title: Model-robust inference for continuous threshold regression models.
abstract: We study threshold regression models that allow the relationship between the outcome and a covariate of interest to change across a threshold value in the covariate. In particular, we focus on continuous threshold models, which experience no jump at the threshold. Continuous threshold regression functions can provide a useful summary of the association between outcome and the covariate of interest, because they offer a balance between flexibility and simplicity. Motivated by collaborative works in studying immune response biomarkers of transmission of infectious diseases, we study estimation of continuous threshold models in this article with particular attention to inference under model misspecification. We derive the limiting distribution of the maximum likelihood estimator, and propose both Wald and test-inversion confidence intervals. We evaluate finite sample performance of our methods, compare them with bootstrap confidence intervals, and provide guidelines for practitioners to choose the most appropriate method in real data analysis. We illustrate the application of our methods with examples from the HIV-1 immune correlates studies.
authors.affiliation: Fred Hutchinson Cancer Research Center, Seattle Washington 98109, U.S.A.
authors.forename: Youyi
authors.initials: Y
authors.lastname: Fong
authors.affiliation: Fred Hutchinson Cancer Research Center, Seattle Washington 98109, U.S.A.
authors.forename: Chongzhi
authors.initials: C
authors.lastname: Di
authors.affiliation: Fred Hutchinson Cancer Research Center, Seattle Washington 98109, U.S.A.
authors.forename: Ying
authors.initials: Y
authors.lastname: Huang
authors.affiliation: Fred Hutchinson Cancer Research Center, Seattle Washington 98109, U.S.A.
authors.forename: Peter B
authors.initials: PB
authors.lastname: Gilbert
mesh_terms: D015497:HIV-1; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical
keywords: Mother-to-child transmission of HIV-1; Profile likelihood ratio under model misspecification; RV144 immune correlates studies; Regression kink