Confidence Intervals on Regression Models with Censored Data

Stute (1993, Consistent estimation under random censorship when covariables are present. Journal of Multivariate Analysis 45, 89–103) proposed a new method to estimate regression models with a censored response variable using least squares and showed the consistency and asymptotic normality for his estimator. This article proposes a new bootstrap-based methodology that improves the performance of the asymptotic interval estimation for the small sample size case. Therefore, we compare the behavior of Stute's asymptotic confidence interval with that of several confidence intervals that are based on resampling bootstrap techniques. In order to build these confidence intervals, we propose a new bootstrap resampling method that has been adapted for the case of censored regression models. We use simulations to study the improvement the performance of the proposed bootstrap-based confidence intervals show when compared to the asymptotic proposal. Simulation results indicate that, for the new proposals, coverage percentages are closer to the nominal values and, in addition, intervals are narrower.