crrQR function

Competing Risks Quantile Regression

quantile regression modeling of subdistribution functions in competing risks

crrQR(ftime, fstatus, X, failcode=1, cencode=0, 
tau.range=c(0.01,0.99), tau.step=0.01, subset, 
na.action=na.omit, rq.method="br", variance=TRUE)

## S3 method for class 'crrQR'
print(x, ...)

Arguments

• ftime: vector of failure/censoring times
• fstatus: vector with a unique code for each failure type and a separate code for censored observations
• X: matrix (nobs x ncovs) of covariates
• failcode: code of fstatus that denotes the failure type of interest
• cencode: code of fstatus that denotes censored observations
• tau.range: vector of length 2 denoting the range of quantiles
• tau.step: grid size on tau.range (spacing between two grid points)
• subset: a logical vector specifying a subset of cases to include in the analysis
• na.action: a function specifying the action to take for any cases missing any of ftime, fstatus, cov1, cov2, cengroup, or subset.
• rq.method: method of computation for quantile regressions. (cf. documentation of method rq.fit in package quantreg for details.)
• variance: if FALSE, then suppresses computation of asymptotic variances
• x: crrQR object (output from crrQR()) for method print
• ...: included for compatibility with the generic functions. Not currently used.

Returns

Returns a list of class crrQR, with components - $beta.seq: the estimated regression coefficients

• $tau.seq: the sequence of quantiles computed

• $var.seq: estimated variance covariance matrix of coef

• $inf.func: list of estimated influence functions

• $call: the call to crr

• $n: the number of observations used in fitting the model

• $n.missing: the number of observations removed from the input data due to missing values

• $cvt.length: number of covariates (columns of X)

Details

Fits the competing risks quantile regression model described in Peng and Fine (2009).

While the use of model formulas is not supported, the model.matrix function can be used to generate suitable matrices of covariates from factors, eg model.matrix(~factor1+factor2)[,-1] will generate the variables for the factor coding of the factors factor1 and factor2. The final [,-1] removes the constant term from the output of model.matrix.

If variance=FALSE, then

some of the functionality in summary.crrQR and print.crrQR

will be lost. This option can be useful in situations where crrQR is called repeatedly for point estimates, but standard errors are not required, such as in bootstrapping the cumulative incidence function for confidence intervals.

The print method prints the estimated coefficients, the estimated standard errors, and the two-sided p-values for the test of the individual coefficients equal to 0.

A first implementation of the estimation procedure was prepared by Limin Peng and Ruosha Li.

References

Peng L and Fine JP (2009) Competing risks quantile regression. JASA 104:1440-1453.

See Also

predict.crrQR plot.predict.crrQR

summary.crrQR rq.fit

Examples

# simulated data to test 
set.seed(10)
ftime <- rexp(200)
fstatus <- sample(0:2,200,replace=TRUE)
X <- matrix(runif(600),nrow=200)
dimnames(X)[[2]] <- c('x1','x2','x3')
#compute model
print(z <- crrQR(ftime,fstatus,X))
summary(z)
# predict and plot cumulative incedences
reference <- as.matrix(rbind(c(.1,.5,.8),c(.1,.5,.2)))
dimnames(reference)[[2]] <- c('x1','x2','x3') 
z.p <- predict(z,reference)
print(z.p)
plot(z.p,lty=1,color=2:3)
crrQR(ftime,fstatus,X,failcode=2)