depCensoring (version 0.1.7)

estimate.cmprsk: Estimate the competing risks model of Rutten, Willems et al. (20XX).

Description

This function estimates the parameters in the competing risks model described in Willems et al. (2024+). Note that this model extends the model of Crommen, Beyhum and Van Keilegom (2024) and as such, this function also implements their methodology.

Usage

estimate.cmprsk(
  data,
  admin,
  conf,
  eoi.indicator.names = NULL,
  Zbin = NULL,
  inst = "cf",
  realV = NULL,
  compute.var = TRUE,
  eps = 0.001
)

Value

A list of parameter estimates in the second stage of the estimation algorithm (hence omitting the estimates for the control function), as well as an estimate of their variance and confidence intervals.

Arguments

data

A data frame, adhering to the following formatting rules:

• The first column, named "y", contains the observed times.

• The next columns, named "delta1", delta2, etc. contain the indicators for each of the competing risks.

• The next column, named da, contains the censoring indicator (independent censoring).

• The next column should be a column of all ones (representing the intercept), names x0.

• The subsequent columns should contain the values of the covariates, named x1, x2, etc.

• When applicable, the next column should contain the values of the endogenous variable. This column should be named z.

• When z is provided and an instrument for z is available, the next column, named w, should contain the values for the instrument.

admin

Boolean value indicating whether the data contains administrative censoring.

conf

Boolean value indicating whether the data contains confounding and hence indicating the presence of z and, possibly, w.

eoi.indicator.names

Vector of names of the censoring indicator columns pertaining to events of interest. Events of interest will be modeled allowing dependence between them, whereas all censoring events (corresponding to indicator columns not listed in eoi.indicator.names) will be treated as independent of every other event. If eoi.indicator.names == NULL, all events will be modeled dependently.

Zbin

Indicator value indicating whether (Zbin = TRUE) or not Zbin = FALSE the endogenous covariate is binary. Default is Zbin = NULL, corresponding to the case when conf == FALSE.

inst

Variable encoding which approach should be used for dealing with the confounding. inst = "cf" indicates that the control function approach should be used. inst = "W" indicates that the instrumental variable should be used 'as is'. inst = "None" indicates that Z will be treated as an exogenous covariate. Finally, when inst = "oracle", this function will access the argument realV and use it as the values for the control function. Default is inst = "cf".

realV

Vector of numerics with length equal to the number of rows in data. Used to provide the true values of the instrumental function to the estimation procedure.

compute.var

Boolean value indicating whether the variance of the parameter estimates should be computed as well (this can be very computationally intensive, so may want to be disabled). Default is estimate.var = TRUE.

eps

Value that will be added to the diagonal of the covariance matrix during estimation in order to ensure strictly positive variances.

References

Willems et al. (2024+). Flexible control function approach under competing risks (in preparation).

Crommen, G., Beyhum, J., and Van Keilegom, I. (2024). An instrumental variable approach under dependent censoring. Test, 33(2), 473-495.

Examples

# \donttest{

n <- 200

# Set parameters
gamma <- c(1, 2, 1.5, -1)
theta <- c(0.5, 1.5)
eta1 <- c(1, -1, 2, -1.5, 0.5)
eta2 <- c(0.5, 1, 1, 3, 0)

# Generate exogenous covariates
x0 <- rep(1, n)
x1 <- rnorm(n)
x2 <- rbinom(n, 1, 0.5)

# Generate confounder and instrument
w <- rnorm(n)
V <- rnorm(n, 0, 2)
z <- cbind(x0, x1, x2, w) %*% gamma + V
realV <- z - (cbind(x0, x1, x2, w) %*% gamma)

# Generate event times
err <- MASS::mvrnorm(n, mu = c(0, 0), Sigma =
matrix(c(3, 1, 1, 2), nrow = 2, byrow = TRUE))
bn <- cbind(x0, x1, x2, z, realV) %*% cbind(eta1, eta2) + err
Lambda_T1 <- bn[,1]; Lambda_T2 <- bn[,2]
x.ind = (Lambda_T1>0)
y.ind <- (Lambda_T2>0)
T1 <- rep(0,length(Lambda_T1))
T2 <- rep(0,length(Lambda_T2))
T1[x.ind] = ((theta[1]*Lambda_T1[x.ind]+1)^(1/theta[1])-1)
T1[!x.ind] = 1-(1-(2-theta[1])*Lambda_T1[!x.ind])^(1/(2-theta[1]))
T2[y.ind] = ((theta[2]*Lambda_T2[y.ind]+1)^(1/theta[2])-1)
T2[!y.ind] = 1-(1-(2-theta[2])*Lambda_T2[!y.ind])^(1/(2-theta[2]))
# Generate adminstrative censoring time
C <- runif(n, 0, 40)

# Create observed data set
y <- pmin(T1, T2, C)
delta1 <- as.numeric(T1 == y)
delta2 <- as.numeric(T2 == y)
da <- as.numeric(C == y)
data <- data.frame(cbind(y, delta1, delta2, da, x0, x1, x2, z, w))
colnames(data) <- c("y", "delta1", "delta2", "da", "x0", "x1", "x2", "z", "w")

# Estimate the model
admin <- TRUE                # There is administrative censoring in the data.
conf <- TRUE                 # There is confounding in the data (z)
eoi.indicator.names <- NULL  # We will not impose that T1 and T2 are independent
Zbin <- FALSE                # The confounding variable z is not binary
inst <- "cf"                 # Use the control function approach
compute.var <- TRUE          # Variance of estimates should be computed.
# Since we don't use the oracle estimator, this argument is ignored anyway
realV <- NULL
estimate.cmprsk(data, admin, conf, eoi.indicator.names, Zbin, inst, realV,
                compute.var)

# }