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.


62G10 Nonparametric hypothesis testing
62P10 Applications of statistics to biology and medical sciences; meta analysis
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