Use of two-segmented logistic regression to estimate change-points in epidemiologic studies

In many epidemiologic data, the dose-response relation between a continuous exposure and the risk of disease abruptly changes when the exposure variable reaches an unknown threshold level, the so-called change-point. Although several methods are available for dose-response assessment with dichotomous outcomes, none of them provide inferential procedures to estimate change-points. In this paper, we describe a two-segmented logistic regression model, in which the linear term associated with a continuous exposure in standard logistic regression is replaced by a two-segmented polynomial function with unknown change-point, which is also estimated. A modified, iteratively reweighted least squares algorithm is presented to obtain parameter estimates and confidence intervals, and the performance of this model is explored through simulation. Finally, a two-segmented logistic regression model is applied to a case-control study of the association of alcohol intake with the risk of myocardial infarction and compared with alternative analyses. The ability of two-segmented logistic regression to estimate and provide inferences for the location of change-points and for the magnitude of other parameters of effect will make this model a useful complement to other methods of dose-response analysis in epidemiologic studies.