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

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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.

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Acknowledgements

The first author acknowledge the financial support of the “Ciência sem Fronteiras” program of CNPq (Brazil) under the process number 200574/2015-9.

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Technology - Paraná, Apucarana, Brazil

    Thiago G. Ramires

  2. Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-Biostat), University of Hasselt, Hasselt, Belgium

    Thiago G. Ramires & Niel Hens

  3. Centre for Health Economic Research and Modelling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerpen, Belgium

    Niel Hens

  4. Department of Statistics, Federal University of Pernambuco, Recife, Brazil

    Gauss M. Cordeiro

  5. Department of Exact Sciences, University of São Paulo, São Paulo, Brazil

    Edwin M. M. Ortega

Authors
  1. Thiago G. Ramires
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  2. Niel Hens
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  3. Gauss M. Cordeiro
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  4. Edwin M. M. Ortega
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Corresponding author

Correspondence to Thiago G. Ramires.

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The authors have declared no conflict of interest.

Appendix: Computational codes

Appendix: Computational codes

Here, we present the codes implemented in the GAMLSS package in the software R. The pdf, cdf, qf and the samples generator functions are

figure a

Next, we present the codes used in the data analysis.

figure b

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Ramires, T.G., Hens, N., Cordeiro, G.M. et al. Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model. Comput Stat 33, 709–730 (2018). https://doi.org/10.1007/s00180-017-0781-8

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  • DOI: https://doi.org/10.1007/s00180-017-0781-8

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