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Ann Thorac Surg 1997;63:1529-1530
© 1997 The Society of Thoracic Surgeons
United States Air Force Academy, USAF Academy, Colorado
Neural network models are becoming increasingly common in medical research as evidenced by the recent surge of articles in the medical literature discussing or using neural network models [1–3]. The attraction of neural networks seems to stem from the potential for improved predictive performance, the loose biological relationship upon which neural network models were originally founded, and the impressive predictive performance reported in many articles. Lippmann and Shahian's article [4] introduces the use of neural network models in coronary artery bypass grafting (CABG) mortality prediction. They do an excellent job addressing concerns and potential limitations of neural network models as well as comparing neural network models with existing methods.
The history of neural network models began with studies that attempted to model the brain. The idea was to have many simple computational units acting in a highly interconnected manner, similar to the brain. However, neural network models presently used in prediction problems have little biological equivalence to the brain. The neural network models typically used for prediction consist of layers of simple computational units. These simple units are often called nodes or neurons (again hinting at a biological motivation). The nodes in a layer receive as input a simple weighted sum of outputs from nodes in previous layers. Each node applies a functional transformation to this weighted input and outputs this result to the nodes in the subsequent layer(s). The weights (also known as synaptic weights) are adjusted through a training procedure (the most common procedure is known as backpropagation) to achieve maximum predictive performance. Once training stops, the weights remain fixed and prediction is accomplished by passing input data through the completed model. The output is then used as the predicted value (for a more comprehensive discussion of neural networks see Lippmann [5]).
See also 1531 and 1635.
The first layer of a neural network model is the input layer and the last layer is the output layer. The layers in between are known as hidden layers. It is the hidden layers that give neural network models their ability to model complex functional relationships. With a sufficient number of hidden units, a neural network can approximate any continuous function [6]. Without the hidden layers, a neural network can be thought of as a traditional regression model. Therefore, the difference between the traditional regression models and neural networks is, on a simplified level, the hidden units. In a traditional regression model, there is an implied additive, or linear, structure between predictor variables. The inclusion of hidden units in a neural network model remove this linearity restriction, enabling the modeling of more complex relationships. In practice, the hidden layers are using the data to find nonlinearities, interactions, and nonlinear interactions in the predictor set. In other words, the hidden units of the neural network models enable the effects of the predictors on the outcome to be nonlinear and also to depend on the levels of the other predictors. It is possible to build regression models that include interaction and nonlinear terms; however, unless there is some prior knowledge these relationships exist, this process is a time-consuming trial and error routine. With a large number of predictor variables, it is impractical to manually search for these relationships. For example, with just 13 predictor variables, 78 different regression models would have to be constructed just to compare all single two-way interactions. Additional regression models are necessary to investigate models with more than one interaction term, nonlinear terms, or interactions of nonlinear terms. The neural network models automate this process to some extent by using the data to find these relationships. From a practical standpoint, a moderate number of predictors makes it impractical to build regression models with the equivalent complexity of neural network models.
Other modeling methods exist that are able to achieve the modeling complexity of neural network models (such as projection pursuit regression and multivariate adaptive regression splines [7, 8]), but their use and discussion is absent from the medical literature. This is in part due to the readily available software for neural network models, the relatively simple conceptual presentation of the model, which includes in some part its crude biological motivation, and the abundance of medical literature reporting success in applying neural network models in prediction problems. It is this last point where Lippmann and Shahian's article makes an important contribution. Although neural network models have the potential to improve predictive performance, it is not a guarantee they will. Lippmann and Shahian illustrate this point for operative mortality prediction in CABG patients by comparing a neural network model and logistic regression model. They establish this result through a careful and thorough process of model building and model comparison. Their results are important because unrealistic expectations of improved predictive performance are established when the only articles published demonstrate a superior performance of neural network models over more conventional models.
A final point to consider is the following: Why is it that neural network models do not improve the predictive performance as compared with the more conventional models for this application? Remember, a neural network model will improve predictive performance over a logistic regression model only if significant interactions, nonlinearities, or nonlinear interactions exist. The lack of superior performance from the neural network model may indicate these relationships do not exist for this problem. Conversely, these relationships could exist, but the data do not contain sufficient information for the neural network model to uncover them. Examining the predictors used to model CABG operative mortality reveals many of the predictors are binary, they take on only two values. With only two values, the neural network model will not be able to learn the effects of the predictor on the outcome outside of these two values. The neural network has been restricted to a simpler model than is possible if the predictor variables take on a range of values. The implication of Lippmann and Shahian's results is that improved prediction of CABG operative mortality is not possible for the current set of risk factors. If improved prediction is possible, it will come from predictor variables that contain more information in use with models that can exploit this information. This means risk factors that are not coded as binary variables or the inclusion of other predictors of operative mortality besides risk variables; for example, variables that measure the processes and structures of care such as total operating room time or surgeon experience. This does not imply improved predictive performance is possible, but only that the potential for increase exists in the appropriate combination of predictors and models.
Footnotes
Address reprint requests to Dr Warner, HQ USAFA/DFMS, 2354 Fairchild Dr, Suite 6D2A, USAF Academy, CO 80840.
References
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