Systematic assessment of Cox proportional hazards, exponential, log-normal survival models in time to event using breast cancer data

• Authors: Uchechukwu Kalu , Lamidi Kehinde Rasheed , Okechukwu Uzoma Iheme , Akorede Yussuf Toheeb , Ugonna Uchechi Iheme
• Languages of publication: EN

Abstracts

EN

This study systematically evaluates the performance of Cox proportional hazards, exponential, and Log-normal survival models using a dataset of 230 breast cancer patients. Descriptive statistics reveal a predominance of female patients (96%) and various cancer stages, with the majority at Stage II (41%). The Kaplan-Meier curve illustrates a gradual decline in overall survival probability over 35 months, dropping to approximately 50% by 20 months. Significant differences in survival probabilities are observed based on smoking status (p = 0.006) and occupation (p = 0.001), while no significant differences are detected across cancer stages (p = 0.5) or treatment types (p = 0.1). The Cox model indicates that smoking status and specific occupations significantly affect hazard ratios, while immunotherapy shows a significant reduction in hazard (HR = 0.609, p = 0.018). The proportional hazards assumption remains largely intact across the covariates in the Cox model. The comparison of survival models using AIC and BIC values shows that the Log-Normal model performs best, with the lowest AIC (1255.282) and BIC (1302.461), indicating a better fit while accounting for model complexity. The Cox Proportional Hazards model ranks second with an AIC of 1385.218 and a BIC of 1424.698. The Exponential model, with the highest AIC (1402.989) and BIC (1464.875), fits the data least effectively. Overall, the Log-Normal model provides the best balance between accuracy and simplicity in this analysis.

Keywords

EN

Breast Cancer Data; Cox Proportional Hazards; Exponential Model; Log-Normal Model; Time-To-Event Analysis

Discipline

• MEDICINE: MEDICINE

• Publisher: Scientific Publishing House „DARWIN”
• Journal: World News of Natural Sciences
• Year: 2025
• Volume: 58
• Pages: 163-182

Contributors

author

Uchechukwu Kalu

• Departement of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria

author

Lamidi Kehinde Rasheed

• Departement of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria

author

Okechukwu Uzoma Iheme

• Key Laboratory of Vegetation Restoration and Management of Degraded Ecosystem, South Botanical Garden, Chinese Academy of Science, Guangzhou, China

author

Akorede Yussuf Toheeb

• Departement of Mathematics and Statistics, Kwara State University, Malete, Kwara State, Nigeria

author

Ugonna Uchechi Iheme

• Department of Dental Technology, Federal University of Technology, PMB 1526, Owerri, Imo State, Nigeria

