Article Sidebar

Submitted
March 21, 2022
Accepted
December 7, 2022
Published
December 10, 2022
Download
PDF
Statistic
Read Counter : 1197 Download : 487

Downloads

Download data is not yet available.

Main Article Content

Abstract

The problem that arises in the Cox model is that there are more than two types of covariates and the presence of random effects is a non-proportional hazard (NPH). One example of a case that involves many factors is student retention. Low student retention can lead to dropping out of college or failure in completing studies. The purpose of this study is to overcome the problem of NPH caused by the presence
of time-independent covariates, time-dependent covariates, and random effects. The research method uses simulation. Some of the modified models are the stratified Cox model, the extended Cox model, and the frailty model. The developed model is applied to distance education student retention data. The results of the study show that frailty and study programs provide considerable diversity in explaining the
total diversity of the model. It can be concluded that frailty needs to be considered by UT to improve the quality of services to students. In addition, other covariates that have a significant effect on UT student learning retention modeling are age, domicile, gender, GPA, marital status, employment status, number of credits taken, and number of registered courses.

Keywords

Universitas Terbuka stratified Cox extended Cox frailty mixed effect model

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Author Biographies

Dewi Juliah Ratnaningsih, Universitas Terbuka

DEWI JULIAH RATNANINGSIH is an Associate Professor of Faculty of Mathematics and Natural Sciences at Universitas Terbuka (UT). Her academic interest areas are statistics, applied statistics in education, studies of services, customer satisfaction, tracer study, developing research instrument, open and distance learning and needs assessment for distance education.  She has three articles that have been published in international indexes and scopus indexed (Asian Association of Open Universities Journal, Open Praxis, and Journal of Applied Statistics).  She was awarded First Prize in Excellent Paper Winner of the 25th International Council for Open and Distance Education (ICDE) World Conference and ICDE Prizes for Innovation and Best Practice (2013). She has published five books on statistics.

Anang Kurnia, IPB University

ANANG KURNIA is an Assosiate Professor of Departemen of Statistics,  Faculty of Mathematics and Natural Sciences at Bogor Agricultural University. His research interests include: small area estimation, generalized linear (mixed) model, robust statistics, and high-dimensional data analysis. He is head of Department of Statistics in Bogor Agricultural University and former head of Indonesian Statistics Higher Education Association.  He has published any journal and conference papers and also coordinated some researches project in statistics.

Asep Saefuddin, IPB University

ASEP SAEFUDDIN is Professor of Departemen of Statistics at Bogor Agricultural University. He obtained a master's and doctorate degrees in Biostatistics and Populations Medicine/ Quantitative Epidemiology from the University of Guelph. He served as Vice Rector for Planning, Development and Cooperation, Bogor Agricultural University in 2003-2008. Year 2013-2017 as Rector of Trilogi University. Currently, he served as Rector at University of Al Azhar Indonesia as well as President of Pusat Bahasa Mandiri University of Al Azhar Indonesia. In addition, he is also active in several national organizations, including Vice President of Dewan Pertimbangan Forum Rektor Indonesia, Vice President of ISSOSS (Islamic Country Society of Statistical Science) (2009-2014), and Chairman of the Advisory Committee of Yayasan Inovasi Teknologi (2007-present ). His research interest include: geoinformatics, spatial analysis, and statistical modelling. He has published any journal and conference papers and also coordinated some researches project in statistics.

I Wayan Mangku, IPB University

I WAYAN MANGKU is Professor of Departemen of Mathematics,  Faculty of Mathematics and Natural Sciences at Bogor Agricultural University. He completed his Master’s degree in Mathematical Modeling at School of Mathematics and Computer Science, Curtin University of Technology, Western Australia. He received his Ph.D degree in Mathematics at University of Amsterdam, The Netherlands. He is the head of Mathematical Modeling Division at Department of Mathematics, Bogor Agricultural University. His research interest include: stochastic process and mathematical statistics. He has published two books and more than 90 articles in scientific journals.

