DeepWei-Cu: A Deep Weibull Network for Cure Fraction Models
Abstract
Introduction: Survival analysis including cure fraction subgroups is heavily used in different fields like economics, engineering and medicine. The main core of the analysis is to understand the relationship between the covariates and the survival function taking into consideration censoring and long-term survival. The analysis can be performed using traditional statistical models or neural networks. Recently, neural network has attracted attention in analyzing lifetime data due to its ability of efficiently estimating the survival function under the existence of complex covariates. To the best of our knowledge, this is the first time a parametric neural network is introduced to analyze mixture cure fraction models.
Methods: In this paper, we introduce a novel neural network based on mixture cure fraction Weibull loss function.
Results: Alzheimer disease dataset as long as synthetic dataset are used to study the efficiency of the model. We compared the results using goodness of fit methods in both datasets with Weibull regression.
Conclusion: The proposed neural network has the flexibility of analyzing continuous data without discretization. Also, it has the advantage of using Weibull distribution properties. For example, it can analyze data with different hazard rates (monotonically decreasing, monotonically increasing and constant). comparing the results with Weibull regression, the proposed neural network performed better.
2. Boag, J., W. Maximum likelihood estimates of patients cured by cancer therapy. Journal of the Royal Statistical Society. Series B. 1949; 11(1): 15-53.
3. Farewell, V., T. The use of mixture models for the analysis of survival data with long-term survivors. Biometrics. 1982; 38: 1041-1046.
4. Yamaguchi, K. Accelerated failure-time regression models with a regression model of surviving fraction: an application to the analysis of "permanent employment" in Japan. Journal of the American Statistical Association. 1992; 87(418): 284-292.
5. Yu, B., Tiwari, R., C., Cronin, K., A. and Feuer, E. J. Cure fraction estimation from the mixture cure models for grouped survival data. Statistics In Medicine. 2004; 23: 1733-1747.
6. Kannan, N., Kundu, D., Nair, P. and Tripathi, R., C. The generalized exponential cure rate model with covariates. Journal of Applied Statistics. 2010; 37(10): 1625-1636.
7. Martinez, E., Z., Achcar, J., A., Jacome, A., A. and Santos, J., S. Mixture and non-mixture cure fraction models based on the generalized modified Weibull distribution with an application on gastric cancer data. Computer Methods And Programs In Biomedicine. 2013, 112(3); 343-355.
8. Swain, P., K., Grover, G. and Goel, K. Mixture and non mixture cure fraction models based on generalized gompertz distribution under Bayesian approach. Tatra Mountains Mathematical Publication. 2016; 66: 11-135.
9. Omer, M., Abu Bakar, M., Adam, M. and Mustafa, M. Cure models with exponentiated Weibull exponential distribution for the analysis of melanoma patients. Mathematics. 2020; 8(11), 1926; https://doi.org/10.3390/math8111926.
10. Faraggi, D., and Simon, R. A neural network model for survival data. Statistics in Medicine. 1995; 14: 73-82.
11. Katzman, J., Shaham, U., Cloninger, A., Bates, J., Jiang, T. and Kluger,'Y. Deep Survival: A Deep Cox Proportional Hazards Network. 2016, https://doi.org/10.1186/s12874-018-0482-1.
12. Zhu, X., Yao, J and Huang, J. Deep Convolutional Neural Network for Survival Analysis with Pathological Images. IEEE International Conference on Bioinformatics and Biomedicine. 2016: DOI: 10.1109/BIBM.2016.7822579.
13. Zhu,X., Yao, J., Zhu, F. and Huang, H. WSISA: Making Survival Prediction from Whole Slide Histopathological Images. IEEE Conference on Computer Vision and Pattern Recognition. 2017: DOI: 10.1109/CVPR.2017.725.
14. Pawley, M. DeepWeibull: a deep learning approach to parametric survival analysis. M.Sc. Thesis, Departement of Mathematics, Imperial College London. 2020.
15. Xie, Y. and Yu, Z. Mixture cure rate models with neural network estimated nonparametric components. Computational Statistics. 2021; 36, 2467-2489.
16. Ng, S,. K., Mclachlan, G., J., Yau, K., W., Lee, A., H. Modelling the distribution of ischaemic stroke-specific survival time using an EM-based mixture approach with random effects adjustment. Statistics in Medicine. 2004; 23: 2729-2744.
17. Velazquez, M., Rodriquez, J., Carmen, M., Murrieta, F. and Eslava, G. Application of the Weibull Distribution to Estimate the Volume of Water Pumping by a Windmill. Journal of Power and Energy Engineering. 2016; 4(9): 36-51.
18. Pascale, E., Freneaux,T., Sista, R., Sannino, P., Marmo, P., Bouillaut, L. Application of the Weibull distribution for the optimization of maintenance policies of an electronic railway signaling system. European Safety and Reliability Conference. 2017; 8p: hal-01521640.
19. Lambert, P., C., Thompson, J., R., Weston, C., L. and Dickman, P., W. Estimating and modeling the cure fraction in population-based cancer survival analysis. Biostatistics. 2007; 8(3): 576-594.
20. Achcar, J., A., Coelho-Barros, E., A. and Mazucheli, J. Cure fraction models using mixture and non- mixture models. Tatra Mountains Mathematical Publications. 2012; 51: 1-9.
21. Chukwu, A., U. and Folorunso, S., A. Determinant of flexible parametric estimation of mixture cure fraction model: an application of gastric cancer data. West African Journal of Industrial and Academic Research. 2015; 15(1): 139-156.
22. Yusuf, M., U. and Bakar, M., R. (2016). Cure models based on Weibull distribution with and without covariates using right censored data. Indian Journal of Science and Technology. 2016; 9(28): 1-12.
Files | ||
Issue | Vol 10 No 1 (2024) | |
Section | Articles | |
DOI | https://doi.org/10.18502/jbe.v10i1.17153 | |
Keywords | ||
Cure fraction Weibull distribution Deep learning Neural Network Random Censoring. |
Rights and permissions | |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |