Fitting the Lindley Survival Model Using Maximum Likelihood and Moments Method for Analysing Leukemia Survival Data in Erbil_Iraq
DOI:
https://doi.org/10.31272/jae.i150.1447Keywords:
Survival Analysis, Lindley parametric survival model, Akaike Information Criterion (AIC), LeukemiaAbstract
The study uses the Lindley distribution to estimate parametric survival models using leukemia survival data in Erbil City, Iraq. We examine two estimate methods for modelling time-to-event data: Maximum Likelihood estimate (MLE), and the Method of Moments (MoM). The MLE approach produces asymptotically efficient estimates, whereas using sample moments, the MoM provides a simpler, non-iterative approach. The goodness of fit tests, Akaike Information Criteria (AIC), Bayesian Information Criterion (BIC) and Mean Square Error (MSE) are used to assess model performance.
The results show that MLE outperforms MoM in terms of precision and resilience, especially with censored data. However, The findings demonstrate the Lindley distribution's relevance in medical survival analysis and provide insight into leukemia survival patterns in Erbil City.
This study adds to the growing literature on parametric survival modelling and helps clinical decision-making for leukemia therapies. The data set of this study was obtained from Rizgari hospital in Erbil city. The results obtained by utilizing the statistical packages (Mat-lab V. 23.2 and R Software V. 2025.05.1+513)
Downloads
References
[1] Ghitany, M. E., Atieh, B., & Nadarajah, S. (2008). Lindley distribution and its application. Mathematics and computers in simulation, 78(4), 493-506.DOI: https://doi.org/10.1016/j.matcom.2007.06.007 DOI: https://doi.org/10.1016/j.matcom.2007.06.007
[2] Bhati, D., Malik, M. A., & Vaman, H. J. (2015). Lindley–exponential distribution: properties and applications. Metron, 73, 335-357.DOI: https://doi.org/10.1007/s40300-015-0060-9 DOI: https://doi.org/10.1007/s40300-015-0060-9
[3] Kartsonaki, C. (2016). Survival analysis. Diagnostic Histopathology, 22(7), 263-270. DOI: https://doi.org/10.1016/j.mpdhp.2016.06.005
DOI: https://doi.org/10.1016/j.mpdhp.2016.06.005 DOI: https://doi.org/10.1016/j.mpdhp.2016.06.005
[4] Mawlood, K. I. (2019). Using logistic regression and cox regression models to studying the most prognostic factors for leukemia patients. QALAAI ZANIST JOURNAL, 4(3), 705-724. DOI: https://doi.org/10.25212/lfu.qzj.4.3.20 DOI: https://doi.org/10.25212/lfu.qzj.4.3.20
[5] Abdullah, I. K., & Rady, A. K. (2021). Comparison of methods for estimating the parameters of the asymmetric Laplace distribution using the quadratic loss function and the maximum possibility method. Journal of Administration and Economics, 46(130).DOI: https://doi.org/10.31272/jae.i130.32 DOI: https://doi.org/10.31272/jae.i130.32
[7 Hassan, A. H., & Shamal, I. H. (2023). Using genetic algorithm to estimate gamma Lindley distribution parameters. Journal of Administration and Economics, 48(141).DOI: https://doi.org/10.31272/jae.i141.1007 DOI: https://doi.org/10.31272/jae.i141.1007
[8] Manal M.R. (2023).Using the genetic algorithm to improve the survival function estimates of the Frechet-Weibull exponential distribution mixed model with a practical application. DOI: https://doi.org/10.31272/jae.i141.1012 DOI: https://doi.org/10.31272/jae.i141.1012
[9] Zhang, T. D., Chen, G. Q., Wang, Z. G., Wang, Z. Y., Chen, S. J., & Chen, Z. (2001). Arsenic trioxide, a therapeutic agent for APL. Oncogene, 20(49), 7146-7153. DOI: https://doi.org/10.1038/sj.onc.1204762 DOI: https://doi.org/10.1038/sj.onc.1204762
[10] Redha, S. M., & Hadia, A. T. A. (2020). Estimate the Survival Function By Using The Genetic Algorithm. Journal of Economics and Administrative Sciences, 26(122). DOI: https://doi.org/10.33095/jeas.v26i122.2018 DOI: https://doi.org/10.33095/jeas.v26i122.2018