How to Cite
Ratnaningsih, D. J., Kurnia, A., Saefuddin, A., & Mangku, I. W. (2022). Mixed Models of Non-Proportional Hazard and Application in The Open Distance Education Students Retention Data. Journal of the Indonesian Mathematical Society, 28(3), 323–344. https://doi.org/10.22342/jims.28.3.1185.323-344
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Abdelaal, M.M. and Zakaria, S.H., Modeling survival data by using cox regression model”. American Journal of Theoretical and Applied Statistics. 4(6) (2015), 504-512, doi: 10.11648/j.ajtas.20150406.21.
  2. Allen, I.E., Seaman, J., Poulin, R. and Straut, T.T., Online report card: Tracking online education in the United States, Babson Park, MA: Babson Survey Research Group Retrieved from http://onlinelearningsurvey.com/re-ports/onlinereport-card. (2016).
  3. Arifin, H., The role of student support services in enhancing student persistence in the open university context: lesson from Indonesia Open University”, Turkish Online Journal of Distance Education-TOJDE, 19(3)(2018), 156-168.
  4. Ata, N. and Sozer, M.T., Cox regression models with nonproportional hazards applied to lung cancer survival data”, Hacettepe Journal of Mathematics and Statistics, 36(2) (2007), 157-167.
  5. Austin, P.C., A tutorial on multilevel survival analysis: methods, models and applications”, International Statistical Review. 85(2) (2017), 185-203. doi:10.11-11/insr.12214.
  6. Belawati, T., Increasing student persistence in Indonesian postecondary distance education”, Distance Education, 19(1)(1998), 81-108, doi: 10.1080/-0158791980190107.
  7. Berger, J. and Lyon, S., Past to present: A historical look at retention. In A. Seidman (Ed.), College student retention, 130. Westport, CT: Praeger, 2005.
  8. Brown, H. and Prescott, R., Applied Mixed Models in Medicine, Second Edition. New York: John Wiley & Sons, 2006.
  9. Callegaro, A. and Iacobelli, S., The Cox shared frailty model with log-skew-normal frailties”, Statistical Modelling, 12(4) (2012), 399-41, doi:10.1177/14-71082X-12460146.
  10. Cambruzzi, W., Rigo, S.J. and Barbosa, J.L.V., Dropout prediction and reduction in distance education courses with the learning analytics multitrail approach”, Journal of Universal Computer Science, 21(1) (2015), 23-47, doi: 10.3217/jucs-021-01-0023.
  11. Cercone, K., Characteristics of adult learners with implication for online learning design”, AACE Journal, 16(2) (2008), 137-159.
  12. Christian, N.J., Ha, I.D. and Jeong, J.H., Hierarchical likelihood inference on clustered competing risk data”, Statistics in Medicine, 35 (2016), 251-267.
  13. Cox, D.R., Regression models and life-tables”, Journal of the Royal Statistical Society Series B (Methodological), 34(2) (1972), 187-220.
  14. Crowther, M.J., Look, M.P and Riley, R.D., Multilevel mixed effects parametric survival models using adaptive Gauss-Hermite quadrature with application to recurrent events and individual participant data meta-analysis”, Statistics in Medicine, 33 (2014), 38443858.
  15. Deepapriya, S. and Ravanan, R., Gamma frailty model to evaluate heterogeneity for a survival data”, International Journal of Scientific Research, 5(4) (2015), 2-5.
  16. Demidenco, E., Mixed Models Theory and Application With R, Second Edition, New Jersey: John Wiley & Sons, 2013.
  17. Dobson A.J., An Introduction to Generalized Linear Models, Second Edition, New York: Chapman & Hall/CRC, 2002.
  18. Duchateau, L. and Janssen, P., The Frailty Model, New York, NY: Springer, 2008.
  19. Dupuy, J.F. and Leconte, E., Estimation in a Partially Observed Stratified Cox Model, accessed 2016 December 05 on https://scholar.google.com/cita-tions?user=cQLxzX8AAAAJ&hl=en, 2006.
  20. Fisher, L.D. and Lin, D.Y., Time-dependent covariates in the Cox proportional-hazard regression model”, Ann. Rev. Public Health, 20(1999), 145-157.
