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Zbl 0715.62087
Pepe, Margaret Sullivan; Fleming, Thomas R.
Weighted Kaplan-Meier statistics: A class of distance tests for censored survival data. (English)
[J] Biometrics 45, No.2, 497-507 (1989). ISSN 0006-341X; ISSN 1541-0420/e

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. \par 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.

MSC 2000:: *62G10 Nonparametric hypothesis testing
62P10 Appl. of statistics to biology

Keywords: random censorship; two-sample problem; Kaplan-Meier estimators; stochastic ordering

Cited in: Zbl 1128.62111 Zbl 1004.62047 Zbl 1209.62106 Zbl 1087.62508 Zbl 1081.62556 Zbl 1009.62036 Zbl 1123.62312 Zbl 1101.62376 Zbl 1059.62583 Zbl 0812.62100

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Zentralblatt MATH Berlin [Germany]