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Weighted Kaplan-Meier statistics: A class of distance tests for censored survival data. (English) Zbl 0715.62087

Summary: A class of statistics based on the integrated weighted difference in Kaplan-Meier estimators is introduced for the two-sample censored data problem. With positive weight functions these statistics are intuitive for and sensitive against the alternative of stochastic ordering. The standard weighted log-rank statistics are not always sensitive against this alternative, particularly if the hazard functions cross.

Qualitative comparisons are made between the weighted log-rank statistics and these weighted Kaplan-Meier (WKM) statistics. A statement of null asymptotic distribution theory is given and the choice of weight functions is discussed in some detail. Results from small-sample simulation studies indicate that these statistics compare favorably with the log-rank procedure even under the proportional hazards alternative, and may perform better than it under the crossing hazards alternative.

62G10Nonparametric hypothesis testing
62P10Applications of statistics to biology and medical sciences