  21. Gaytan J., Comparing faculty and student perceptions regarding factors that affect student retention in online education”, American Journal of Distance Education,29(1) (2015), 56-66.
  22. Gellar, J.E., Colantuoni, E., Needhan, D.M. and Crainiceanu, C.M., Cox regression models with functional covariates for survival data”. Statistical Modelling. 15(3) (2015) , 123, doi:10.1177/1471082X14565526.
  23. Goldstein, H., Multilevel Statistical Models, United Kingdom: John Wiley & Sons, 2011.
  24. Ha, I.D., Lee, Y. and Song, J.K., Hierarchical likelihood approach for frailty models”, Biometrics, 88(1 (2001), 233-243.
  25. Ha, I.D., Lee, Y. and Song, J., Hierarchical-likelihood approach for mixed linear models with censored data”, Lifetime Data Analysis, 8 (2002), 63-176.
  26. Ha, I.D., Lee. Y. and MacKenzie, G., Model selection for multi-component frailty models”, Statistics in Medicine, 26(26) (2007), 4790-807.
  27. Ha I.D., Legrand C., MacKenzie G., Sylverter R., Frailty modelling for survival data from multi-centre clinical trials”, Statistics in Medicine, 30(17) (2011), 2144-59.
  28. Ha, I.D., Lee, Y. and Noh, M., FrailtyHL: Frailty Models using H-Likelihood”, R package version, 1.1 (2012), 28-30.
  29. Jeon J., Hsu L., Gorfine M., Bias correction in the hierarchical likelihood approach to the analysis of multivariate survival data”, Biostatistics, 13(3) (2012), 384-397.
  30. Kara, M., Erdogdu, F., Kokoc, M. and Cagiltay, K., Challenges faced by adult leaners in online distance education: a literature review”, Open Praxis International Council for Open and Distance Education, 11(1) (2019), 5-22, doi: https://doi.org-/10.5944/openpraxis.11.1.929.
  31. Keele, L., Proportionally difficult: testing for nonproportional hazards in cox models”, Political Analysis, 18 (2010), 189205, doi:10.1093/pan/mpp044.
  32. Kleinbaum, D.G. and Klein, M., Survival Analysis: A Self-Learning Text, Third Edition, New York (US): Springer, doi: 10.1007/978-1-4419-6646-9, 2012
  33. Lee, Y. and Nelder, J.A., Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions”, Biometrika, 88(4) (2001), 987-1006.
  34. Lee, Y., Nelder, J.A. and Pawitan, Y., Generalized Linear Models with Random Effects: Unified Analysis via Hlikelihood, London: Chapman & Hall, (2006).
  35. Lee M, Ha I.D., Lee Y., Frailty modeling for clustered competing risks data with missing cause of failure”, Statistical Methods in Medical Research, 0(0):118 (2014), doi:10.1177/0962280214545639.
  36. McCormick N.J., Lucas M.S., Student retention and success: Faculty initiatives at Middle Tennessee State University”, Journal of Student Success and Retension, 1(1) (2014), 1-12.
  37. McCulloch, C.E. and Searle, S.R., Generalized, Linear, and Mixed Models, New York: John Wiley & Sons, Inc. 2001.
  38. McGilchrist, C.A. and Aisbett, C.W., Regression with frailty in survival analysis”, Biometrics. 47(1991), 461466.
  39. Mehrotra, D.V. and Su, S.C., An efficient alternative to the stratified cox model analysis”, Statistics Medicine, 31(17) (2012), 1849-56, doi: 10.1002/sim.5327.
  40. Merriam, S.B. and Caffarella, R.S., Learning in Adulthood (2nd ed.), San Francisco: JosseyBass, 1999.
  41. Muljana, P.S. and Luo, T., Factors contributing to student retention in online learning and recommended strategies for improvement: A systematic literature review”, Journal of Information Technology Education, 18 (2019), 19-57.
  42. Noh. M., Ha, I.D. and Lee, Y., Dispersion frailty models and HGLMs”, Statistics in Medicine, 25(8) (2006), 13411354, doi:10.1002/sim.2284.
  43. Olliveira, P.R., Oesterreich, S.A. and Almeida, V.L., School dropout in gradutae distance education: evidence from a study in the interior of Brazil”, Educ. Pesqui., So Paulo, 4(e165786) (2018), 1-20, doi: http://dx.doi.org/10.1590/S1678463420-1708165786.