[11] Austin, P. C. (2017). A tutorial on multilevel survival analysis: methods, models and applications. International Statistical Review, 85(2), 185-203.DOI: https://doi.org/10.1111/insr.12214 DOI: https://doi.org/10.1111/insr.12214
[12] Harrell, F. E. (2001). Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis (Vol. 608). New York: springer.DOI: https://doi.org/10.1007/978-1-4757-3462-1 DOI: https://doi.org/10.1007/978-1-4757-3462-1
[13] Lindley, D. V. (1970). The estimation of many parameters. ETS Research Bulletin Series, 1970(1), i-20. DOI: https://doi.org/10.1002/j.2333-8504.1970.tb00411.x DOI: https://doi.org/10.1002/j.2333-8504.1970.tb00411.x
[14] Shanker, R., Sharma, S., & Shanker, R. (2013). A two-parameter Lindley distribution for modeling waiting and survival times data. Applied Mathematics, 4(2), 363-368. DOI: http://dx.doi.org/10.4236/am.2013.42056 DOI: https://doi.org/10.4236/am.2013.42056
[15] Ramos, P. L., & Louzada, F. (2016). The generalized weighted Lindley distribution: Properties, estimation, and applications. Cogent Mathematics, 3(1), 1256022. DOI: https://doi.org/10.1080/23311835.2016.1256022 DOI: https://doi.org/10.1080/23311835.2016.1256022
[16] Bhati, D., Sastry, D. V. S., & Qadri, P. M. (2015). A new generalized Poisson-Lindley distribution: Applications and properties. Austrian Journal of Statistics, 44(4), 35-51.DOI: https://doi.org/10.17713/ajs.v44i4.54 DOI: https://doi.org/10.17713/ajs.v44i4.54
[17] Van Den Hout, A. (2016). Multi-state survival models for interval-censored data. Chapman and Hall/CRC. DOI: https://doi.org/10.1201/9781315374321 DOI: https://doi.org/10.1201/9781315374321
[18] Khan, M. J. S., Sharma, A., & Iqrar, S. (2020). On moments of Lindley distribution based on generalized order statistics. American Journal of Mathematical and Management Sciences, 39(3), 214-233. DOI: https://doi.org/10.1080/01966324.2020.1718568 DOI: https://doi.org/10.1080/01966324.2020.1718568
[19] Sultan, K. S., & Al-Thubyani, W. S. (2016). Higher order moments of order statistics from the Lindley distribution and associated inference. Journal of Statistical computation and Simulation, 86(17), 3432-3445. DOI: https://doi.org/10.1080/00949655.2016.1163361 DOI: https://doi.org/10.1080/00949655.2016.1163361
[20] Moore, D. F. (2016). Applied survival analysis using R (Vol. 473, pp. 1-10). Cham: Springer. DOI: https://doi.org/10.1007/978-3-319-31245-3 DOI: https://doi.org/10.1007/978-3-319-31245-3
[21] Ibrahim, J. G., Chen, M. H., & Sinha, D. (2013). Bayesian survival analysis. Springer Science & Business Media. DOI: https://doi.org/10.1201/b16248 DOI: https://doi.org/10.1201/b16248
[22] Balan, T. A., & Putter, H. (2020). A tutorial on frailty models. Statistical methods in medical research, 29(11), 3424-3454.DOI: https://doi.org/10.1177/0962280220921889 DOI: https://doi.org/10.1177/0962280220921889
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Ibrahim A. Othman, Kurdistan I. Mawlood
This work is licensed under a Creative Commons Attribution 4.0 International License.
The journal of Administration & Economics is an open- access journal that all contents are free of charge. Articles of this journal are licensed under the terms of the Creative Commons Attribution International Public License CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/legalcode) that licensees are unrestrictly allowedto search, download, share, distribute, print, or link to the full text of the articles, crawl them for indexing and reproduce any medium of the articles provided that they give the author(s) proper credits (citation). The journal allows the author(s) to retain the copyright of their published article.
Creative Commons-Attribution (BY) 
