splineCox (version 0.0.8)

splineCox.reg1: Fitting the five-parameter spline Cox model giving a specified shape

Description

splineCox.reg1 estimates the parameters of a five-parameter spline Cox model based on a specified shape for the baseline hazard function. The function calculates the estimates for the model parameters (beta) and the baseline hazard scale parameter (gamma), using non-linear optimization. If a numeric vector is provided for the model parameter, it will be normalized to have an L1 norm of 1. Additionally, if plot = TRUE, the function generates a plot of the estimated baseline hazard function with 95% confidence intervals. The x-axis represents time, and the y-axis represents the estimated hazard. The solid line indicates the estimated hazard function, while the dashed red lines represent the confidence intervals.

Usage

splineCox.reg1(
  t.event,
  event,
  Z,
  xi1 = min(t.event),
  xi3 = max(t.event),
  model = "constant",
  p0 = rep(0, 1 + ncol(as.matrix(Z))),
  plot = TRUE
)

Value

A list containing the following components:

• model: A shape of the baseline hazard function or the normalized custom numeric vector used.

• parameter: A numeric vector of the parameters defining the baseline hazard shape.

• beta: A named vector with the estimates, standard errors, and 95\

• gamma: A named vector with the estimate, standard error, and 95\

• loglik: A named vector containing the log-likelihood (LogLikelihood), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC).

• plot: A baseline hazard function plot (if plot = TRUE).

Arguments

t.event

a vector for time-to-event

event

a vector for event indicator (=1 event; =0 censoring)

Z

a matrix for covariates; nrow(Z)=sample size, ncol(Z)=the number of covariates

xi1

lower bound for the hazard function; the default is min(t.event)

xi3

upper bound for the hazard function; the default is max(t.event)

model

A character string specifying the shape of the baseline hazard function or a numeric vector of length 5 representing custom weights. If a numeric vector is provided, it will be normalized to have an L1 norm of 1. Available options include: "increase", "constant", "decrease", "unimodal1", "unimodal2", "unimodal3", "bathtub1", "bathtub2", "bathtub3". Default is "constant"

p0

Initial values to maximize the likelihood (1 + p parameters; baseline hazard scale parameter and p regression coefficients)

plot

A logical value indicating whether to plot the estimated baseline hazard function. If TRUE, a plot is generated displaying the estimated baseline hazard function along with its 95% confidence intervals. The x-axis represents time, and the y-axis represents the estimated hazard. The solid line indicates the estimated hazard function, while the dashed red lines represent the confidence intervals. Default is TRUE.

References

Teranishi, R.; Furukawa, K.; Emura, T. (2025). A Two-Stage Estimation Approach to Cox Regression Under the Five-Parameter Spline Model Mathematics 13(4), 616. tools:::Rd_expr_doi("10.3390/math13040616") Available at https://www.mdpi.com/2227-7390/13/4/616

Examples

# Example data
library(joint.Cox)
data(dataOvarian)
t.event = dataOvarian$t.event
event = dataOvarian$event
Z = dataOvarian$CXCL12

reg1 <- splineCox.reg1(t.event, event, Z, model = "constant")
print(reg1)