kolay gelsin

Makalelerde log-rank testi olarak geçiyor, katmanlı veya katmansız olabilir.

Aşağıdaki açıklama verdiğim tanımı destekliyor.

The Neyman Seminar: 1011 Evans, 4:10-5:00 pm Wednesday, February 5, 2003
Combining Stratified and Unstratified Log-Rank Tests for Matched Pairs Survival Data

David Oakes and Changyong Fong

University of Rochester, Dept. of Biostatistics and Computational Biology

Abstract

We consider the problem of testing for a treatment effect in matched pairs survival data, with one member of each pair receiving active treatment, the other member receiving the control treatment. The stratified log-rank test, which is commonly used in this situation, reduces to a simple counting of the "preferences" (treatment, control, or indeterminate) established by each pair. The unstratified log-rank test is optimal under the proportional hazards model when the two members of a pair are independent, but loses this optimality property under models allowing dependence. Moreover the variance estimate for the log-rank statistic requires adjustment due to the within-pair dependence (Jung, 1999). While the stratified log-rank test and the unstratified log-rank tests are optimal (under proportional hazards models) in the cases of extreme dependence and independence respectively, in intermediate cases, a linear combination of the two statistics may be locally more powerful than either individual statistic. Under Hougaard's positive stable frailty model, which allows proportional hazards both marginally and conditionally, we derive the optimal linear combination and show how this may be estimated from the data. We show that for moderate dependence this combined test statistic is noticeably more powerful than either individual statistic. We examine the robustness of the procedure to the choice of frailty distribution and briefly consider extensions from pairs to blocks of arbitrary size.