| Criteria are developed for measuring information in the randomly right-censored model. Measures which are appropriate include an extension of Shannon's entropy. The measures are seen to satisfy some fundamental properties including (1) information decreases as censoring increases stochastically, (2) the uncensored case is always at least as informative as any censored model, and (3) the information gain is marginally decreasing.;Information is also studied in terms of asymptotic efficiency. We consider the proportional hazards model where the distribution G of the censoring random variable is related to the distribution F of the lifetime variable via (1-G) = (1-F)(beta). Nonparametric estimators of F are developed for the case where (beta) is unknown and the case where (beta) is known. Of interest in their own right, these estimators also enable us to study the robustness of the Kaplan-Meier estimator (KME) in a nonparametric model for which it is not the preferred estimator. Comparisons are based on asymptotic efficiencies and exact mean square errors. We also compare the KME to the empirical survival function thereby providing, in a nonparametric setting, a measure of the loss in efficiency due to censoring.;Measures of information in censored models can also be developed by adapting measures of dependence between the lifetime variable and the observed variable. Some common notions of bivariate dependence enjoy property (1) cited above. An exception occurs when dependence is defined in terms of association. Conditions under which the coefficients of divergence satisfy (1) and (2) are established. |