References

• [1] Barker, L. E., & O’Connell, J. (2021). The Importance of Survival Model Selection in Cancer Research: A Focus on Breast Cancer. Cancer Epidemiology, Biomarkers & Prevention, 30(5), 889-895. https://doi.org/10.1158/1055-9965.EPL-20-0968
• [2] Bray, F., Ferlay, J., Soerjomataram, I., Siegel, R. L., Torre, L. A., & Jemal, A. (2018). Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA: A Cancer Journal for Clinicians, 68(6), 394-424. https://doi.org/10.3322/caac.21492
• [3] Carroll K.J (2021). On the use and utility of the Weibull model in the analysis of survival data. Control Clinical Trials 2003; 24: 682-701
• [4] Cox, D. R. (1972). Regression Models and Life-Tables. Journal of the Royal Statistical Society: Series B (Methodological), 34(2), 187-220
• [5] Ghosh, A., Roy, S., & Bhattacharyya, S. (2020). Survival Analysis: A Comparative Study of Cox Proportional Hazards and Accelerated Failure Time Models. JAMA Oncol. 2020; 6(12): 1983-1984. doi:10.1001/jamaoncol.2020.5158
• [6] Giordano, S. H., Elias, A. D., & Gradishar, W. J. (2018). NCCN Guidelines updates Breast cancer. JNCCN–Journal of the National Comprehensive Cancer Network, 16(5S), 605-610. https://doi.org/10.6004/jnccn.2018.0035
• [7] Gomez, J. R., & Lammers, A. E. (2022). Statistical modeling of quality of life and patient-reported outcomes in breast cancer: Current practices and future directions. Journal of Clinical Oncology, 40(10), 1120-1129. https://doi.org/10.1200/JCO.2021.40.10_suppl.1120
• [8] Kim, H. J., & Kim, H. (2021). Comparison of survival analysis methods for breast cancer: A comprehensive review. Journal of Biomedical Informatics, 113, 103661 .https://doi.org/10.1016/j.jbi.2020.103661
• [9] Kleinbauim D.G & Klein M. Survival Analysis: A Self-Learning Text. Springer Science+Business Media, LLC, part of Springer Nature 2012. https://doi.org/10.1007/978-1-4419-6646-9
• [10] Lee, E. T., & Wang, J. W. (2020). Statistical Methods for Survival Data Analysis. John Wiley & Sons, Inc. Online ISBN:9780471458548. DOI: 10.1002/0471458546
• [11] Medhat Mohamed Ahmed Abdelaal & Sally Hossam Eldin Ahmed Zakria (2015). Modeling Survival Data by Using Cox Regression Model. American Journal of Theoretical and Applied Statistics 4(6): 504-512
• [12] Miller, A. B., & Hodge, W. (2020). Evaluating the Assumptions of Survival Analysis: A Practical Guide for Researchers. Journal of Clinical Epidemiology, 123, 51-57. https://doi.org/10.1016/j.jclinepi.2019.12.010
• [13] Miller, T. R., Olsen, K., & Williams, P. (2023). Parametric models in oncology: A review with applications to breast cancer survival data. Statistics in Medicine, 42(1), 52-68. https://doi.org/10.1002/sim.9323
• [14] Nassif EF, Cope B, Traweek R, Witt RG, Erstad DJ, Scally CP, Thirasastr P, Zarzour MA, Ludwig J, Benjamin R, Bishop AJ, Guadagnolo BA, Ingram D, Wani K, Wang WL, Lazar AJ, Torres KE, Hunt KK, Feig BW, Roland CL, Somaiah N, Keung EZ. Real-world use of palbociclib monotherapy in retroperitoneal liposarcomas at a large volume sarcoma center. Int J Cancer. 2022 Jun 15; 150(12): 2012-2024. doi: 10.1002/ijc.33956
• [15] Nguyen, T., & Chen, R. (2021). Understanding censoring mechanisms and their impact on survival analysis models in clinical trials. Statistical Methods in Medical Research, 30(4), 905-916. https://doi.org/10.1177/0962280220984105
• [16] Ryosuke Fujii (2023). Visualization of Relative Measures of Association: Points and Error Bars With an Appropriate Axis Scale. Journal of Epidemiology 33(9). https://doi.org/10.2188/jea.JE20230052
• [17] Rahman, H., Liu, Q., & Zhang, Y. (2022). A comparative study of survival models for breast cancer patients: Cox proportional hazards, parametric models, and their performance. Journal of Cancer Research and Clinical Oncology, 148(5), 1012-1024. https://doi.org/10.1007/s00432-021-03650-9
• [18] Schober P, Vetter TR. Survival Analysis and Interpretation of Time-to-Event Data: The Tortoise and the Hare. Anesth Analg. 2018 Sep; 127(3): 792-798. doi: 10.1213/ANE.0000000000003653
• [19] Smith, R. E., Anderson, R. E., & Smith, M. L. (2021). Survival Analysis in Medicine and Epidemiology: A Comprehensive Overview. Journal of Epidemiology & Community Health, 75(5), 445-452. doi:10.1136/jech-2020-213209
• [20] Sung, H., Ferlay, J., Siegel, R. L., Laversanne, M., Soerjomataram, I., Jemal, A., & Bray, F. (2021). Global cancer statistics 2020: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA: A Cancer Journal for Clinicians, 71(3), 209–249. DOI: 10.3322/caac.21660
• [21] Wang, K., & Wei, Z. (2020). The Cox Proportional Hazards Model: Applications and Practical Issues. Current Problems in Cancer, 44(5), 100501. https://doi.org/10.1016/j.currproblcancer.2020.100501
• [22] Zhu, Y., Li, F., & Chen, X. (2021). Assessing the performance of survival models in breast cancer research: Cox PH, exponential, Weibull, and log-normal comparisons. BMC Medical Research Methodology, 21(48), 1-14. https://doi.org/10.1186/s12874-021-01244-8

• Document Type: article