A goodness-of-fit test for generalised conditional linear models under left truncation and right censoring

• Published in: Journal of nonparametric statistics Vol. 22; no. 5; pp. 547 - 566
• Main Authors: Teodorescu, Bianca, Van Keilegom, Ingrid
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.07.2010; Taylor & Francis Ltd
• Subjects: additive hazards model; Approximation; bootstrap; Bootstrap method; goodness-of-fit; least squares estimator; Mathematical models; Nonparametric statistics; proportional hazards model; Regression; Regression analysis; semiparametric regression; survival analysis; time-varying coefficients
• ISSN: 1048-5252; 1029-0311
• DOI: 10.1080/10485250903302788

Consider a semiparametric time-varying coefficients regression model of the following form: φ(S(z|X))=β(z) t X, where φ is a known link function, S(·|X) is the survival function of a response Y; given a covariate X, X=(1, X, X 2 , ..., X p ) and β(z)=(β 0 (z), ..., β p (z)) t is the unknown vector of regression coefficients. This model reduces for special choices of φ to, e.g. the additive hazards model or the Cox proportional hazards model with time-dependent coefficients. The response is subject to left truncation and right censoring. An omnibus goodness-of-fit test is developed to test whether the model fits the data. A bootstrap version, to approximate the critical values of the test, is proposed and proved to work from a practical point of view as well. The test is also applied to real data.