IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v59y2010i1p35-55.html
   My bibliography  Save this article

Estimating the cure fraction in population‐based cancer studies by using finite mixture models

Author

Listed:
  • P. C. Lambert
  • P. W. Dickman
  • C. L. Weston
  • J. R. Thompson

Abstract

Summary. The cure fraction (the proportion of patients who are cured of disease) is of interest to both patients and clinicians and is a useful measure to monitor trends in survival of curable disease. The paper extends the non‐mixture and mixture cure fraction models to estimate the proportion cured of disease in population‐based cancer studies by incorporating a finite mixture of two Weibull distributions to provide more flexibility in the shape of the estimated relative survival or excess mortality functions. The methods are illustrated by using public use data from England and Wales on survival following diagnosis of cancer of the colon where interest lies in differences between age and deprivation groups. We show that the finite mixture approach leads to improved model fit and estimates of the cure fraction that are closer to the empirical estimates. This is particularly so in the oldest age group where the cure fraction is notably lower. The cure fraction is broadly similar in each deprivation group, but the median survival of the ‘uncured’ is lower in the more deprived groups. The finite mixture approach overcomes some of the limitations of the more simplistic cure models and has the potential to model the complex excess hazard functions that are seen in real data.

Suggested Citation

  • P. C. Lambert & P. W. Dickman & C. L. Weston & J. R. Thompson, 2010. "Estimating the cure fraction in population‐based cancer studies by using finite mixture models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 35-55, January.
    • Handle: RePEc:bla:jorssc:v:59:y:2010:i:1:p:35-55
    DOI: 10.1111/j.1467-9876.2009.00677.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9876.2009.00677.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9876.2009.00677.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Li, Chin-Shang & Taylor, Jeremy M. G. & Sy, Judy P., 2001. "Identifiability of cure models," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 389-395, October.
    2. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
    3. Paul C. Lambert, 2007. "Modeling of the cure fraction in survival studies," Stata Journal, StataCorp LP, vol. 7(3), pages 351-375, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Patricia Guyot & Anthony E. Ades & Matthew Beasley & Béranger Lueza & Jean-Pierre Pignon & Nicky J. Welton, 2017. "Extrapolation of Survival Curves from Cancer Trials Using External Information," Medical Decision Making, , vol. 37(4), pages 353-366, May.
    2. Therese M.-L. Andersson & Paul C. Lambert, 2012. "Fitting and modeling cure in population-based cancer studies within the framework of flexible parametric survival models," Stata Journal, StataCorp LP, vol. 12(4), pages 623-638, December.
    3. Beibei Guo & Elizabeth Garrett‐Mayer & Suyu Liu, 2021. "A Bayesian phase I/II design for cancer clinical trials combining an immunotherapeutic agent with a chemotherapeutic agent," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1210-1229, November.
    4. Yilong Zhang & Xiaoxia Han & Yongzhao Shao, 2021. "The ROC of Cox proportional hazards cure models with application in cancer studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 195-215, April.
    5. Karri Seppä & Timo Hakulinen & Esa Läärä, 2014. "Regional variation in relative survival—quantifying the effects of the competing risks of death by using a cure fraction model with random effects," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 175-190, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vicente G. Cancho & Márcia A. C. Macera & Adriano K. Suzuki & Francisco Louzada & Katherine E. C. Zavaleta, 2020. "A new long-term survival model with dispersion induced by discrete frailty," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 221-244, April.
    2. Guoqing Diao & Ao Yuan, 2019. "A class of semiparametric cure models with current status data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 26-51, January.
    3. Hu, Tao & Xiang, Liming, 2016. "Partially linear transformation cure models for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 257-269.
    4. Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    5. Weibin Zhong & Guoqing Diao, 2023. "Semiparametric Density Ratio Model for Survival Data with a Cure Fraction," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 217-241, April.
    6. Hu, Tao & Xiang, Liming, 2013. "Efficient estimation for semiparametric cure models with interval-censored data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 139-151.
    7. Reza Azimi & Mahdy Esmailian & Diego I. Gallardo & Héctor J. Gómez, 2022. "A New Cure Rate Model Based on Flory–Schulz Distribution: Application to the Cancer Data," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    8. Peng, Yingwei & Zhang, Jiajia, 2008. "Identifiability of a mixture cure frailty model," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2604-2608, November.
    9. Das, Ujjwal & Das, Kalyan, 2018. "Inference on zero inflated ordinal models with semiparametric link," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 104-115.
    10. Scolas, Sylvie & Legrand, Catherine & Oulhaj, Abderrahim & El Ghouch, Anouar, 2016. "Diagnostic checks in mixture cure models with interval-censoring," LIDAM Discussion Papers ISBA 2016014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Mário Castro & Ming-Hui Chen & Joseph G. Ibrahim & John P. Klein, 2014. "Bayesian Transformation Models for Multivariate Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 187-199, March.
    12. Kiron Chatterjee & Kang-Rae Ma, 2009. "Time taken for residents to adopt a new public transport service: examining heterogeneity through duration modelling," Transportation, Springer, vol. 36(1), pages 1-25, January.
    13. Yu, Binbing & Peng, Yingwei, 2008. "Mixture cure models for multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1524-1532, January.
    14. Durga H. Kutal & Lianfen Qian, 2018. "A Non-Mixture Cure Model for Right-Censored Data with Fréchet Distribution," Stats, MDPI, vol. 1(1), pages 1-13, November.
    15. Suvra Pal & N. Balakrishnan, 2017. "Likelihood inference for the destructive exponentially weighted Poisson cure rate model with Weibull lifetime and an application to melanoma data," Computational Statistics, Springer, vol. 32(2), pages 429-449, June.
    16. Li, Shuwei & Hu, Tao & Wang, Peijie & Sun, Jianguo, 2017. "Regression analysis of current status data in the presence of dependent censoring with applications to tumorigenicity experiments," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 75-86.
    17. Weiyu Li & Valentin Patilea, 2018. "A dimension reduction approach for conditional Kaplan–Meier estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 295-315, June.
    18. Shuangge Ma, 2011. "Additive risk model for current status data with a cured subgroup," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 117-134, February.
    19. Chen, Chyong-Mei & Lu, Tai-Fang C., 2012. "Marginal analysis of multivariate failure time data with a surviving fraction based on semiparametric transformation cure models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 645-655.
    20. Lu Wang & Pang Du & Hua Liang, 2012. "Two-Component Mixture Cure Rate Model with Spline Estimated Nonparametric Components," Biometrics, The International Biometric Society, vol. 68(3), pages 726-735, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssc:v:59:y:2010:i:1:p:35-55. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.