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Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model

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  • Thiago G. Ramires

    (Federal University of Technology - Paraná
    University of Hasselt)

  • Niel Hens

    (University of Hasselt
    University of Antwerp)

  • Gauss M. Cordeiro

    (Federal University of Pernambuco)

  • Edwin M. M. Ortega

    (University of São Paulo)

Abstract

Nonlinear effects between explanatory and response variables are increasingly present in new surveys. In this paper, we propose a flexible four-parameter semi-parametric cure rate survival model called the sinh Cauchy cure rate distribution. The proposed model is based on the generalized additive models for location, scale and shape, for which any or all parameters of the distribution are parametric linear and/or nonparametric smooth functions of explanatory variables. The new model is used to fit the nonlinear behavior between explanatory variables and cure rate. The biases of the cure rate parameter estimates caused by not incorporating such non-linear effects in the model are investigated using Monte Carlo simulations. We discuss diagnostic measures and methods to select additive terms and their computational implementation. The flexibility of the proposed model is illustrated by predicting lifetime and cure rate proportion as well as identifying factors associated to women diagnosed with breast cancer.

Suggested Citation

  • Thiago G. Ramires & Niel Hens & Gauss M. Cordeiro & Edwin M. M. Ortega, 2018. "Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model," Computational Statistics, Springer, vol. 33(2), pages 709-730, June.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0781-8
    DOI: 10.1007/s00180-017-0781-8
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    References listed on IDEAS

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    1. Gauss M. Cordeiro & Vicente G. Cancho & Edwin M. M. Ortega & Gladys D. C. Barriga, 2016. "A model with long-term survivors: negative binomial Birnbaum-Saunders," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1370-1387, March.
    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. Beatriz R. Lanjoni & Edwin M. M. Ortega & Gauss M. Cordeiro, 2016. "Extended Burr XII Regression Models: Theory and Applications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 203-224, March.
    4. Vlasios Voudouris & Robert Gilchrist & Robert Rigby & John Sedgwick & Dimitrios Stasinopoulos, 2012. "Modelling skewness and kurtosis with the BCPE density in GAMLSS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1279-1293, November.
    5. Edwin M.M. Ortega & Gauss M. Cordeiro & Elizabeth M. Hashimoto & Kahadawala Cooray, 2014. "A log-linear regression model for the odd Weibull distribution with censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1859-1880, September.
    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.
    7. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    8. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
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    Cited by:

    1. Peizhi Li & Yingwei Peng & Ping Jiang & Qingli Dong, 2020. "A support vector machine based semiparametric mixture cure model," Computational Statistics, Springer, vol. 35(3), pages 931-945, September.
    2. Vicente G. Cancho & Elizbeth C. Bedia & Gauss M. Cordeiro & Fábio Prataviera & Edwin M. M. Ortega & Ana P. J. E. Santo, 2023. "A survival regression with cure fraction applied to cervical cancer," Computational Statistics, Springer, vol. 38(1), pages 403-418, March.

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