Information loss from censoring in rank-based procedures

Although the problems of measuring information based on entropy are well explored, a few studies have applied to the loss of information from censoring in the survival data. The censoring inherently causes loss of information and, following Lindley's suggestion (1956), the degree of loss in information has been measured by relative change in entropy between experiments with censoring and without censoring, that is, with complete data. In this paper, we propose new indices of quantifying information loss through Fisher information and relative efficiency. It is shown that these indices are asymptotically equivalent to each other, in particular to the entropy-based measure. All these indices will then be used to measure the information loss in ranks or rank-based statistics which is commonly considered in the survival data analysis rather than direct measurements. Evaluation of the indices is also provided for a variety of examples.