Bootstrap-type confidence intervals for quantiles of the survival distribution

In this paper we outline and illustrate an easy to program method for analytically calculating both parametric and non-parametric bootstrap-type confidence intervals for quantiles of the survival distribution based on right censored data. This new approach allows for the incorporation of covariates within the framework of parametric models. The procedure is based upon the notion of fractional order statistics and is carried forth using a simple beta transformation of the estimated survival function (parametric or non-parametric). It is the only direct method currently available in the sense that all other methods are based on inverting test statistics or employing confidence intervals for other survival quantities. We illustrate that the new method has favourable coverage probabilities for median confidence intervals as compared to six other competing methods.