Multistate Models for the Analysis of Time to Type II Chronic Diabetic Complications in Debre Markos Referral Hospital, Northwest Ethiopia
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Abstract
Introduction: Diabetes is a chronic, non-communicable disease characterized by elevated blood glucose levels. The purpose of this study was to jointly model the transition of diabetic patients in a series of clinical states and to assess the relationship between each state and different patient characteristics.
Methods: A hospital-based retrospective study was conducted on 524 patients with type II diabetes, aged 18 years or older, who attended their medication between January 1, 2005, and December 31, 2017. Multistate models with different assumptions were considered to explore the effects of different prognostic factors on the transition intensity of type II diabetes mellitus patients.
Results: During a median follow-up time of 7.4 years (Inter-Quartile Range=4.01), 54.8% of diabetic patients developed either microvascular or macrovascular complications, and 10.5% of them experienced both microand macrocomplications, and 16.66% of diabetes patients died. The assumption Markov was assessed by using the likelihood ratio test showed that Markov assumption was not held just for the transition. The transition rate of patients from the macrovascular state to the death state was affected by the residence of the patients (P=0.05) and age at diagnosis (p=0.01). The transition rates of patients with microvascular complications to death were significantly affected by baseline triglyceride level (P<0.001), age at first diagnosis (P=0.01), baseline glucose level (P=0.03, and baseline serum creatinine level (P=0.04).
Conclusion: The semi-Markov model fitted the data well and could be used as a convenient model for the analysis of time to diabetes-related complications or death.
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14. de Wreede, L.C., M. Fiocco, and H. Putter, mstate: an R package for the analysis of competing risks and multi-state models. Journal of statistical software, 2011. 38(7): p. 1-30.
15. Machado, R.J. and A. van den Hout, Flexible multistate models for interval‐ censored data: Specification, estimation, and an application to ageing research. Statistics in medicine, 2018. 37(10): p. 1636-1649.
16. Meira-Machado, L., et al., Multi-state models for the analysis of time-to-event data. Statistical methods in medical research, 2009. 18(2): p. 195-222.
17. Putter, H., Tutorial in biostatistics: Competing risks and multi-state models Analyses using the mstate package. Companion file for the mstate package, 2011.
18. Therneau, T., C. Crowson, and E. Atkinson, Multi-state models and competing risks. CRAN-R (https://cran. r-project. org/ web/packages/survival/vignettes/compete. pdf), 2020.
19. Foucher, Y., et al., A flexible semiMarkov model for interval-censored data and goodness-of-fit testing. Statistical methods in medical research, 2010. 19(2): p. 127-145.
20. Kalbfleisch, J.D. and R.L. Prentice, The statistical analysis of failure time data. Vol. 360. 2011: John Wiley & Sons.
21. Aalen, O.O. and S. Johansen, An empirical transition matrix for nonhomogeneous Markov chains based on censored observations. Scandinavian Journal of Statistics, 1978: p. 141-150.
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25. Developer Core Team, R., R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing, 2019.
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27. Jerez, J.M., et al., Missing data imputation using statistical and machine learning methods in a real breast cancer problem. Artificial intelligence in medicine, 2010. 50(2): p. 105-115.
28. Nakagawa, S., Missing data: mechanisms, methods and messages. Ecological statistics: Contemporary theory and application, 2015: p. 81-105.
29. Kotzé, L., Markov modelling of disease progression in the presence of missing covariates. 2019, Stellenbosch: Stellenbosch University.
30. Honaker, J., G. King, and M. Blackwell, Amelia II: A program for missing data. Journal of statistical software, 2011. 45(7): p. 1-47.
31. Buuren, S.v. and K. GroothuisOudshoorn, mice: Multivariate imputation by chained equations in R. Journal of statistical software, 2010: p. 1-68
32. Kowarik, A. and M. Templ, Imputation with the R Package VIM. Journal of Statistical Software, 2016. 74(7): p. 1-16.
33. Stekhoven, D.J. and M.D.J. Stekhoven, Package ‘missForest’. 2012.
34. Stekhoven, D.J. and P. Bühlmann, MissForest—non-parametric missing value imputation for mixed-type data. Bioinformatics, 2012. 28(1): p. 112-118.
