Abstract

this paper we investigated whether neural nets are worth to be considered as an alternative to logistic models in settings relevant for biomedical research. The first drawback of neural nets is that they give us no direct information on the value of a single covariate for the prediction. The examples in section 8 illustrate that there are no simple strategies to interpret the weights in this sense. It remains the question, whether even in those applications which focus on the estimation of the regression function, it is justified to neglect the possible gain in scientific knowledge available from the identification of influential factors. If we restrict ourselves to estimation of the regression function many biomedical applications involve less than 400 observations and/or more than five covariates. Larger samples are the exception, but the investigations in Section 10 reveal that neural networks need large samples to take advantage of their flexibility. Even if we have large samples, neural nets will be superior to the considered model selection procedures only if the true regression function cannot be approximated by a parsimonious member of the class (8.2). Hence it remains the question about the need of more complex regression functions in a particular biomedical application. In our opinion for most applications such complex functions are not very plausible, because the covariates represent meaningful biological factors. It should be emphasized that the successful use of neural networks appears mainly in fields like pattern recognition, where covariates like the grey scale of a pixel are more or less meaningless with respect to their single values and we can expect results only from combining the values of many pixels. As a final point we should mention that neural ...

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