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

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

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