Partial Logistic Artificial Neural Network for Competing Risks Regularized With Automatic Relevance Determination

Abstract

Time-to-event analysis is important in a wide range of applications from clinical prognosis to risk modeling for credit scoring and insurance. In risk modeling, it is sometimes required to make a simultaneous assessment of the hazard arising from two or more mutually exclusive factors. This paper applies to an existing neural network model for competing risks (PLANNCR), a Bayesian regularization with the standard approximation of the evidence to implement automatic relevance determination (PLANNCR-ARD). The theoretical framework for the model is described and its application is illustrated with reference to local and distal recurrence of breast cancer, using the data set of Veronesi (1995).

Hybrid intelligent systems in survival prediction of breast cancer

“…The work of [12] further extended Biganzoli's initial study by applying Automatic Relevance Determination in the previous neural network model.…”

Model Selection with PLANN-CR-ARD

“…In Fig. 2 is shown two different numerical results of the marginalized and the nonmarginalized outputs [2][3] [4] of the PLANN-CR-ARD compared to the NelsonAalen non-parametric estimates [11] with 95% confidence intervals [12]. Each numerical result is obtained for different initialization points of the network parameters, which are used by the optimization algorithms of the PLANN-CR-ARD.…”

“…In [2][3] is presented a Partial Logistic Artificial Neural Network (PLANN) which includes regularization of the network parameters within the Bayesian framework with Automatic Relevance Determination (ARD), initially developed for single risk cases [2] [3], which was then extended for the analysis of Competing Risks (PLANN-CR-ARD) in [4] [5]. In this paper is presented the model selection of the PLANN-CR-ARD model in the context of a novel compensation mechanism and the convergence properties of the same model.…”

Patient stratification with competing risks by multivariate Fisher distance

“…This was carried out with a Partial Logistic Artificial Neural Network for Competing Risks (PLANNCR) which is similar in structure to a multi-layer perceptron with four output nodes and softmax activation. This is a generic framework model introduced to model grouped survival times with a single or multiple failure risks [4], [5], [6]: hidden nodes have standard non-linear activations and time is an additional covariate whose value is discretised from 1 to 90 days.…”

“…As regards modifications to the CoRe and KM algorithms, we need to include the effect of the Fisher distance at the stage where unit activation is computed. In particular, at some point both algorithms compute the Euclidean distance between the current sample x and the unit centroid tru: such distance calculation is now computed by means of the Fisher metrics in (6). As regards learning, both algorithms update the prototype m, in the direction given by the gradient ax Given that eex writes as in (9), we can solve (11) using the product rule, yielding 81og(P(PI JD , PlcRlx)) = -(Bx+!3o-p,fZ:;-l B.…”