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Generalized time-dependent conditional linear models under left truncation and right censoring

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Abstract

Consider the model \({\phi(S(z|X))}\) = \({\pmb{\beta}(z) {\vec{X}}}\), where \({\phi}\) is a known link function, S(·|X) is the survival function of a response Y given a covariate X, \({\vec{X}}\) = (1, X, X 2 , . . . , X p) and \({\pmb{\beta}(z)}\) is an unknown vector of time-dependent regression coefficients. The response is subject to left truncation and right censoring. Under this model, which reduces for special choices of \({\phi}\) to e.g. Cox proportional hazards model or the additive hazards model with time dependent coefficients, we study the estimation of the vector \({\pmb{\beta}(z)}\) . A least squares approach is proposed and the asymptotic properties of the proposed estimator are established. The estimator is also compared with a competing maximum likelihood based estimator by means of simulations. Finally, the method is applied to a larynx cancer data set.

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Authors and Affiliations

  1. Institute of Statistics, Université catholique de Louvain, Voie du Roman Pays 20, 1348, Louvain-la-Neuve, Belgium

    Bianca Teodorescu & Ingrid Van Keilegom

  2. Departamento de Matemáticas, Facultad de Informática, Universidade da Coruña, Campus de Elviña, 15071, A Coruña, Spain

    Ricardo Cao

Authors
  1. Bianca Teodorescu
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  2. Ingrid Van Keilegom
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  3. Ricardo Cao
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Correspondence to Bianca Teodorescu.

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Teodorescu, B., Van Keilegom, I. & Cao, R. Generalized time-dependent conditional linear models under left truncation and right censoring. Ann Inst Stat Math 62, 465–485 (2010). https://doi.org/10.1007/s10463-008-0187-z

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  • DOI: https://doi.org/10.1007/s10463-008-0187-z

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