Estimation of the hazard function in a semiparametric model with covariate measurement error
ESAIM: Probability and Statistics, Tome 13 (2009), pp. 87-114.

We consider a failure hazard function, conditional on a time-independent covariate Z, given by η γ 0 (t)f β 0 (Z). The baseline hazard function η γ 0 and the relative risk f β 0 both belong to parametric families with θ 0 =(β 0 ,γ 0 ) m+p . The covariate Z has an unknown density and is measured with an error through an additive error model U=Z+ε where ε is a random variable, independent from Z, with known density f ε . We observe a n-sample (X i ,D i ,U i ), i = 1, ..., n, where X i is the minimum between the failure time and the censoring time, and D i is the censoring indicator. Using least square criterion and deconvolution methods, we propose a consistent estimator of θ 0 using the observations (X i ,D i ,U i ), i = 1, ..., n. We give an upper bound for its risk which depends on the smoothness properties of f ε and f β (z) as a function of z, and we derive sufficient conditions for the n-consistency. We give detailed examples considering various type of relative risks f β and various types of error density f ε . In particular, in the Cox model and in the excess risk model, the estimator of θ 0 is n-consistent and asymptotically gaussian regardless of the form of f ε .

DOI : 10.1051/ps:2008004
Classification : 62G05, 62F12, 62G99, 62J02
Mots clés : semiparametric estimation, errors-in-variables model, measurement error, nonparametric estimation, excess risk model, Cox model, censoring, survival analysis, density deconvolution, least square criterion
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     title = {Estimation of the hazard function in a semiparametric model with covariate measurement error},
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     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ps:2008004/}
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Martin-Magniette, Marie-Laure; Taupin, Marie-Luce. Estimation of the hazard function in a semiparametric model with covariate measurement error. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 87-114. doi : 10.1051/ps:2008004. http://archive.numdam.org/articles/10.1051/ps:2008004/

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