Package 'fastcmprsk'

Akaike's An Information Criterion

Description

Similar functional utility to coef methods.

Usage

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

Arguments

object	fcrr object
...	Additional arguments. Not implemented.
k	Numeric, the penalty per parameter to be used; the default k = 2 is the classical AIC.

Value

A numeric value with the corresponding AIC (or BIC, or ..., depending on k).

---

Akaike's An Information Criterion

Description

Similar functional utility to coef methods.

Usage

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

Arguments

object	fcrrp object
...	Additional arguments. Not implemented.
k	Numeric, the penalty per parameter to be used; the default k = 2 is the classical AIC.

Value

A numeric value with the corresponding AIC (or BIC, or ..., depending on k).

---

Extract coefficients from an "fcrr" object.

Description

Similar functional utility to coef methods.

Usage

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

Arguments

object	fcrr object
...	Additional arguments. Not implemented.

Value

Coefficients extracted from the model object object.

---

Extract coefficients from an "fcrrp" object.

Description

Similar functional utility to coef methods.

Usage

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

Arguments

object	fcrrp object
...	Additional arguments. Not implemented.

Value

Coefficients extracted from the model object object.

---

Confidence Intervals for Model Parameters

Description

Computes confidence intervals for one or more parameters in a fitted model of class fcrr.

Usage

## S3 method for class 'fcrr'
confint(object, parm, level = 0.95, digits = max(options()$digits - 5, 2), ...)

Arguments

object	fcrr object (output from fastCrr())
parm	a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
level	the confidence level required
digits	Number of significant difits to round to.
...	Additional arguments. Not implemented.

Details

Prints out table of confidence intervals for the Fine-Gray model.

Value

A matrix (or vector) with columns giving lower and upper confidence limits for each coefficient estimate.

---

Create a Competing Risk Object

Description

Create a competing risk object, used as a response variable in the model formula for fastCrr and fastCrrp. Adapted from the Surv object.

Usage

Crisk(ftime, fstatus, cencode = 0, failcode = 1, silent = TRUE)

Arguments

ftime	A vector of event/censoring times.
fstatus	A vector with unique code for each event type and a separate code for censored observations.
cencode	Integer: code of fstatus that denotes censored observations (default is 0)
failcode	Integer: code of fstatus that event type of interest (default is 1)
silent	Logical: print information about coding.

Value

Returns an object, used as a response variable, of class Crisk.

time	vector of observed event times
status	vector of event indicators. 0 = censored, 1 = event of interest, 2 = competing risks

References

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

See Also

Surv

Examples

library(fastcmprsk)

set.seed(10)
ftime <- rexp(200)
fstatus <- sample(0:2, 200, replace = TRUE)
obj <- Crisk(ftime, fstatus, silent = FALSE)

---

Fast Fine-Gray Model Estimation

Description

Estimates parameters for the proportional subdistribution hazards model using two-way linear scan approach.

Usage

fastCrr(
  formula,
  data,
  eps = 1e-06,
  max.iter = 1000,
  getBreslowJumps = TRUE,
  standardize = TRUE,
  variance = TRUE,
  var.control = varianceControl(B = 100, useMultipleCores = FALSE),
  returnDataFrame = FALSE
)

Arguments

formula	a formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a Crisk object as returned by the Crisk function.
data	a data.frame in which to interpret the variables named in the formula.
eps	Numeric: algorithm stops when the relative change in any coefficient is less than eps (default is 1E-6)
max.iter	Numeric: maximum iterations to achieve convergence (default is 1000)
getBreslowJumps	Logical: Output jumps in Breslow estimator for the cumulative hazard.
standardize	Logical: Standardize design matrix.
variance	Logical: Get standard error estimates for parameter estimates via bootstrap.
var.control	List of options for variance estimation.
returnDataFrame	Logical: Return (ordered) data frame.

Details

Fits the 'proportional subdistribution hazards' regression model described in Fine and Gray (1999) using a novel two-way linear scan approach. By default, the Crisk object will specify which observations are censored (0), the event of interest (1), or competing risks (2).