35. Tang, F., Random Forest Missing Data Approaches. 2017: University of Miami.
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37. Anderson, D. and K. Burnham, Model selection and multi-model inference. Second. NY: Springer-Verlag, 2004. 63(2020): p. 10.
38. Li, X. and M. Fiocco, Estimation for Non-Markov Multi-states Models. 2014.
39. Andersen, P.K., L.S. Hansen, and N. Keiding, Non-and semi-parametric estimation of transition probabilities from censored observation of a non-homogeneous Markov process. Scandinavian Journal of Statistics, 1991: p. 153-167.
40. Zare, A., et al., Assessing Markov and time homogeneity assumptions in multi-state models: application in patients with gastric cancer undergoing surgery in the Iran cancer institute. Asian Pacific Journal of Cancer Prevention, 2014. 15(1): p. 441-447.
41. Conlon, A., J. Taylor, and D. Sargent, Multi‐state models for colon cancer recurrence and death with a cured fraction. Statistics in medicine, 2014. 33(10): p. 1750-1766.
42. Andersen, P.K., et al., Statistical models based on counting processes. 2012: Springer Science & Business Media.
43. Kalbfleisch, J. and J.F. Lawless, The analysis of panel data under a Markov assumption. Journal of the american statistical association, 1985. 80(392): p. 863-871.
44. Kay, R., A Markov model for analysing cancer markers and disease states in survival studies. Biometrics, 1986: p. 855-865.
45. Aalen, O., Nonparametric inference for a family of counting processes. The Annals of Statistics, 1978: p. 701-726.
46. Tierney, N., visdat: Visualising whole data frames. Journal of Open Source Software, 2017. 2(16): p. 355.
47. Ghazali, S.M., N. Shaadan, and Z. Idrus, Missing data exploration in air quality data set using R-package data visualisation tools. Bulletin of Electrical Engineering and Informatics, 2020. 9(2): p. 755-763.
48. Madley-Dowd, P., et al., The proportion of missing data should not be used to guide decisions on multiple imputation. Journal of clinical epidemiology, 2019. 110: p. 63-73.
49. Jakobsen, J.C., et al., When and how should multiple imputation be used for handling missing data in randomised clinical trials–a practical guide with flowcharts. BMC medical research methodology, 2017. 17(1): p. 1-10.
50. Asanjarani, A., B. Liquet, and Y. Nazarathy, Estimation of semi-Markov multistate models: a comparison of the sojourn times and transition intensities approaches. The International Journal of Biostatistics, 2020. 1(ahead-of-print).
51. Janssen, J., Semi-Markov models: theory and applications. 2013: Springer Science & Business Media.
52. Świderski, A., et al., Evaluation of Machinery Readiness Using Semi-MarkovProcesses. Applied Sciences, 2020. 10(4): p. 1541.
53. Liu, P., L. Liao, and J. Liu. Chronic Disease Progression Modeling using SemiMarkov Model with Noisy Observations. in IIE Annual Conference. Proceedings. 2015. Institute of Industrial and Systems Engineers (IISE).
54. Brookmeyer, R. and N. Abdalla, Multistate models and lifetime risk estimation: Application to Alzheimer's disease. Statistics in medicine, 2019. 38(9): p. 1558-1565.
55. Zoungas, S., et al., Impact of age, age at diagnosis and duration of diabetes on the risk of macrovascular and microvascular complications and death in type 2 diabetes. Diabetologia, 2014. 57(12): p. 2465-2474.
56. Li, J., et al., Prevalence and associated factors of vascular complications among inpatients with type 2 diabetes: A retrospective database study at a tertiary care department, Ningbo, China. PloS one, 2020. 15(6): p. e0235161.
57. Rangel, E.B., C.O. Rodrigues, and J.R. De Sa, Micro-and macrovascular complications in diabetes mellitus: preclinical and clinical studies. 2019, Hindawi.
