title: Change point testing in logistic regression models with interaction term.
abstract: A threshold effect takes place in situations where the relationship between an outcome variable and a predictor variable changes as the predictor value crosses a certain threshold/change point. Threshold effects are often plausible in a complex biological system, especially in defining immune responses that are protective against infections such as HIV-1, which motivates the current work. We study two hypothesis testing problems in change point models. We first compare three different approaches to obtaining a p-value for the maximum of scores test in a logistic regression model with change point variable as a main effect. Next, we study the testing problem in a logistic regression model with the change point variable both as a main effect and as part of an interaction term. We propose a test based on the maximum of likelihood ratios test statistic and obtain its reference distribution through a Monte Carlo method. We also propose a maximum of weighted scores test that can be more powerful than the maximum of likelihood ratios test when we know the direction of the interaction effect. In simulation studies, we show that the proposed tests have a correct type I error and higher power than several existing methods. We illustrate the application of change point model-based testing methods in a recent study of immune responses that are associated with the risk of mother to child transmission of HIV-1.
authors.affiliation: Vaccine and Infectious Disease Division and Public Health Sciences Division, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N, Seattle, WA 98006, U.S.A.
authors.forename: Youyi
authors.initials: Y
authors.lastname: Fong
authors.forename: Chongzhi
authors.initials: C
authors.lastname: Di
authors.forename: Sallie
authors.initials: S
authors.lastname: Permar
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D015987:Effect Modifier, Epidemiologic; D015658:HIV Infections / Q000635:transmission; D015497:HIV-1 / Q000276:immunology; D006801:Humans; D018445:Infectious Disease Transmission, Vertical / Q000517:prevention & control; D016013:Likelihood Functions; D016015:Logistic Models; D009010:Monte Carlo Method
keywords: change point testing; effect modification; maximum of likelihood ratios; maximum of scores; mother to child transmission of HIV-1