crrstep: Stepwise Regression for Fine-Gray Competing Risks Model

In crrstep: Stepwise Covariate Selection for the Fine & Gray Competing Risks Regression Model

Stepwise Regression for Fine-Gray Competing Risks Model

Description

Performs forward and backward stepwise variable selection for the Fine-Gray subdistribution hazard model in competing risks analysis. The procedure uses AIC, BIC, or BICcr as selection criteria. BICcr uses a penalty of k = \log(d), where d is the number of events of interest.

Usage

crrstep(formula, scope.min = ~1, etype, ..., subset, data, 
        direction = c("backward", "forward"), 
        criterion = c("AIC", "BICcr", "BIC"), 
        crr.object = FALSE, trace = TRUE, steps = 100)

## S3 method for class 'crrstep'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'crrstep'
summary(object, conf.level = 0.95, ...)

## S3 method for class 'summary.crrstep'
print(x, digits = max(3L, getOption("digits") - 3L),
        signif.stars = getOption("show.signif.stars"), ...)

## S3 method for class 'crrstep'
coef(object, ...)

## S3 method for class 'crrstep'
vcov(object, ...)

## S3 method for class 'crrstep'
confint(object, parm, level = 0.95, ...)

## S3 method for class 'crrstep'
logLik(object, ...)

## S3 method for class 'crrstep'
AIC(object, ..., k = 2)

## S3 method for class 'crrstep'
BIC(object, ...)

Arguments

formula	A formula object where the left-hand side (LHS) is the failure time variable and the right-hand side (RHS) specifies the linear predictors (e.g., time ~ x1 + x2 + x3). Factors, interactions, and polynomial terms are supported.
scope.min	A one-sided formula specifying the minimum model (lower scope) for backward selection or the starting model for forward selection. Default is ~1 (null model).
etype	An integer variable denoting the event type for each observation. By default, 1 indicates the event of interest, 2 indicates competing events, and 0 indicates censoring. These can be modified using failcode and cencode arguments passed to crr.
...	Additional arguments passed to crr. Important arguments include: failcode Integer value denoting the event of interest (default is 1). cencode Integer value denoting censoring (default is 0). For print and summary methods, additional arguments are passed to printCoefmat.
subset	An optional vector specifying a subset of observations to use in the analysis.
data	A data frame containing all variables referenced in the formula and etype. Only complete cases are used; rows with missing values in any predictor are automatically removed.
direction	Character string specifying the direction of stepwise search. Either "backward" (default) starting from the full model, or "forward" starting from scope.min.
criterion	Character string specifying the model selection criterion: "AIC" Akaike Information Criterion (default): -2 \log L + 2p "BIC" Bayesian Information Criterion: -2 \log L + p \log(n) "BICcr" BIC for competing risks: -2 \log L + p \log(d) where L is the partial likelihood, p is the number of parameters, n is the sample size, and d is the number of events of interest.
crr.object	Logical. If TRUE, returns the crr object from the final model instead of a crrstep object. Default is FALSE.
trace	Logical. If TRUE (default), displays the stepwise model selection process including criterion values at each step.
steps	Maximum number of steps allowed in the stepwise selection. Default is 100.
x	An object of class "crrstep" or "summary.crrstep".
object	An object of class "crrstep".
digits	Integer specifying the number of significant digits to display.
conf.level	Numeric value specifying the confidence level for confidence intervals. Default is 0.95.
signif.stars	Logical. If TRUE, significance stars are printed alongside p-values.
parm	A specification of which parameters to compute confidence intervals for. Can be a vector of numbers (indices) or names. If missing, all parameters are included.
level	The confidence level for confint. Default is 0.95.
k	Numeric penalty parameter for AIC. Default is 2.

Details

This function performs stepwise model selection for the Fine-Gray competing risks regression model implemented in crr. The implementation is based on the approach of stepAIC from the MASS package, adapted for the competing risks setting.

The function properly handles:

• Factor variables (automatically expanded to dummy variables)

• Interaction terms (e.g., x1:x2, x1*x2)

• Polynomial terms (e.g., I(x^2))

• Complex terms (e.g., I(x^2):factor)

The BICcr criterion, proposed by Volinsky and Raftery (2000) and adapted for competing risks by Kuk and Varadhan (2013), uses the number of events of interest rather than the total sample size in the penalty term. This is appropriate because the effective sample size in survival analysis is determined by the number of events, not the total number of observations.