58. Chia, C.W., J.M. Egan, and L. Ferrucci, Age-related changes in glucose metabolism, hyperglycemia, and cardiovascular risk. Circulation research, 2018. 123(7): p. 886- 904.
59. Kalyani, R.R. and J.M. Egan, Diabetes and altered glucose metabolism with aging. Endocrinology and Metabolism Clinics, 2013. 42(2): p. 333-347.
60. Awa, W.L., et al., Type 2 diabetes from pediatric to geriatric age: analysis of gender and obesity among 120183 patients from the German/Austrian DPV database. European Journal of Endocrinology, 2012. 167(2): p. 245.
61. Agrawal, R., et al., Prevalence of micro and macrovascular complications and their risk factors in type-2 diabetes mellitus. JAPI, 2014. 62: p. 505.
62. Tracey, M.L., et al., Risk factors for macro-and microvascular complications among older adults with diagnosed type 2 diabetes: findings from the Irish longitudinal study on ageing. Journal of diabetes research, 2016. 2016.
2. Association, A.D, Diagnosis and classification of diabetes mellitus. Diabetes care, 2014. 37(Supplement 1): p. S81-S90.
3. Baena-Díez, J.M., et al., Risk of causespecific death in individuals with diabetes: a competing risks analysis. Diabetes care, 2016. 39(11): p. 1987-1995.
4. Shaw, J.E., R.A. Sicree, and P.Z. Zimmet, Global estimates of the prevalence of diabetes for 2010 and 2030. Diabetes research and clinical practice, 2010. 87(1): p. 4-14.
5. Cho, N., et al., IDF Diabetes Atlas: Global estimates of diabetes prevalence for 2017 and projections for 2045. Diabetes research and clinical practice, 2018. 138: p. 271-281.
6. Ogurtsova, K., et al., IDF Diabetes Atlas: Global estimates for the prevalence of diabetes for 2015 and 2040. Diabetes research and clinical practice, 2017. 128: p. 40-50.
7. Organization, W.H., Global report on diabetes: executive summary. 2016, World Health Organization.
8. Skyler, J.S., et al., Differentiation of diabetes by pathophysiology, natural history, and prognosis. Diabetes, 2017. 66(2): p. 241- 255.
9. Alemu, F., Prevalence of diabetes mellitus disease and its association with level of education among adult patients attending at Dilla Referral Hospital, Ethiopia. J Diabetes Metab, 2015. 6(4): p. 1-5.
10. Patil, P.D., et al., Past and current perspective on new therapeutic targets for Type-II diabetes. Drug design, development and therapy, 2017. 11: p. 1567.
11. Konstantinos, P., et al., Complications of diabetes 2016. Journal of diabetes research, 2016.
12. Kidanie, B.B., et al., Determinants of Diabetic Complication Among Adult Diabetic Patients in Debre Markos Referral Hospital, Northwest Ethiopia, 2018: Unmatched Case Control Study. Diabetes, metabolic syndrome and obesity: targets and therapy, 2020. 13: p. 237.
13. Wolde, H.F., et al., Predictors of vascular complications among type 2 diabetes mellitus patients at University of Gondar Referral Hospital: a retrospective follow-up study. BMC endocrine disorders, 2018. 18(1): p. 1-8.
14. de Wreede, L.C., M. Fiocco, and H. Putter, mstate: an R package for the analysis of competing risks and multi-state models. Journal of statistical software, 2011. 38(7): p. 1-30.
15. Machado, R.J. and A. van den Hout, Flexible multistate models for interval‐ censored data: Specification, estimation, and an application to ageing research. Statistics in medicine, 2018. 37(10): p. 1636-1649.
16. Meira-Machado, L., et al., Multi-state models for the analysis of time-to-event data. Statistical methods in medical research, 2009. 18(2): p. 195-222.
17. Putter, H., Tutorial in biostatistics: Competing risks and multi-state models Analyses using the mstate package. Companion file for the mstate package, 2011.
18. Therneau, T., C. Crowson, and E. Atkinson, Multi-state models and competing risks. CRAN-R (https://cran. r-project. org/ web/packages/survival/vignettes/compete. pdf), 2020.
