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

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  • Bianca Teodorescu
  • Ingrid Van Keilegom

Abstract

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, X2, …, Xp) and β(z)=(β0(z), …, βp(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.

Suggested Citation

  • Bianca Teodorescu & Ingrid Van Keilegom, 2010. "A goodness-of-fit test for generalised conditional linear models under left truncation and right censoring," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 547-566.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:547-566
    DOI: 10.1080/10485250903302788
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    Cited by:

    1. Marco Munda & Catherine Legrand & Luc Duchateau & Paul Janssen, 2016. "Testing for decreasing heterogeneity in a new time-varying frailty model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 591-606, December.
    2. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    3. Legrand, Catherine & Munda, Marco & Janssen, P. & Duchateau, L., 2012. "A general class of time-varying coefficients models for right censored data," LIDAM Discussion Papers ISBA 2012041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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