Neural Computing and Applications

, Volume 31, Issue 3, pp 719–736 | Cite as

Generalized additive neural network with flexible parametric link function: model estimation using simulated and real clinical data

  • Carlos Brás-GeraldesEmail author
  • Ana Papoila
  • Patricia Xufre
Original Article


Artificial neural networks have been proposed in medical research as an alternative to some regression models such as the generalized linear models, being the multilayer perceptron (MLP) the most used architecture. However, inspired in the generalized additive models (GAM), recent studies proposed the more transparent generalized additive neural network (GANN) architecture. In fact, while a MLP may be seen as a black box in which the effect of a variable on the outcome is not clear, a GANN has the advantage of being able to study objectively, through a graphical approach, the effect of an input variable on a certain outcome of interest [9]. In this study, the GANN’s architecture was updated, considering some features already available in the GAM, namely the use of a flexible parametric link function based on the Aranda-Ordaz transformations family for a binary response. Also, the interpretability was improved by obtaining the partial functions with the corresponding confidence intervals through the bootstrap method. The performance of the proposed model was evaluated with simulated data and further applied to a real clinical dataset.


Generalized additive neural network Flexible link function Mortality prediction Aranda-Ordaz transformations family 



Research was partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal—FCT under the project PEst-OE/MAT/UI0006/2014.

Compliance with ethical standards

Conflict of interest

The authors certify that there is no actual or potential conflict of interest in relation to this article.


