title: Transition models for change-point estimation in logistic regression.
abstract: Although a wide variety of change-point models are available for continuous outcomes, few models are available for dichotomous outcomes. This paper introduces transition methods for logistic regression models in which the dose-response relationship follows two different straight lines, which may intersect or may present a jump at an unknown change-point. In these models, the logit includes a differentiable transition function that provides parametric control of the sharpness of the transition at the change-point, allowing for abrupt changes or more gradual transitions between the two different linear trends, as well as for estimation of the location of the change-point. Linear-linear logistic models are particular cases of the proposed transition models. We present a modified iteratively reweighted least squares algorithm to estimate model parameters, and we provide inference procedures including a test for the existence of the change-point. These transition models are explored in a simulation study, and they are used to evaluate the existence of a change-point in the association between plasma glucose after an oral glucose tolerance test and mortality using data from the Mortality Follow-up of the Second National Health and Nutrition Examination Survey.
authors.affiliation: Department of Epidemiology and Biostatistics, National School of Public Health, Instituto de Salud Carlos III, Madrid, Spain. rpastor@isciii.es
authors.forename: Roberto
authors.initials: R
authors.lastname: Pastor-Barriuso
authors.forename: Eliseo
authors.initials: E
authors.lastname: Guallar
authors.forename: Josef
authors.initials: J
authors.lastname: Coresh
mesh_terms: D000328:Adult; D000368:Aged; D000465:Algorithms; D003198:Computer Simulation; D003920:Diabetes Mellitus / Q000097:blood / Q000401:mortality; D004305:Dose-Response Relationship, Drug; D005951:Glucose Tolerance Test; D006801:Humans; D016015:Logistic Models; D008875:Middle Aged; D015233:Models, Statistical