Value

Returns a list of class fcrr.

coef	the estimated regression coefficients
var	estimated variance-covariance matrix via bootstrap (if variance = TRUE)
logLik	log-pseudo likelihood at the estimated regression coefficients
logLik.null	log-pseudo likelihood when the regression coefficients are 0
lrt	log-pseudo likelihood ratio test statistic for the estimated model vs. the null model.
iter	iterations of coordinate descent until convergence
converged	logical.
breslowJump	Jumps in the Breslow baseline cumulative hazard (used by predict.fcrr)
uftime	vector of unique failure (event) times
isVariance	logical to return if variance is chosen to be estimated
df	returned ordered data frame if returnDataFrame = TRUE.

References

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

#' Kawaguchi, E.S., Shen J.I., Suchard, M. A., Li, G. (2020) Scalable Algorithms for Large Competing Risks Data, Journal of Computational and Graphical Statistics

Examples

library(fastcmprsk)

set.seed(10)
ftime <- rexp(200)
fstatus <- sample(0:2, 200, replace = TRUE)
cov <- matrix(runif(1000), nrow = 200)
dimnames(cov)[[2]] <- c('x1','x2','x3','x4','x5')
fit <- fastCrr(Crisk(ftime, fstatus) ~ cov, variance = FALSE)

# Not run: How to set up multiple cores for boostrapping
# library(doParallel) #  make sure necessary packages are loaded
# myClust <- makeCluster(2)
# registerDoParallel(myClust)
# fit1 <- fastCrr(Crisk(ftime, fstatus) ~ cov, variance = TRUE,
# var.control = varianceControl(B = 100, useMultipleCores = TRUE))
# stopCluster(myClust)

---

Penalized Fine-Gray Model Estimation via two-way linear scan

Description

Performs penalized regression for the proportional subdistribution hazards model. Penalties currently include LASSO, MCP, SCAD, and ridge regression. User-specificed weights can be assigned to the penalty for each coefficient (e.g. implementing adaptive LASSO and broken adaptive ridge regerssion).

Usage

fastCrrp(
  formula,
  data,
  eps = 1e-06,
  max.iter = 1000,
  getBreslowJumps = TRUE,
  standardize = TRUE,
  penalty = c("LASSO", "RIDGE", "MCP", "SCAD", "ENET"),
  lambda = NULL,
  alpha = 0,
  lambda.min.ratio = 0.001,
  nlambda = 25,
  penalty.factor,
  gamma = switch(penalty, scad = 3.7, 2.7)
)

Arguments

formula	a formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a Crisk object as returned by the Crisk function.
data	a data.frame in which to interpret the variables named in the formula.
eps	Numeric: algorithm stops when the relative change in any coefficient is less than eps (default is 1E-6)
max.iter	Numeric: maximum iterations to achieve convergence (default is 1000)
getBreslowJumps	Logical: Output jumps in Breslow estimator for the cumulative hazard (one for each value of lambda).
standardize	Logical: Standardize design matrix.
penalty	Character: Penalty to be applied to the model. Options are "lasso", "scad", "ridge", "mcp", and "enet".
lambda	A user-specified sequence of lambda values for tuning parameters.
alpha	L1/L2 weight for elastic net regression.
lambda.min.ratio	Smallest value for lambda, as a fraction of lambda.max (if lambda is NULL).
nlambda	Number of lambda values (default is 25).
penalty.factor	A vector of weights applied to the penalty for each coefficient. Vector must be of length equal to the number of columns in X.
gamma	Tuning parameter for the MCP/SCAD penalty. Default is 2.7 for MCP and 3.7 for SCAD and should be left unchanged.

Details

The fastCrrp functions performed penalized Fine-Gray regression. Parameter estimation is performed via cyclic coordinate descent and using a two-way linear scan approach to efficiently calculate the gradient and Hessian values. Current implementation includes LASSO, SCAD, MCP, and ridge regression.

Value

Returns a list of class fcrrp.

coef	fitted coefficients matrix with nlambda columns and nvars columns
logLik	vector of log-pseudo likelihood at the estimated regression coefficients
logLik.null	log-pseudo likelihood when the regression coefficients are 0
lambda.path	sequence of tuning parameter values
iter	number of iterations needed until convergence at each tuning parameter value
converged	convergence status at each tuning parameter value
breslowJump	Jumps in the Breslow baseline cumulative hazard (used by predict.fcrr)
uftime	vector of unique failure (event) times
penalty	same as above
gamma	same as above
above	same as above

References

Fu, Z., Parikh, C.R., Zhou, B. (2017) Penalized variable selection in competing risks regression. Lifetime Data Analysis 23:353-376.

