Controlling for a confounder monotonically related to exposure by means of isotonic quantile regression

We present a new approach to evaluating the effect of a continuous exposure factor when that factor increases with a covariate (for example, age) which is regarded as a potential confounder. The basic idea is to estimate, as functions of the covariate, some selected quantiles of the exposure distribution, under the assumption that the dependence of each quantile on the covariate is monotonic. The resulting estimates are then used to divide the data into different exposure categories. This method of categorizing the data implies that the covariate distribution will be almost the same in each exposure group. We illustrate the approach with a study of blood pressure and cardiovascular mortality.