Inference in a Survival Cure Model with Mismeasured Covariates using a SIMEX Approach

Abstract

In many situations in survival analysis, it may happen that a fraction of individuals will never experience the event of interest: they are considered to be cured. The promotion time cure model is one of the survival models taking this feature into account. We consider the case where one or more explanatory variables in the model are subject to measurement error. This error should be taken into account in the estimation of the model, to avoid biased estimators. A general approach that exists in the literature is the SIMEX algorithm, a method based on simulations which allows one to estimate the e_ect of mea- surement error on the bias of the estimators and to reduce this bias. We extend the SIMEX approach to the promotion time cure model. We explain how the algorithm works, and we show that the proposed estimator is consistent and asymptotically normally distributed. We also show via simulations that the sug- gested method performs well in _nite samples. Finally, we analyze a database in cardiology: among the explanatory variables of interest is the ejection fraction, which is known to be measured with error. There are supplementary materials online for this paper

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