Two-sample location–scale estimation from semiparametric random censorship models

When two survival functions belong to a location–scale family of distributions, and the available two-sample data are each right censored, the location and scale parameters can be estimated using a minimum distance criterion combined with Kaplan–Meier quantiles. In this paper, it is shown that using the estimated quantiles from a semiparametric random censorship framework produces improved parameter estimates. The semiparametric framework was originally proposed for the one-sample case (Dikta, 1998), and uses a model for the conditional probability that an observation is uncensored given the observed minimum. The extension to the two-sample setting assumes the availability of good fitting models for the group-specific conditional probabilities. When the models are correctly specified for each group, the new location and scale estimators are shown to be asymptotically as or more efficient than the estimators obtained using the Kaplan–Meier based quantiles. Individual and joint confidence intervals for the parameters are developed. Simulation studies show that the proposed method produces confidence intervals that have correct empirical coverage and that are more informative. The proposed method is illustrated using two real data sets.