R: Competing Risks Regression

crr {cmprsk} | R Documentation

## 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 a*z+b*z*t+c*z*t*t 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

[Package cmprsk version 2.2-7 Index]