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 . 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.
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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 267–281
Amaral Turkman MA, Silva G (2000) Modelos Lineares Generalizados–da Teoria á Prática. Edições SPE, Lisbon
Aranda-Ordaz FJ (1981) On two families of transformations to additivity for binary response data. Biometrika 68(2):357–363
Baum EB, Haussler D (1989) What size net gives valid generalization? Neural Comput 1(1):151–160
Bishop C (1995) Neural networks for pattern recognition. Clarendon Press, Oxford
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. IEEE
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):1169–1184
Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst 2:303–314
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. IEEE
de Waal DA, du Toit JV (2011) Automation of generalized additive neural networks for predictive data mining. Appl Artif Intell 25(5):380–425
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)
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)
Dobson A (2010) An introduction to generalized linear models. Chapman & Hall/CRC texts in statistical science, 2nd edn. Taylor & Francis, London
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 Africa
du Toit JV, de Waal DA (2010) Spam detection using generalized additive neural networks. In Southern Africa telecommunication networks and applications conference (SATNAC)
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 298–326
Efron B, Tibshirani R (1994) An introduction to the bootstrap. Chapman & Hall/CRC monographs on statistics & applied probability. Taylor & Francis, London (1994)
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 325:159–174
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 38:860–871
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, Reading
Hastie T, Tibshirani R (1990) Generalized additive models. CRC monographs on statistics & applied probability. Chapman & Hall/CRC, London
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 176–182
Papoila AL (2006) Modelos aditivos generalizados em análise de sobrevivência. Ph.D. thesis, Faculdade de Ciências, Universidade de Lisboa, Lisbon
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):2–19
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)
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)
R Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna
Riedmiller M, Braun H (1993) A direct adaptive method for faster backpropagation learning: the RPROP algorithm. In: IEEE international conference on neural networks, pp 586–591
Sarle WS (1994) Neural networks and statistical models. In: Proceedings of the nineteenth annual SAS users group international conference. SAS Institute, Cary, pp 1538–1550
Tibshirani R, Hastie T (1987) Local likelihood estimation. J Am Stat Assoc 82:559–567
Tu JV (1996) Advantages and disadvantages of using artificial neural networks versus logistic regression for predicting medical outcomes. J Clin Epidemiol 49(11):1225–1231
Wood S (2006) Generalized additive models: an introduction with R. Chapman & Hall/CRC texts in statistical science. Taylor & Francis, London
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.
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Brás-Geraldes, C., Papoila, A. & Xufre, P. Generalized additive neural network with flexible parametric link function: model estimation using simulated and real clinical data. Neural Comput & Applic 31, 719–736 (2019). https://doi.org/10.1007/s00521-017-3105-6
- Generalized additive neural network
- Flexible link function
- Mortality prediction
- Aranda-Ordaz transformations family