Missing values are handled by complete case analysis. Observations with missing values in any predictor variable are removed before model fitting, and a message is displayed if trace = TRUE.

Value

If crr.object = TRUE, returns the crr object from the final selected model.

Otherwise, returns an object of class "crrstep" with the following components:

call	The matched function call.
formula	The formula for the final selected model.
direction	The direction of stepwise selection used.
criterion	The selection criterion used.
criterion_value	The value of the selection criterion for the final model.
coefficients	Named numeric vector of estimated coefficients.
std.error	Standard errors of the coefficients.
zvalue	Wald z-statistics (coefficients / std.error).
pvalue	Two-sided p-values based on the normal distribution.
conf.int	Matrix of confidence intervals for the coefficients.
conf.level	The confidence level used for conf.int.
loglik	Log partial likelihood of the final model.
loglik_null	Log partial likelihood of the null model.
n	Number of observations used.
nevent	Number of events of interest.
converged	Logical indicating whether the crr algorithm converged.
is_null_model	Logical indicating whether the final model is the null model.
crr_fit	The crr object from the final model.

The summary method returns an object of class "summary.crrstep" containing:

call	The matched function call.
formula	The formula for the final selected model.
direction	The direction of stepwise selection.
criterion	The selection criterion used.
criterion_value	The criterion value for the final model.
coefficients	Formatted coefficient table with estimates, hazard ratios, standard errors, z-values, and p-values.
conf.int	Confidence intervals for hazard ratios.
conf.level	The confidence level used.
loglik	Log partial likelihood of the final model.
loglik_null	Log partial likelihood of the null model.
lr_test	List containing the likelihood ratio test statistic, degrees of freedom, and p-value.
n	Number of observations.
nevent	Number of events of interest.
converged	Logical indicating convergence.
is_null_model	Logical indicating if the null model was selected.

Author(s)

Ravi Varadhan and Deborah Kuk

References

Fine, J. P. and Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94(446), 496-509.

Volinsky, C. T. and Raftery, A. E. (2000). Bayesian information criterion for censored survival models. Biometrics, 56(1), 256-262.

Kuk, D. and Varadhan, R. (2013). Model selection in competing risks regression. Statistics in Medicine, 32(18), 3077-3088.

See Also

crr for the underlying Fine-Gray model, stepAIC for stepwise selection in other model classes, AIC, BIC for information criteria

Examples

# Load required package
library(cmprsk)

# Simulate example data
set.seed(123)
n <- 500
ftime <- rexp(n)
fstatus <- sample(0:2, n, replace = TRUE)
cov1 <- matrix(runif(5 * n), nrow = n)
x6 <- as.factor(sample(3, size = n, replace = TRUE))
x7 <- as.factor(sample(5, size = n, replace = TRUE))
cov1 <- cbind(cov1, x6, x7)
dimnames(cov1)[[2]] <- c('x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7')
mydata <- as.data.frame(cov1)
mydata$ftime <- ftime
mydata$fstatus <- fstatus

# Define formula with factors
formula1 <- ftime ~ x1 + x2 + x3 + x4 + x5 + as.factor(x6) + as.factor(x7)

# Backward selection with BIC
fit1 <- crrstep(formula1, etype = fstatus, data = mydata, 
                direction = "backward", criterion = "BIC")
print(fit1)

# Forward selection with AIC (event of interest = 2)
fit2 <- crrstep(formula1, etype = fstatus, data = mydata, 
                direction = "forward", criterion = "AIC",
                failcode = 2, trace = FALSE)
print(fit2)
summary(fit2)

# Extract model components
coef(fit2)
confint(fit2)
confint(fit2, level = 0.90)
AIC(fit2)
BIC(fit2)
logLik(fit2)
vcov(fit2)

# Model with interactions
formula2 <- ftime ~ x1 + x2 + x3 + x4 + x4:as.factor(x6) + x5:as.factor(x7)
fit3 <- crrstep(formula2, etype = fstatus, data = mydata, 
                direction = "backward", criterion = "AIC",
                trace = FALSE)
print(fit3)
summary(fit3)

# Return crr object for further analysis
fit_crr <- crrstep(formula1, etype = fstatus, data = mydata,
                   direction = "backward", criterion = "BICcr",
                   crr.object = TRUE, trace = FALSE)

crrstep documentation built on Jan. 15, 2026, 1:06 a.m.