[go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

A support vector machine based semiparametric mixture cure model

  • Original paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

The mixture cure model is an extension of standard survival models to analyze survival data with a cured fraction. Many developments in recent years focus on the latency part of the model to allow more flexible modeling strategies for the distribution of uncured subjects, and fewer studies focus on the incidence part to model the probability of being uncured/cured. We propose a new mixture cure model that employs the support vector machine (SVM) to model the covariate effects in the incidence part of the cure model. The new model inherits the features of the SVM to provide a flexible model to assess the effects of covariates on the incidence. Unlike the existing nonparametric approaches for the incidence part, the SVM method also allows for potentially high-dimensional covariates in the incidence part. Semiparametric models are also allowed in the latency part of the proposed model. We develop an estimation method to estimate the cure model and conduct a simulation study to show that the proposed model outperforms existing cure models, particularly in incidence estimation. An illustrative example using data from leukemia patients is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Boag JW (1949) Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J R Stat Soc 11:15–53

    MATH  Google Scholar 

  • Breslow NE (1974) Covariate analysis of censored survival data. Biometrics 30:89–99

    Article  Google Scholar 

  • Cai C, Zou Y, Peng Y, Zhang J (2012) SMCURE: an R-package for estimating semiparametric mixture cure models. Comput Methods Programs Biomed 108:1255–1260

    Article  Google Scholar 

  • Chang C-C, Lin C-J (2011) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol (TIST) 2:27

    Google Scholar 

  • Copelan EA, Biggs JC, Thompson JM, Crilley P, Szer J, Klein JP, Kapoor N, Avalos BR, Cunningham I, Atkinson K, Downs K, Harmon GS, Daly MB, Brodsky I, Bulova SI, Tutschka PJ (1991) Treatment for acute myelocytic leukemia with allogeneic bone marrow transplantation following preparation with Bu/Cy. Blood 78:838–843

    Article  Google Scholar 

  • Corbiere F, Joly P (2007) A SAS macro for parametric and semiparametric mixture cure models. Comput Methods Programs Biomed 85:173–180

    Article  Google Scholar 

  • Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20:273–297

    MATH  Google Scholar 

  • Denham JW, Denham EE, Dear KBG, Hudson GV (1996) The follicular non-Hodgkin’s lymphomas—I. The possibility of cure. Eur J Cancer 32:470–479

    Article  Google Scholar 

  • Farewell VT (1982) The use of mixture models for the analysis of survival data with long-term survivors. Biometrics 38:1041–46

    Article  Google Scholar 

  • Farewell VT (1986) Mixture models in survival analysis: are they worth the risk? Can J Stat 14:257–262

    Article  MathSciNet  Google Scholar 

  • Gu Y, Sinha D, Banerjee S (2011) Analysis of cure rate survival data under proportional odds model. Lifetime Data Anal 17:123–134

    Article  MathSciNet  Google Scholar 

  • Jiang W, Sun H, Peng Y (2017) Prediction accuracy for the cure probabilities in mixture cure model. Stat Methods Med Res 26:2029–2041

    Article  MathSciNet  Google Scholar 

  • Klein JP, Moeschberger ML (2003) Survival Analysis, Techniques for Censored and Truncated Data, 2nd edn. Spinger, New York

    Book  Google Scholar 

  • Kuk AYC, Chen C (1992) A mixture model combining logistic regression with proportional hazards regression. Biometrika 79:531–41

    Article  Google Scholar 

  • Li C-S, Taylor JMG (2002) A semi-parametric accelerated failure time cure model. Stat Med 21:3235–3247

    Article  Google Scholar 

  • López-Cheda A, Cao R, Jacome MA, van Keilegom I (2017) Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models. Comput Stat Data Anal 105:144–165

    Article  MathSciNet  Google Scholar 

  • Mao M, Wang J-L (2010) Semiparametric efficient estimation for a class of generalized proportional odds cure models. J Am Stat Assoc 105:302–311

    Article  MathSciNet  Google Scholar 

  • Peng Y (2003) Fitting semiparametric cure models. Comput Stat Data Anal 41:481–490

    Article  MathSciNet  Google Scholar 

  • Peng Y, Dear KBG (2000) A nonparametric mixture model for cure rate estimation. Biometrics 56:237–243

    Article  Google Scholar 

  • Platt J (1998) Sequential minimal optimization: a fast algorithm for training support vector machines. https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/tr-98-14.pdf. Accessed 3 Nov 2019

  • Platt J et al (1999) Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. Adv Large Margin Classif 10:61–74

    Google Scholar 

  • Ramires TG, Hens N, Cordeiro GM, Ortega EM (2018) Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model. Comput Stat 33:709–730

    Article  MathSciNet  Google Scholar 

  • Sy JP, Taylor JMG (2000) Estimation in a Cox proportional hazards cure model. Biometrics 56:227–236

    Article  MathSciNet  Google Scholar 

  • Taylor JMG (1995) Semi-parametric estimation in failure time mixture models. Biometrics 51:899–907

    Article  Google Scholar 

  • Tong EN, Mues C, Thomas LC (2012) Mixture cure models in credit scoring: if and when borrowers default. Eur J Oper Res 218:132–139

    Article  MathSciNet  Google Scholar 

  • Wu Y, Yin G (2013) Cure rate quantile regression for censored data with a survival fraction. J Am Stat Assoc 108:1517–1531

    Article  MathSciNet  Google Scholar 

  • Xu J, Peng Y (2014) Nonparametric cure rate estimation with covariates. Can J Stat 42:1–17

    Article  MathSciNet  Google Scholar 

  • Zhang J, Peng Y (2007a) An alternative estimation method for the accelerated failure time frailty model. Comput Stat Data Anal 51:4413–4423

    Article  MathSciNet  Google Scholar 

  • Zhang J, Peng Y (2007b) A new estimation method for the semiparametric accelerated failure time mixture cure model. Stat Med 26:3157–3171

    Article  MathSciNet  Google Scholar 

  • Zhang J, Peng Y (2009) Accelerated hazards mixture cure model. Lifetime Data Anal 15:455–467

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The first and the last authors gratefully acknowledge the financial support from China Scholarship Council. The first author’s work was partially supported by Liaoning Social Science Planning Fund (L19CTJ001). The second author’s work was partially supported by a research grant from the Natural Sciences and Engineering Research Council of Canada. The last author’s work was also supported by the Fundamental Research Funds for the Central Universities (DUT19RC(3)042).

Author information

Authors and Affiliations

  1. School of Finance, Dongbei University of Finance and Economics, Dalian, China

    Peizhi Li

  2. Department of Public Health Sciences, Queen’s University, Kingston, ON, Canada

    Yingwei Peng

  3. Department of Mathematics and Statistics, Queen’s University, Kingston, ON, Canada

    Yingwei Peng

  4. School of Statistics, Dongbei University of Finance and Economics, Dalian, China

    Ping Jiang

  5. Faculty of Management and Economics, Dalian University of Technology, Dalian, China

    Qingli Dong

Authors
  1. Peizhi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yingwei Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ping Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qingli Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yingwei Peng.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, P., Peng, Y., Jiang, P. et al. A support vector machine based semiparametric mixture cure model. Comput Stat 35, 931–945 (2020). https://doi.org/10.1007/s00180-019-00931-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-019-00931-w

Keywords