19. Foucher, Y., et al., A flexible semiMarkov model for interval-censored data and goodness-of-fit testing. Statistical methods in medical research, 2010. 19(2): p. 127-145.
20. Kalbfleisch, J.D. and R.L. Prentice, The statistical analysis of failure time data. Vol. 360. 2011: John Wiley & Sons.
21. Aalen, O.O. and S. Johansen, An empirical transition matrix for nonhomogeneous Markov chains based on censored observations. Scandinavian Journal of Statistics, 1978: p. 141-150.
22. Abner, E.L., R.J. Charnigo, and R.J. Kryscio, Markov chains and semi-Markov models in time-to-event analysis. Journal of biometrics & biostatistics, 2013(e001): p. 19522.
23. Eulenburg, C., et al., A systematic model specification procedure for an illnessdeath model without recovery. PloS one, 2015. 10(4): p. e0123489.
24. Le-Rademacher, J.G., et al., Application of multi-state models in cancer clinical trials. Clinical Trials, 2018. 15(5): p. 489-498.
25. Developer Core Team, R., R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing, 2019.
26. Therneau, T. and T. Lumley, R survival package. 2013.
27. Jerez, J.M., et al., Missing data imputation using statistical and machine learning methods in a real breast cancer problem. Artificial intelligence in medicine, 2010. 50(2): p. 105-115.
28. Nakagawa, S., Missing data: mechanisms, methods and messages. Ecological statistics: Contemporary theory and application, 2015: p. 81-105.
29. Kotzé, L., Markov modelling of disease progression in the presence of missing covariates. 2019, Stellenbosch: Stellenbosch University.
30. Honaker, J., G. King, and M. Blackwell, Amelia II: A program for missing data. Journal of statistical software, 2011. 45(7): p. 1-47.
31. Buuren, S.v. and K. GroothuisOudshoorn, mice: Multivariate imputation by chained equations in R. Journal of statistical software, 2010: p. 1-68
32. Kowarik, A. and M. Templ, Imputation with the R Package VIM. Journal of Statistical Software, 2016. 74(7): p. 1-16.
33. Stekhoven, D.J. and M.D.J. Stekhoven, Package ‘missForest’. 2012.
34. Stekhoven, D.J. and P. Bühlmann, MissForest—non-parametric missing value imputation for mixed-type data. Bioinformatics, 2012. 28(1): p. 112-118.
35. Tang, F., Random Forest Missing Data Approaches. 2017: University of Miami.
36. Bjerg, L., et al., Development of microvascular complications and effect of concurrent risk factors in type 1 diabetes: a multistate model from an observational clinical cohort study. Diabetes Care, 2018. 41(11): p. 2297-2305.
37. Anderson, D. and K. Burnham, Model selection and multi-model inference. Second. NY: Springer-Verlag, 2004. 63(2020): p. 10.
38. Li, X. and M. Fiocco, Estimation for Non-Markov Multi-states Models. 2014.
39. Andersen, P.K., L.S. Hansen, and N. Keiding, Non-and semi-parametric estimation of transition probabilities from censored observation of a non-homogeneous Markov process. Scandinavian Journal of Statistics, 1991: p. 153-167.
40. Zare, A., et al., Assessing Markov and time homogeneity assumptions in multi-state models: application in patients with gastric cancer undergoing surgery in the Iran cancer institute. Asian Pacific Journal of Cancer Prevention, 2014. 15(1): p. 441-447.
41. Conlon, A., J. Taylor, and D. Sargent, Multi‐state models for colon cancer recurrence and death with a cured fraction. Statistics in medicine, 2014. 33(10): p. 1750-1766.
42. Andersen, P.K., et al., Statistical models based on counting processes. 2012: Springer Science & Business Media.
43. Kalbfleisch, J. and J.F. Lawless, The analysis of panel data under a Markov assumption. Journal of the american statistical association, 1985. 80(392): p. 863-871.