Breheny, P. and Huang, J. (2011) Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Ann. Appl. Statist., 5: 232-253.

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

Kawaguchi, E.S., Shen J.I., Suchard, M. A., Li, G. (2020) Scalable Algorithms for Large Competing Risks Data, Journal of Computational and Graphical Statistics

Examples

library(fastcmprsk)
set.seed(10)
ftime <- rexp(200)
fstatus <- sample(0:2, 200, replace = TRUE)
cov <- matrix(runif(1000), nrow = 200)
dimnames(cov)[[2]] <- c('x1','x2','x3','x4','x5')
fit <- fastCrrp(Crisk(ftime, fstatus) ~ cov, lambda = 1, penalty = "RIDGE")
fit$coef

---

Extract log-pseudo likelihood from an "fcrr" object.

Description

Similar functional utility to coef methods.

Usage

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

Arguments

object	fcrr object
...	Additional arguments. Not implemented.

Value

Returns the log-pseudo likelihood of object object.

---

Extract log-pseudo likelihood from an "fcrrp" object.

Description

Similar functional utility to coef methods.

Usage

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

Arguments

object	fcrrp object
...	Additional arguments. Not implemented.

Value

Returns the log-pseudo likelihood of object object.

---

Plots solution path for penalized methods

Description

Plots solution path for penalized methods

Usage

## S3 method for class 'fcrrp'
plot(x, ...)

Arguments

x	fcrrp object (output from fastCrrp())
...	additional arguments to plot()

Details

Plots solution path for penalized methods. x-axis: log tuning parameter values. y-axis: coeffcient estimates.

Value

A plot of the solution path for the chosen penalized method.

---

Plots predicted cumulative incidence function

Description

Plots predicted cumulative incidence function

Usage

## S3 method for class 'predict.fcrr'
plot(x, ...)

Arguments

x	predict.fcrr object (output from predict(fcrr x))
...	additional arguments to plot()

Value

A plot of the estimated cumulative incidence function.

---

Cumulative Incidence Function Estimation

Description

Predicts cumulative incidence function from a fcrr object.

Usage

## S3 method for class 'fcrr'
predict(
  object,
  newdata,
  getBootstrapVariance = TRUE,
  var.control = varianceControl(B = 100, useMultipleCores = FALSE),
  type = "none",
  alpha = 0.05,
  tL = NULL,
  tU = NULL,
  ...
)

Arguments

object	Output from fcrr object.
newdata	A set of covariate values to predict the CIF.
getBootstrapVariance	Logical: Calculate variance for CIF via bootstrap.
var.control	List of variance parameters from varianceControl().
type	Confidence intervals or confidence bands.
alpha	Significance level to compute intervals or bands
tL	Lower time for band estimation.
tU	Upper time for band estimation.
...	additional arguments affecting the fastCrr procedure.
B	Number of bootstrap samples for variance estimation.

Details

Calculates the CIF using fcrr output conditional on newdata.

Value

Returns a list of class predict.fcrr.

ftime	Unique observed failure times
CIF	predicted CIF at time ftime
lower	lower interval/band limit
upper	upper interval/band limit
type	same as original argument

References

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

Examples

library(fastcmprsk)
set.seed(10)
ftime <- rexp(200)
fstatus <- sample(0:2, 200, replace = TRUE)
cov <- matrix(runif(1000), nrow = 200)
dimnames(cov)[[2]] <- c('x1','x2','x3','x4','x5')
fit <- fastCrr(Crisk(ftime, fstatus) ~ cov, returnDataFrame = TRUE)
cov2 <- rnorm(5)
predict(fit, newdata = cov2)

---

Prints summary of a fcrr x

Description

Prints summary statistics of a fcrr x

Usage

## S3 method for class 'summary.fcrr'
print(x, digits = max(options()$digits - 4, 3), ...)

Arguments

x	output from fastCrr().
digits	digits for rounding.
...	additional arguments to print().

Details

Prints the convergence status, log-pseudo likelihood, the estimated coefficients, the estimated standard errors, and the two-sided p-values for the test of the individual coefficients equal to 0.

Value

Prints the convergence status, log-pseudo likelihood, the estimated coefficients, the estimated standard errors, and the two-sided p-values for the test of the individual coefficients equal to 0.