  1. 1.
    Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csaki F (eds) Second international symposium on information theory. Akadémiai Kiado, Budapest, pp 267–281Google Scholar
  2. 2.
    Amaral Turkman MA, Silva G (2000) Modelos Lineares Generalizados–da Teoria á Prática. Edições SPE, LisbonGoogle Scholar
  3. 3.
    Aranda-Ordaz FJ (1981) On two families of transformations to additivity for binary response data. Biometrika 68(2):357–363MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Baum EB, Haussler D (1989) What size net gives valid generalization? Neural Comput 1(1):151–160CrossRefGoogle Scholar
  5. 5.
    Bishop C (1995) Neural networks for pattern recognition. Clarendon Press, OxfordzbMATHGoogle Scholar
  6. 6.
    Bras-Geraldes C, Papoila A, Xufre P, Diamantino F (2013) Generalized additive neural networks for mortality prediction using automated and genetic algorithms. In: IEEE 2nd international conference on serious games and applications for health, SeGAH 2013, Vilamoura, pp 1–8. IEEEGoogle Scholar
  7. 7.
    Cadarso-Suárez C, Roca-Pardiñas J, Figueiras A, González-Manteiga W (2005) Non-parametric estimation of the odds ratios for continuous exposures using generalized additive models with an unknown link function. Stat Med 24(8):1169–1184MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst 2:303–314MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    de Waal DA, du Toit J (2007) Generalized additive models from a neural network perspective. In: Proceedings of the 7th IEEE international conference on data mining, ICDM 2007, Omaha, NE, pp 265–270. IEEEGoogle Scholar
  10. 10.
    de Waal DA, du Toit JV (2011) Automation of generalized additive neural networks for predictive data mining. Appl Artif Intell 25(5):380–425CrossRefGoogle Scholar
  11. 11.
    de Waal DA, du Toit JV, de la Rey T (2009) A flexible generalized link function for credit scoring. In: Credit Scoring and Credit Control XI. University of Edinburgh Management School, Scotland (2009)Google Scholar
  12. 12.
    Dicker RC, Coronado F, Koo D, Parrish RG (2006) Principles of epidemiology in public health practice; an introduction to applied epidemiology and biostatistics. U.S. Department of Health and Human Services, Centers for Disease Control and Prevention (CDC)Google Scholar
  13. 13.
    Dobson A (2010) An introduction to generalized linear models. Chapman & Hall/CRC texts in statistical science, 2nd edn. Taylor & Francis, LondonGoogle Scholar
  14. 14.
    du Toit JV (2006) Automated construction of generalized additive neural networks for predictive data mining. PhD thesis, School for Computer, Statistical and Mathematical Sciences, North-West University, South AfricaGoogle Scholar
  15. 15.
    du Toit JV, de Waal DA (2010) Spam detection using generalized additive neural networks. In Southern Africa telecommunication networks and applications conference (SATNAC)Google Scholar
  16. 16.
    Dybowski R, Roberts SJ (2001) Confidence intervals and prediction intervals for feed-forward neural networks. In: Clinical applications of artificial neural networks. Cambridge University Press, Cambridge, pp 298–326Google Scholar
  17. 17.
    Efron B, Tibshirani R (1994) An introduction to the bootstrap. Chapman & Hall/CRC monographs on statistics & applied probability. Taylor & Francis, London (1994)Google Scholar
  18. 18.
    Gaxiola F, Melin P, Valdez F, Castillo O (2015) Generalized type-2 fuzzy weight adjustment for backpropagation neural networks in time series prediction. Inf Sci 325:159–174MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Gaxiola F, Melin P, Valdez F, Castro JR, Castillo O (2016) Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO. Appl Soft Comput 38:860–871CrossRefGoogle Scholar
  20. 20.
    Gosling J, Joy B, Steele GL Jr, Bracha G, Buckley A (2013) The Java language specification, Java SE 7 edition, 1st edn. Addison-Wesley Professional, ReadingGoogle Scholar
  21. 21.
    Hastie T, Tibshirani R (1990) Generalized additive models. CRC monographs on statistics & applied probability. Chapman & Hall/CRC, LondonGoogle Scholar
  22. 22.
    Heskes T (1997) Practical confidence and prediction intervals. In: Jordan MI, Petsche T (eds) Advances in neural information processing systems, vol 9. MIT Press, Cambridge, pp 176–182Google Scholar
  23. 23.
    Papoila AL (2006) Modelos aditivos generalizados em análise de sobrevivência. Ph.D. thesis, Faculdade de Ciências, Universidade de Lisboa, LisbonGoogle Scholar
  24. 24.
    Papoila AL, Rocha C (2011) Modelling current status data using generalized additive models with flexible links: the additive gamma-logit model. Int J Appl Math Stat 24(SI–11A):2–19MathSciNetGoogle Scholar
  25. 25.
    Papoila AL, Rocha C, Geraldes C, Xufre P (2013) Generalized linear models, generalized additive models and neural networks: comparative study in medical applications. In: Advances in regression, survival analysis, extreme values, Markov processes and other statistical applications, pp. 317–324 (2013)Google Scholar
  26. 26.
    Potts WJE (1999) Generalized additive neural networks. In: Proceedings of the fifth ACM SIGKDD international conference on Knowledge Discovery and Data mining, KDD ’99. ACM, New York, pp 194–200)Google Scholar
  27. 27.
    R Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  28. 28.
    Riedmiller M, Braun H (1993) A direct adaptive method for faster backpropagation learning: the RPROP algorithm. In: IEEE international conference on neural networks, pp 586–591Google Scholar
  29. 29.
    Sarle WS (1994) Neural networks and statistical models. In: Proceedings of the nineteenth annual SAS users group international conference. SAS Institute, Cary, pp 1538–1550Google Scholar
  30. 30.
    Tibshirani R, Hastie T (1987) Local likelihood estimation. J Am Stat Assoc 82:559–567MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Tu JV (1996) Advantages and disadvantages of using artificial neural networks versus logistic regression for predicting medical outcomes. J Clin Epidemiol 49(11):1225–1231CrossRefGoogle Scholar
  32. 32.
    Wood S (2006) Generalized additive models: an introduction with R. Chapman & Hall/CRC texts in statistical science. Taylor & Francis, LondonCrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.NOVA Medical SchoolLisbonPortugal
  2. 2.Centro de Estatistica e AplicaçõesUniversidade de LisboaLisbonPortugal
  3. 3.NOVA School of Business and EconomicsLisbonPortugal

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