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Abstract:
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Polynomial splines provide a flexible alternative to parametric regression modeling and are frequently used when the underlying data generating mechanism is unknown or when a parametric model is not appropriate. When modeling failure time data, the use of polynomial splines with the Cox proportional hazard model is a standard practice in a variety of fields including epidemiology. The use of splines with the Cox model is available in many different statistical packages where the practitioner seldom considers the underlying assumptions of the model when using polynomial splines. Specifically, when there is no probability, or very small probability, of observing a failure at background with non-zero probability at all other levels, the use of polynomial splines may result in erroneous, but statistically significant inference, due to an ill-defined likelihood. The result of this is the prediction of a hormetic or 'J' shaped exposure-response relationship when no such relationship exists in truth. We show this using a dataset as well as simulations and show how different regularization techniques can be used to provide valid inference.
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