Survival models with a cure fraction and mismeasured covariates

In traditional time-to-event analysis, all subjects in the population are assumed to be susceptible to the event of interest: every subject has already experienced the event or will experience it in the future. In many situations, however, it may happen that a fraction of individuals will never experience the event: they are considered to be cured. Cure models are survival models taking this feature into account. An additional phenomenon which appears quite often in practice is the fact that some of the covariates are measured with error. This measurement error should in general be taken into account in the estimation of the model, to avoid biased estimators. In the first part of this thesis, we propose a method to deal with survival data with a cure fraction and mismeasured covariates. We adapt and study a general method designed to take the measurement error into account, the SIMEX algorithm, to one general cure model, the semiparametric promotion time cure model. In the second part, we compare the performance of our method with an existing competitor in terms of robustness with respect to their underlying assumptions, which may not be met in practice. Finally, since most of the methods dealing with measurement error assume that the error variance is known, we develop a method to estimate this variance using only a single sample of the mismeasured covariates.