  44. Pierrakeas, C., Xenos, M., Panagiotakopoulos, C. and Vergidis, D., A comparative study of dropout rates and causes for two different distance education courses”, International Review of Research in Open and Distance Learning, 5(2) (2004), 1-15.
  45. Polat, E. and Gunay, S., A new approach to robust of partial least squares regression analysis”, International Journal of Mathematics Trends and Technology, 9(3) (2014), 132-141.
  46. Ratnaningsih D.J., Saefuddin A., Wijayanto H., An analysis of drop-out students survival in distance higher education”, Journal of Open Distance Education, 9(2) (2008), 01110.
  47. Ratnaningsih, D.J., Saefuddin, A., Kurnia, A. and Mangku, I.W., Stratified-extended Cox model in survival modeling of non proportional hazard”, IOP Conference Series: Earth and Environmental Science, 299(1) (2019), 012023, doi:10.1088/1755-1315/299/1/012023.
  48. Ratnaningsih, D.J., Saefuddin, A., Kurnia, A. and Mangku, I.W., Stratified-Extended Cox with Frailty Model for Non Proportional Hazard: A Statistical Approach to Student Retention Data from Universitas Terbuka in Indonesia”, Thailand Statistician Journal, (2020), Article in Press (ID: TS 192490).
  49. Rovai, A.P., In search of higher persistence rates in distance education online program”, The Internet and Higher Education, 6(1) (2008), 1-16, doi:10.1016/S1096-7516(02)00158-6.
  50. Saegusa, T., Di, C. and Chen, Y.Q., Hypothesis testing for an extended cox model with time-varying coefficients”. Biometrics. 70 (2014), 619628, doi:10.1111/bi-om.12185
  51. Schuemer, R., Some Psychological Aspects of Distance Education”, Hagen, Germany: Institute for Research into Distance Education. ED 357 266 (1993).
  52. Sembiring, M.G., Modeling the determinants of student retention in distance education institutions”, International Journal of Continuing Education and Lifelong Learning, 6(2) (2014), 15-28.
  53. Stroup, W.W., Generalized Linear Mixed Models Modern Concepts, Methods and Applications, New York: Taylor & Francis Group, 2013.
  54. Sylvestre, M.P., Edens, T., MacKenzie, T. and Abrahamowicz, M., PermAlgo: Permutational Algoritm to Simulate Survival Data, Package R can accessed in https://CRAN.Rproject.org/package=PermAlgo, 2015.
  55. Therneau, T.M., Grambsch, P.M. and Pankratz, V.S., Penalized survival models and frailty”, Journal of Computational and Graphical Statistics, 12(1) (2003) , 156-175.
  56. Therneau, T. and Clinic, M., Mixed Effect Cox Models, [Accessed 10 Februari 2017]. On: https://cran.rproject.org/web/packages/coxme/vig-nettes/cox-me.pdf. 2015.
  57. Thomas, L. and Reyes, E.M., Tutorial: Survival estimation for Cox regression models with
  58. time-varying coefficients using SAS and R”, Journal of St0atistical Software, 61 (2014), 1-2, doi: 10.18637/jss.v061.c01.
  59. Vaupel, J.W., Manton, K.G. and Stallard, E., The impact of heterogeneity in individual frailty on the dynamics Panof mortality”, Demography, 16(1979), 439-454.
  60. Wang, N., Xu, S. and Fang, J., Hierarchical likelihood approach for the Weibull frailty model”, Journal of Statistical Computation and Simulation, 81(3) (2011), 343-356.
  61. Wienke, A., Frailty Models in Survival Data, First Edition, New York: Chapman and Hall, 2011.
  62. Wu, L., Mixed Effects Models for Complex Data (Monographs on Statistics and Applied Probability; 113), Boca raton: CRC Press, Taylor & Francis Group, 2010.
  63. Xenos, M., Pierrakeas, C. and Pintelas, P., A survey on student dropout rates and dropout causes concerning the students in the Course of Informatics of the Hellenic Open University”, Computers & Education, 39(4) (2002), 361 377.
  64. Yadav, A.K. and Yadav, R.J., A study on childhood mortality using shared frailty modeling approach”, Journal of Applied Sciences, 16(1)(2016), 11-17, doi: 10.3923/jas.2016.11.17.
  65. Yau, K.W., Multilevel models for survival analysis with random effects”, Biometrics, 57(1) (2001), 96-102