Robustness of estimation methods in a survival cure model with mismeasured covariates

In medical applications, time-to-event data is frequently encountered. While classical survival methods are well known and broadly used to analyze such data, they do not take into account two phenomena which appear quite often in practice: the presence of individuals who will never experience the event of interest (they are cured from this event) and of measurement error in the continuous covariates. Two approaches exist in the literature to estimate a model, taking these features into account. However, they require information about the distribution of the measurement error which is rarely fully known in practice. A theoretical study of bias motivates the need to take the measurement error into account. The conclusions of an extensive simulation study investigating the robustness of both correction approaches with respect to their assumptions then provide some practical recommendations for similar situations. Finally, the time until recurrence after surgery for rectal cancer patients is analyzed, taking into account the results from the simulations. Both correction methods were implemented in the R package miCoPTCM.