11];15(12):2959–64. Available from: https:// jasn.asnjournals.org/content/15/12/2959.
37. Isakova T, Gutierrez OM, Chang Y, Shah A, Tamez H, Smith K, et al. Phosphorus binders and survival on hemodialysis. J Am Soc Nephrol [Internet] 2009 [cited 2020 Nov 11];20(2):388–96. Available from: www.jasn. org.
38. Block GA, Klassen PS, Lazarus JM, Ofsthun N, Lowrie EG, Chertow GM. Mineral metabolism, mortality, and morbidity in maintenance hemodialysis. J Am Soc Nephrol [Internet] 2004 [cited 2020 Nov 11];15(8):2208–18. Available from: https:// jasn.asnjournals.org/content/15/8/2208.
39. Tsuchihashi K, Takizawa H, Torii TA, Ikeda R, Nakahara N, Yuda S, et al. Hypoparathyroidism potentiates cardiovascular complications through disturbed calcium metabolism: Possible risk of vitamin D3 analog administration in dialysis patients with endstage renal disease. Nephron [Internet] 2000 [cited 2020 Nov 11];84(1):13–20. Available from: https://www.karger.com/Article/ FullText/45533.
IssueVol 7 No 3 (2021) QRcode
SectionOriginal Article(s)
DOI https://doi.org/10.18502/jbe.v7i3.7299
Chronic Kidney Disease Survival Data Hazard modeling Shape parameter

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Taheri SS, Baghestani A, Minoo F, Saeedi A. Identifying Influential Prognostic Factors of Death Hazard Rates in Patients with Chronic Kidney Disease (CKD) Using Weibull Model with Non-Constant Shape Parameter. jbe. 2021;7(3):272-284.