44. Kay, R., A Markov model for analysing cancer markers and disease states in survival studies. Biometrics, 1986: p. 855-865.
45. Aalen, O., Nonparametric inference for a family of counting processes. The Annals of Statistics, 1978: p. 701-726.
46. Tierney, N., visdat: Visualising whole data frames. Journal of Open Source Software, 2017. 2(16): p. 355.
47. Ghazali, S.M., N. Shaadan, and Z. Idrus, Missing data exploration in air quality data set using R-package data visualisation tools. Bulletin of Electrical Engineering and Informatics, 2020. 9(2): p. 755-763.
48. Madley-Dowd, P., et al., The proportion of missing data should not be used to guide decisions on multiple imputation. Journal of clinical epidemiology, 2019. 110: p. 63-73.
49. Jakobsen, J.C., et al., When and how should multiple imputation be used for handling missing data in randomised clinical trials–a practical guide with flowcharts. BMC medical research methodology, 2017. 17(1): p. 1-10.
50. Asanjarani, A., B. Liquet, and Y. Nazarathy, Estimation of semi-Markov multistate models: a comparison of the sojourn times and transition intensities approaches. The International Journal of Biostatistics, 2020. 1(ahead-of-print).
51. Janssen, J., Semi-Markov models: theory and applications. 2013: Springer Science & Business Media.
52. Świderski, A., et al., Evaluation of Machinery Readiness Using Semi-MarkovProcesses. Applied Sciences, 2020. 10(4): p. 1541.
53. Liu, P., L. Liao, and J. Liu. Chronic Disease Progression Modeling using SemiMarkov Model with Noisy Observations. in IIE Annual Conference. Proceedings. 2015. Institute of Industrial and Systems Engineers (IISE).
54. Brookmeyer, R. and N. Abdalla, Multistate models and lifetime risk estimation: Application to Alzheimer's disease. Statistics in medicine, 2019. 38(9): p. 1558-1565.
55. Zoungas, S., et al., Impact of age, age at diagnosis and duration of diabetes on the risk of macrovascular and microvascular complications and death in type 2 diabetes. Diabetologia, 2014. 57(12): p. 2465-2474.
56. Li, J., et al., Prevalence and associated factors of vascular complications among inpatients with type 2 diabetes: A retrospective database study at a tertiary care department, Ningbo, China. PloS one, 2020. 15(6): p. e0235161.
57. Rangel, E.B., C.O. Rodrigues, and J.R. De Sa, Micro-and macrovascular complications in diabetes mellitus: preclinical and clinical studies. 2019, Hindawi.
58. Chia, C.W., J.M. Egan, and L. Ferrucci, Age-related changes in glucose metabolism, hyperglycemia, and cardiovascular risk. Circulation research, 2018. 123(7): p. 886- 904.
59. Kalyani, R.R. and J.M. Egan, Diabetes and altered glucose metabolism with aging. Endocrinology and Metabolism Clinics, 2013. 42(2): p. 333-347.
60. Awa, W.L., et al., Type 2 diabetes from pediatric to geriatric age: analysis of gender and obesity among 120183 patients from the German/Austrian DPV database. European Journal of Endocrinology, 2012. 167(2): p. 245.
61. Agrawal, R., et al., Prevalence of micro and macrovascular complications and their risk factors in type-2 diabetes mellitus. JAPI, 2014. 62: p. 505.
62. Tracey, M.L., et al., Risk factors for macro-and microvascular complications among older adults with diagnosed type 2 diabetes: findings from the Irish longitudinal study on ageing. Journal of diabetes research, 2016. 2016.
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| Issue | Vol 7 No 3 (2021) | |
| Section | Original Article(s) | |
| DOI | https://doi.org/10.18502/jbe.v7i3.7300 | |
| Keywords | ||
| Diabetes mellitus Vascular complications Multistate models | ||
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How to Cite
1.
Ayaneh M, Iyasu A. Multistate Models for the Analysis of Time to Type II Chronic Diabetic Complications in Debre Markos Referral Hospital, Northwest Ethiopia. JBE. 2021;7(3):285-304.
