Logrank.stat.tie {depend.truncation}

The weighted log-rank statistics for testing quasi-independence (with ties in data)

Description

The three log-rank statistics (L_0, L_1, and L_log) corresponding to 3 different weights.

Usage

Logrank.stat.tie(x.trunc, z.trunc, d)

Arguments

x.trunc

vector of variables satisfying x.trunc<=z.trunc

z.trunc

vector of variables satisfying x.trunc<=z.trunc

d

censoring indicator(0=censoring,1=failure) for z.trunc

Details

If there is no tie in the data, the function "Logrank.stat.tie" and "Logrank.stat" give identical results. However, "Logrank.stat" is computationally more efficient. The simulations of Emura & Wang (2010) are based on "Logrank.stat" since simulated data are generated from continuous distributions. The real data analyses of Emura & Wang (2010) are based on "Logrank.stat.tie" since there are many ties in the data.

Value

L0

Logrank statistics (most powerfull to detect the Clayton copula type dependence)

L1

Logrank statistics (most powerfull to detect the Frank copula type dependence)

Llog

Logrank statistics (most powerfull to detect the Gumbel copula type dependence)

Author(s)

Takeshi Emura

References

Emura T, Wang W (2010) Testing quasi-independence for truncation data. Journal of Multivariate Analysis 101, 223-239

Examples

x.trunc=c(10,5,7,1,3,9)
z.trunc=c(12,11,8,6,4,13)
d=c(1,1,1,1,0,1)
Logrank.stat.tie(x.trunc,z.trunc,d)
Logrank.stat(x.trunc,z.trunc,d) ## since there is no tie, the results are the same.