lmomco (version 1.7.3)

lmomsRCmark: Sample L-moments Moments for Right-Tail Censoring by a Marking Variable

Description

Compute the sample L-moments for right-tail censored data set in which censored data values are identified by a marking variable. Extension of left-tail censoring can be made using fliplmoms and the example therein.

Usage

lmomsRCmark(x, rcmark=NULL, nmom=5, sort=TRUE, flip=NA,
               flipfactor=1.1)

Arguments

x

A vector of data values.

rcmark

The right-tail censoring (upper) marking variable for unknown threshold: 0 is uncensored, 1 is censored.

nmom

Number of L-moments to return.

sort

Does the data need sorting?

flip

Does the data require flipping so that left-censored data can be processed as such. If the flip is a logical and TRUE, then flipfactor times the maximum of x is used. If the flip is a numeric, then it is used as the flip. The mean is NOT unflip

flipfactor

The value that is greater than 1, which is multiplied on the maximum of x to determine the flip, if the flip is not otherwise provided.

Value

• An R list is returned.
• lambdas
  Vector of the L-moments. First element is $\hat{\lambda}^{(0,0)}_1$, second element is $\hat{\lambda}^{(0,0)}_2$, and so on.
• ratios
  Vector of the L-moment ratios. Second element is $\hat{\tau}^{(0,0)}$, third element is $\hat{\tau}^{(0,0)}_3$ and so on.
• trim
  Level of symmetrical trimming used in the computation, which will equal NULL if asymmetrical trimming was used. This is not currently implemented as no one has done the derivations.
• leftrim
  Level of left-tail trimming used in the computation. This is not currently implemented as no one has done the derivations.
• rightrim
  Level of right-tail trimming used in the computation. This is not currently implemented as no one has done the derivations.
• n
  The complete sample size.
• n.cen
  The number of right-censored data values.
• flip
  The flip used in the computations for support of left-tail censoring.
• source
  An attribute identifying the computational source of the L-moments: lmomsRCmark.

References

Wang, Dongliang, Hutson, A.D., Miecznikowski, J.C., 2010, L-moment estimation for parametric survival models given censored data: Statistical Methodology, v. 7, no. 6, pp. 655--667.

Helsel, D.R., 2005, Nondetects and data analysis---Statistics for censored environmental data: Hoboken, New Jersey, John Wiley, 250 p.

See Also

lmomRCmark, fliplmoms

Examples

# Efron, B., 1988, Logistic regression, survival analysis, and the
# Kaplan-Meier curve: Journal of the American Statistical Association,
# v.83, no.402, pp.414--425
# Survival time measured in days for 51 patients with a marking
# variable in the "time,mark" ensemble. If marking variable is 1,
# then the time is right-censored by an unknown censoring threshold.
Efron <-
c(7,0,  34,0,  42,0,  63,0,  64,0,  74,1,  83,0,  84,0,  91,0,
108,0,  112,0,  129,0,  133,0,  133,0,  139,0,  140,0,  140,0,
146,0,  149,0,  154,0,  157,0,  160,0,  160,0,  165,0,  173,0,
176,0,  185,1,  218,0,  225,0,  241,0,  248,0,  273,0,  277,0,
279,1,  297,0,  319,1,  405,0,  417,0,  420,0,  440,0,  523,1,
523,0,  583,0,  594,0,  1101,0,  1116,1,  1146,0,  1226,1,
1349,1,  1412,1, 1417,1);

# Break up the ensembles into to vectors
ix <- seq(1,length(Efron),by=2)
T  <- Efron[ix]
Efron.data <- T;
Efron.rcmark <- Efron[(ix+1)]

lmr.RC <- lmomsRCmark(Efron.data, rcmark=Efron.rcmark)
lmr.ub <- lmoms(Efron.data)
lmr.noRC <- lmomsRCmark(Efron.data)
PP <- pp(Efron.data)
plot(PP, Efron.data, col=(Efron.rcmark+1), ylab="DATA")
lines(PP, qlmomco(PP, lmom2par(lmr.noRC, type="kap")), lwd=3, col=8)
lines(PP, qlmomco(PP, lmom2par(lmr.ub, type="kap")))
lines(PP, qlmomco(PP, lmom2par(lmr.RC, type="kap")), lwd=2, col=2)
legend(0,1000,c("uncensored L-moments by indicator (Kappa distribution)",
                "unbiased L-moments (Kappa)",
           "right-censored L-moments by indicator (Kappa distribution)"),
                lwd=c(3,1,2), col=c(8,1,2))