---

Simulate data from the Fine-Gray Model

Description

Simulate data from the model proposed in Fine and Gray (1999) for two causes. Cause 1 is assumed to be of primary importance.

Usage

simulateTwoCauseFineGrayModel(
  nobs,
  beta1,
  beta2,
  X = NULL,
  u.min = 0,
  u.max,
  p = 0.5,
  returnX = FALSE
)

Arguments

nobs	Integer: Number of observations in simulated dataset.
beta1	A vector of effect sizes for cause 1 of length ncovs
beta2	A vector of effect sizes for cause 2 of length ncovs
X	A matrix of fixed covariates (nobs x ncovs). If X is NULL (default) then X will be simulated from MVN(O, I) with n = nobs and p = length(beta1).
u.min	Numeric: controls lower bound of censoring distribution where C ~ U(u.min, u.max)
u.max	Numeric: controls upper bound of censoring distribution where C ~ U(u.min, u.max)
p	Numeric: value between 0 and 1 which controls the mixture probability.
returnX	Logical: Whether to return X or not. Default is TRUE. Recommended if X is NULL.

Details

The function simulates data according to the setup by Fine and Gray (1999). See their paper for more information.

Value

Returns a list with the following:

ftime	vector of nobs simulated event times
ftime	vector of nobs simulated event indicators (0/1/2)
X	design matrix if returnX = TRUE. (simulated design matrix if X = NULL.)

References

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

Examples

set.seed(2019)
nobs <- 500
beta1 <- c(0.40, -0.40,  0, -0.50,  0,  0.60,  0.75,  0,  0, -0.80)
beta2 <- -beta1
Z <- matrix(rnorm(nobs * length(beta1)), nrow = nobs)
dat <- simulateTwoCauseFineGrayModel(nobs, beta1, beta2, Z, u.min = 0, u.max = 1, p = 0.5)

---

Summary method for fastCrr

Description

Generate and print summaries of fastCrr output.

Usage

## S3 method for class 'fcrr'
summary(
  object,
  conf.int = TRUE,
  alpha = 0.05,
  digits = max(options()$digits - 5, 2),
  ...
)

Arguments

object	fcrr x (output from fastCrr())
conf.int	Logical. Whether or not to outut confidence intervals.
alpha	Significance level of the confidence intervals.
digits	Numer of significant difits to round to.
...	additional arguments to print()

Details

The summary method produces an ANOVA table for the coefficient estimates of the Fine-Gray model.

Value

The form of the value returned by summary depends on the class of its argument. See the documentation of the particular methods for details of what is produced by that method.

---

Controls for Variance Calculation

Description

Controls for variance calculation for the fastcmprsk package.

Usage

varianceControl(
  B = 100L,
  seed = 1991L,
  useMultipleCores = FALSE,
  extractMatrix = FALSE
)

Arguments

B	Integer: Number of bootstrap samples needed for variance estimation.
seed	Integer: Seed value for bootstrapping. Results may differ if parallelized.
useMultipleCores	Logical: Set to TRUE if parallelizing. (Default is FALSE).
extractMatrix	Logical: Extract matrix of bootstrap estimates (Default is FALSE)

Details

Variance-covariance estimation is done via bootstrap. Independent bootstrap runs can be performed both in serial and parallel. Parallelization is done via the doParallel package.

Value

Returns a list for variance options inputted into fastCrr.

B	same as what is defined in argument.
seed	same as what is defined in argument.
mcores	same as what is defined in argument useMultipleCores.
extract	same as what is defined in argument extractMatrix.

Examples

library(fastcmprsk)
set.seed(10)
ftime <- rexp(200)
fstatus <- sample(0:2, 200, replace = TRUE)
cov <- matrix(runif(1000), nrow = 200)
dimnames(cov)[[2]] <- c('x1','x2','x3','x4','x5')
vc <- varianceControl(B = 100, seed = 2019, useMultipleCores = FALSE)
fit1 <- fastCrr(Crisk(ftime, fstatus) ~ cov, variance = TRUE, var.control = vc)
fit1$var # Estimated covariance matrix via bootstrap

---

Extract variance-covariance matrix from an "fcrr" object.

Description

Similar functional utility to vcov methods.

Usage

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

Arguments

object	fcrr object.
...	Additional arguments. Not implemented.

Value

Returns the estimated variance-covariance matrix (via bootstrap) from object object.

---