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Breast cancer survival, competing risks and mixture cure model: a Bayesian analysis

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  • Sanjib Basu
  • Ram C. Tiwari

Abstract

Summary. Cancer is a major public health burden and is the second leading cause of death in the USA. The US National Cancer Institute estimated overall costs of cancer in 2007 at $219.2 billion. Breast cancer has the highest cancer incidence rates among women and is the second leading cause of cancer death among women. The ‘Surveillance, epidemiology, and end results’ programme of the National Cancer Institute collects and publishes cancer survival data from 17 population‐based cancer registries. The CANSURV software of the National Cancer Institute analyses cancer survival data from the programme by using parametric and semiparametric mixture cure models. Another popular approach in cancer survival is the competing risks approach which considers the simultaneous risks from cancer and various other causes. The paper develops a model that unifies the mixture cure and competing risks approaches and that can handle the masked causes of death in a natural way. Markov chain sampling is used for Bayesian analysis of this model, and modelling and computational issues of general and restricted structures are discussed. The various model structures are compared by using Bayes factors. This Bayesian model is used to analyse survival data for the approximately 620000 breast cancer cases from the programme. The estimated cumulative probabilities of death from breast cancer from the proposed mixture cure competing risks model is found to be lower than the estimates that are obtained from the CANSURV software. Whereas the estimate of the cure fraction is found to be dependent on the modelling assumptions, the survival and cumulative probability estimates are not sensitive to these assumptions. Breast cancer survival in different ethnic subgroups, in different age subgroups and in patients with localized, regional and distant stages of the disease are compared. The risk of mortality from breast cancer is found to be the dominant cause of death in the beginning part of the follow‐up whereas the risk from other competing causes often became the dominant cause in the latter part. This interrelation between breast cancer and other competing risks varies among the different ethnic groups, the different stages and the different age groups.

Suggested Citation

  • Sanjib Basu & Ram C. Tiwari, 2010. "Breast cancer survival, competing risks and mixture cure model: a Bayesian analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(2), pages 307-329, April.
    • Handle: RePEc:bla:jorssa:v:173:y:2010:i:2:p:307-329
    DOI: 10.1111/j.1467-985X.2009.00618.x
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    References listed on IDEAS

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    1. Sanjib Basu & Ananda Sen & Mousumi Banerjee, 2003. "Bayesian analysis of competing risks with partially masked cause of failure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 77-93, January.
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    3. Kaifeng Lu & Anastasios A. Tsiatis, 2001. "Multiple Imputation Methods for Estimating Regression Coefficients in the Competing Risks Model with Missing Cause of Failure," Biometrics, The International Biometric Society, vol. 57(4), pages 1191-1197, December.
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    6. Cooner, Freda & Banerjee, Sudipto & Carlin, Bradley P. & Sinha, Debajyoti, 2007. "Flexible Cure Rate Modeling Under Latent Activation Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 560-572, June.
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    1. Mioara Alina Nicolaie & Jeremy M. G. Taylor & Catherine Legrand, 2019. "Vertical modeling: analysis of competing risks data with a cure fraction," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 1-25, January.

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