sicure (version 0.1.1)

sicure.f: Estimation of the vector of parameters in a single-index mixture cure model with a functional covariate

Description

This function provides the estimation of the vector of parameters in a single-index mixture cure model with a functional covariate (see Piñeiro-Lamas, 2024, Section 4.1, pages 83-84). A Functional Principal Components Analysis (FPCA) representation that explains at least the (propvar\(*100\))% of the variability of the data is considered (for more details, see Ramsay and Silverman, 2005).

Usage

sicure.f(x_cov, time, delta, propvar = 0.9, randomsearch = FALSE)

Value

A list with the following components:

par

A numeric vector of the estimated parameters. The last four correspond to the logarithms of the bandwidths.

value

The value of the objective function (negative log-likelihood) at the estimated parameters.

si

The estimated single-index variable.

Arguments

x_cov

A matrix or data frame \(n\) x \(m\) giving the functional covariate values. Each row represents an individual (a curve); \(m\) is the number of observed points in each curve.

time

A numeric vector giving the observed times.

delta

A numeric vector giving the values of the uncensoring indicator, where 1 indicates that the event of interest has been observed and 0 indicates that the observation is censored.

propvar

Minimum proportion of explained variability with the FPCA representation.

randomsearch

A logical value, FALSE by default, specifying whether a random search of the initial iterant is considered.

Details

The infinite-dimensional nature of the functional data is reduced via FPCA. This basis representation is then truncated, reducing the dimension to \(K\), where each functional observation is summarized into a vector of scores, \((\xi_1, \xi_2, \dots, \xi_K)\). After this reduction, the model can be treated similarly to the vector covariate case. For more details on the estimation process and the specific arguments, see sicure.v function, which focuses on single-index mixture cure models with a vector of covariates.

References

Piñeiro-Lamas, B. (2024). High dimensional single-index mixture cure models [PhD thesis]. Universidade da Coruña. Available at https://ruc.udc.es/dspace/handle/2183/37035

Ramsay, J. O., and Silverman, B. W. (2005). Functional Data Analysis, 2nd ed., Springer, New York.

See Also

sicure.v, sicure.vf

Examples

# Some artificial data
set.seed(123)
n <- 50
x <- runif(n, -2, 2) # Covariate values
y <- rweibull(n, shape = 0.5 * (x + 4)) # True lifetimes
c <- rexp(n) # Censoring values
p <- exp(2*x)/(1 + exp(2*x)) # Probability of being susceptible
u <- runif(n)
t  <- ifelse(u < p, pmin(y, c), c) # Observed times
delta  <- ifelse(u < p, ifelse(y < c, 1, 0), 0) # Uncensoring indicator
# Number of individuals (rows)
n <- 50
# Numbers of observations per individual (columns)
m <- 100
# Observation times (between 0 and 1)
x <- seq(0, 1, length.out = m)
# Auxiliar function to simulate the other functions by adding some noise
# Shift controls the horizontal displacement of the functions
sim_func <- function(x, shift, sd_noise) {
  # positive-negative-negative waves
  sin(2*pi*(x + shift))+sin(4*pi*(x + shift))-sin(6*pi*(x + shift))+rnorm(m, 0, sd_noise)
}
# Simulated functions
data_matrix <- matrix(NA, nrow=n, ncol=m)
for (i in 1:n) {
  shift <- runif(1, -0.05, 0.05)
  data_matrix[i, ] <- sim_func(x, shift, sd_noise = 0.03)
}
matplot(x, t(data_matrix), type = "l", lty = 1, ylab='f(x)')
# \donttest{
suppressWarnings(sicure.f(data_matrix, t, delta, 0.9))
# }