id: 05134220
dt: j
an: 05134220
au: Gillen, Daniel L.; Emerson, Scott S.
ti: Nontransitivity in a class of weighted logrank statistics under
    nonproportional hazards.
so: Stat. Probab. Lett. 77, No. 2, 123-130 (2007).
py: 2007
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: censored data; clinical trials; logrank statistic; nonproportional hazards;
    transitivity
ci: Zbl 0727.62069; Zbl 0727.62096
li: doi:10.1016/j.spl.2006.06.001
ab: Summary: Transitivity is an important property of any statistic applied in
    the setting of multi-arm clinical trials and non-inferiority trials
    where active-controls are used. The $G^{ρ,γ}$ class of weighted
    logrank statistics for right-censored survival data as proposed by {\it
    T. R. Fleming} and {\it D. Harrington} [Counting processes and survival
    analysis. (1991; Zbl 0727.62096)] is often used to improve efficiency
    in the setting of nonproportional hazards. These statistics utilize a
    weighting scheme based upon the combined Kaplan‒Meier estimate of
    survival for all comparison groups. Members of this class include the
    usual logrank statistic as well as the generalized Wilcoxon statistic.
    It is demonstrated that all useful members of this class exhibit
    nontransitivity. We propose a general modification of the $G^{ρ,γ}$
    statistic which asymptotically achieves transitivity.
rv: