Assessing continuous bivariate effects among different groups through nonparametric regression models: An application to breast cancer detection

  • Authors:

  • Javier Roca-Pardiñas;Carmen Cadarso-Suárez;Pablo G. Tahoces;María J. Lado

  • Affiliations:

  • Department of Statistics and Operations Research, University of Vigo, Spain;Department of Statistics and Operations Research, University of Santiago, Spain;Department of Electronics and Computer Science, University of Santiago, Spain;Department of Computer Science, ESEI, University of Vigo, Spain

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2008

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Abstract

In many applications, the joint effect of two continuous covariates on the target binary response may vary across groups defined by levels of a given factor. A testing procedure that would enable this type of surface-by-factor interactions to be detected has been designed. To accomplish this goal, a logistic generalized additive model (GAM) with bivariate continuous interactions varying across groups defined by levels of a factor is considered. A local scoring algorithm based on local linear kernel smoothers was implemented to estimate the proposed logistic GAM. Bootstrap resampling techniques were used for the purpose of testing for factor-by-surface interactions. Given the high computational cost involved, binning techniques were used to speed up computation in the estimation and testing processes. The adequacy of the bootstrap-based test was assessed by means of a simulation study. If a factor-by-surface interaction is detected in the model, it is then established that the use of the odds-ratio curves is very useful in obtaining a direct interpretation of the fitted model. The benefits of using this methodology when analyzing real data are illustrated by applying the technique to the outputs produced by a computerized system dedicated to the early detection of breast cancer.