crr {cmprsk}

Competing Risks Regression

Description

regression modeling of subdistribution functions in competing risks

Usage

crr(ftime, fstatus, cov1, cov2, tf, cengroup, failcode=1, cencode=0,
subset, na.action=na.omit, gtol=1e-06, maxiter=10, init, variance=TRUE)

Arguments

ftime

vector of failure/censoring times

fstatus

vector with a unique code for each failure type and a separate code for censored observations

cov1

matrix (nobs x ncovs) of fixed covariates (either cov1, cov2, or both are required)

cov2

matrix of covariates that will be multiplied by functions of time; if used, often these covariates would also appear in cov1 to give a prop hazards effect plus a time interaction

tf

functions of time. A function that takes a vector of times as an argument and returns a matrix whose jth column is the value of the time function corresponding to the jth column of cov2 evaluated at the input time vector. At time tk, the model includes the term cov2[,j]*tf(tk)[,j] as a covariate.

cengroup

vector with different values for each group with a distinct censoring distribution (the censoring distribution is estimated separately within these groups). All data in one group, if missing.

failcode

code of fstatus that denotes the failure type of interest

cencode

code of fstatus that denotes censored observations

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.

gtol

iteration stops when a function of the gradient is < gtol

maxiter

maximum number of iterations in Newton algorithm (0 computes scores and var at init, but performs no iterations)

init

initial values of regression parameters (default=all 0)

variance

If FALSE, then suppresses computation of the variance estimate and residuals

Details

Fits the 'proportional subdistribution hazards' regression model described in Fine and Gray (1999). This model directly assesses the effect of covariates on the subdistribution of a particular type of failure in a competing risks setting. The method implemented here is described in the paper as the weighted estimating equation.

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.

The basic model assumes the subdistribution with covariates z is a constant shift on the complementary log log scale from a baseline subdistribution function. This can be generalized by including interactions of z with functions of time to allow the magnitude of the shift to change with follow-up time, through the cov2 and tfs arguments. For example, if z is a vector of covariate values, and uft is a vector containing the unique failure times for failures of the type of interest (sorted in ascending order), then the coefficients a, b and c in the quadratic (in time) model az+bzt+zt^2 can be fit by specifying cov1=z, cov2=cbind(z,z), tf=function(uft) cbind(uft,uft*uft).

This function uses an estimate of the survivor function of the censoring distribution to reweight contributions to the risk sets for failures from competing causes. In a generalization of the methodology in the paper, the censoring distribution can be estimated separately within strata defined by the cengroup argument. If the censoring distribution is different within groups defined by covariates in the model, then validity of the method requires using separate estimates of the censoring distribution within those groups.

The residuals returned are analogous to the Schoenfeld residuals in ordinary survival models. Plotting the jth column of res against the vector of unique failure times checks for lack of fit over time in the corresponding covariate (column of cov1).

If variance=FALSE, then some of the functionality in summary.crr and print.crr will be lost. This option can be useful in situations where crr is called repeatedly for point estimates, but standard errors are not required, such as in some approaches to stepwise model selection.

Value

Returns a list of class crr, with components

$coef

the estimated regression coefficients

$loglik

log pseudo-liklihood evaluated at coef

$score

derivitives of the log pseudo-likelihood evaluated at coef

$inf

-second derivatives of the log pseudo-likelihood

$var

estimated variance covariance matrix of coef

$res

matrix of residuals giving the contribution to each score (columns) at each unique failure time (rows)

$uftime

vector of unique failure times

$bfitj

jumps in the Breslow-type estimate of the underlying sub-distribution cumulative hazard (used by predict.crr())

$tfs

the tfs matrix (output of tf(), if used)

$converged

TRUE if the iterative algorithm converged

$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

$loglik.null

The value of the log pseudo-likelihood when all the coefficients are 0

$invinf

- inverse of second derivative matrix of the log pseudo-likelihood

References

Fine JP and Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. JASA 94:496-509.

See Also

predict.crr print.crr plot.predict.crr summary.crr

Examples

# simulated data to test 
set.seed(10)
ftime <- rexp(200)
fstatus <- sample(0:2,200,replace=TRUE)
cov <- matrix(runif(600),nrow=200)
dimnames(cov)[[2]] <- c('x1','x2','x3')
print(z <- crr(ftime,fstatus,cov))
summary(z)
z.p <- predict(z,rbind(c(.1,.5,.8),c(.1,.5,.2)))
plot(z.p,lty=1,color=2:3)
crr(ftime,fstatus,cov,failcode=2)
# quadratic in time for first cov
crr(ftime,fstatus,cov,cbind(cov[,1],cov[,1]),function(Uft) cbind(Uft,Uft^2))
#additional examples in test.R