Artif Intell Med - Training artificial neural networks directly on the concordance index for censored data using genetic algorithms.

Tópicos

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Resumo

JECTIVE: The concordance index (c-index) is the standard way of evaluating the performance of prognostic models in the presence of censored data. Constructing prognostic models using artificial neural networks (ANNs) is commonly done by training on error functions which are modified versions of the c-index. Our objective was to demonstrate the capability of training directly on the c-index and to evaluate our approach compared to the Cox proportional hazards model.METHOD: We constructed a prognostic model using an ensemble of ANNs which were trained using a genetic algorithm. The individual networks were trained on a non-linear artificial data set divided into a training and test set both of size 2000, where 50% of the data was censored. The ANNs were also trained on a data set consisting of 4042 patients treated for breast cancer spread over five different medical studies, 2/3 used for training and 1/3 used as a test set. A Cox model was also constructed on the same data in both cases. The two models' c-indices on the test sets were then compared. The ranking performance of the models is additionally presented visually using modified scatter plots.RESULTS: Cross validation on the cancer training set did not indicate any non-linear effects between the covariates. An ensemble of 30 ANNs with one hidden neuron was therefore used. The ANN model had almost the same c-index score as the Cox model (c-index=0.70 and 0.71, respectively) on the cancer test set. Both models identified similarly sized low risk groups with at most 10% false positives, 49 for the ANN model and 60 for the Cox model, but repeated bootstrap runs indicate that the difference was not significant. A significant difference could however be seen when applied on the non-linear synthetic data set. In that case the ANN ensemble managed to achieve a c-index score of 0.90 whereas the Cox model failed to distinguish itself from the random case (c-index=0.49).CONCLUSIONS: We have found empirical evidence that ensembles of ANN models can be optimized directly on the c-index. Comparison with a Cox model indicates that near identical performance is achieved on a real cancer data set while on a non-linear data set the ANN model is clearly superior.

Resumo Limpo

jectiv concord index cindex standard way evalu perform prognost model presenc censor data construct prognost model use artifici neural network ann common done train error function modifi version cindex object demonstr capabl train direct cindex evalu approach compar cox proport hazard modelmethod construct prognost model use ensembl ann train use genet algorithm individu network train nonlinear artifici data set divid train test set size data censor ann also train data set consist patient treat breast cancer spread five differ medic studi use train use test set cox model also construct data case two model cindic test set compar rank perform model addit present visual use modifi scatter plotsresult cross valid cancer train set indic nonlinear effect covari ensembl ann one hidden neuron therefor use ann model almost cindex score cox model cindex respect cancer test set model identifi similar size low risk group fals posit ann model cox model repeat bootstrap run indic differ signific signific differ howev seen appli nonlinear synthet data set case ann ensembl manag achiev cindex score wherea cox model fail distinguish random case cindexconclus found empir evid ensembl ann model can optim direct cindex comparison cox model indic near ident perform achiev real cancer data set nonlinear data set ann model clear superior

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