Estimation of relative risk functions

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Abstract
The risk associated with different levels of a quantitative factor X is often measured relative to the level corresponding to X = 0. There are situations, however, where there is no natural zero for X, for example where the risk factor is the age of an individual. In this case it is more natural to measure risk relative to an overall average for the study population. To use the whole population in this way also raises the possibility of regarding X as truly continuous, rather than as a grouped variable. This gives rise to the concept of a relative risk function. Methods for estimating such functions are discussed, concentrating for the most part on the discrete case. The extension to higher dimensions permits the investigation of joint effects of several factors, while the problem of controlling for confounding variables can be handled by fitting multiplicative risk models. Relating the latter to the log‐linear model permits the estimation of adjusted relative risk functions. The method is illustrated using data on childhood cancer. The continuous case can in principle be handled in a similar way using density estimation techniques.

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