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Information loss from censoring in rank-based procedures. (English) Zbl 1098.62005

Summary: 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 survival data. The censoring inherently causes loss of information and, following D. V. Lindley’s suggestion [On a measure of the information provided by an experiment. Ann. Math. Stat. 27, 986–1005 (1956; Zbl 0073.14103)], 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.
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 are commonly considered in survival data analysis rather than direct measurements. Evaluation of the indices is also provided for a variety of examples.

MSC:

62B10 Statistical aspects of information-theoretic topics
62N01 Censored data models

Citations:

Zbl 0073.14103
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References:

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