Stepwise regression procedure for the Fine & Gray regression model in competing risks

Description

Performs forward and backward stepwise regression for the Fine & Gray regression model in competing risks. Procedure uses AIC, BIC and BICcr as selection criteria. BICcr has a penalty of k = log(n*), where n* is the number of Type I events.

Details

The package contains a singe function crrstep, which implements backward and forward stepwise regression for the Fine & Gray regression model. The Fine & Gray model (Fine & Gray, 1999) estimates the hazard that corresponds to the cumulative incidence function of a certain event type. Selection criteria that are can be used are: AIC, BIC and BICcr. BICcr is a selection criteria based on the work by Volinksy and Raftery in which the penalty is k = log(n*), where n* is the total number of Type I events.

Author(s)

Ravi Varadhan & Deborah Kuk.

Maintainers: Ravi Varadhan <rvaradhan@jhmi.edu>

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.

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

Kuk, D. and Varadhan, R. (2013). Model selection in competing risks regression. Statistics in Medicine.

Examples

set.seed(123)
n <- 500
ftime <- rexp(n)
fstatus <- sample(0:2,n,replace=TRUE)
cov1 <- matrix(runif(5*n),nrow=n)
x61 <- as.factor(sample(3, size=n, rep=TRUE))
x71 <- as.factor(sample(5, size=n, rep = TRUE))
cov1 <- cbind(cov1, x61, x71)
dimnames(cov1)[[2]] <- c('x1','x2','x3','x4','x5', 'x6', 'x7')
formula1 <- ftime ~ 1 + x1 + x2 + x3 + x4 + x5 + as.factor(x6) + as.factor(x7) 

crrstep(formula1, , fstatus, data = as.data.frame(cov1), direction = "backward", criterion = "BIC")
crrstep(formula1, , fstatus, data = as.data.frame(cov1), direction = "backward", criterion = "AIC")

ans2 <- crrstep(formula1, , fstatus, data = as.data.frame(cov1), direction = "forward", 
		failcode=2, criterion = "AIC")
ans2

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

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:

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

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)