A neural network model for survival data.

Neural networks have received considerable attention recently, mostly by non-statisticians. They are considered by many to be very promising tools for classification and prediction. In this paper we present an approach to modelling censored survival data using the input-output relationship associated with a simple feed-forward neural network as the basis for a non-linear proportional hazards model. This approach can be extended to other models used with censored survival data. The proportional hazards neural network parameters are estimated using the method of maximum likelihood. These maximum likelihood based models can be compared, using readily available techniques such as the likelihood ratio test and the Akaike criterion. The neural network models are illustrated using data on the survival of men with prostatic carcinoma. A method of interpreting the neural network predictions based on the factorial contrasts is presented.

[1]  Elie Bienenstock,et al.  Neural Networks and the Bias/Variance Dilemma , 1992, Neural Computation.

[2]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[3]  M. E. Johnson,et al.  Generalized simulated annealing for function optimization , 1986 .

[4]  Sidney Addelman,et al.  trans-Dimethanolbis(1,1,1-trifluoro-5,5-dimethylhexane-2,4-dionato)zinc(II) , 2008, Acta crystallographica. Section E, Structure reports online.

[5]  J N Weinstein,et al.  Neural computing in cancer drug development: predicting mechanism of action. , 1992, Science.

[6]  N. H. Mann,et al.  Artificial intelligence in the diagnosis of low back pain. , 1991, The Orthopedic clinics of North America.

[7]  J. Hanley,et al.  The meaning and use of the area under a receiver operating characteristic (ROC) curve. , 1982, Radiology.

[8]  P Sherman,et al.  Classification of ultrasonic image texture by statistical discriminant analysis of neutral networks. , 1991, Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society.

[9]  F. Harrell,et al.  Regression modelling strategies for improved prognostic prediction. , 1984, Statistics in medicine.

[10]  I. James,et al.  Linear regression with censored data , 1979 .

[11]  Brian D. Ripley,et al.  Statistical aspects of neural networks , 1993 .

[12]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[13]  M. Ebell.  Artificial neural networks for predicting failure to survive following in-hospital cardiopulmonary resuscitation. , 1993, The Journal of family practice.

[14]  Bradley Efron,et al.  Comparing Non-Nested Linear Models , 1984 .

[15]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[16]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[17]  J D Kalbfleisch,et al.  Hazard rate models with covariates. , 1979, Biometrics.

[18]  J. Tu,et al.  Use of a neural network as a predictive instrument for length of stay in the intensive care unit following cardiac surgery. , 1993, Computers and biomedical research, an international journal.

[19]  M. Karplus,et al.  Protein secondary structure prediction with a neural network. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Philip D. Wasserman,et al.  Neural computing - theory and practice , 1989 .

[21]  D. Cox.  Regression Models and Life-Tables , 1972 .

[22]  B. Efron.  The jackknife, the bootstrap, and other resampling plans , 1987 .