splineCox.reg2: Fitting the five-parameter spline Cox model with a specified...

In splineCox: A Two-Stage Estimation Approach to Cox Regression Using M-Spline Function

Fitting the five-parameter spline Cox model with a specified shape, selecting the best fit

Description

splineCox.reg2 estimates the parameters of a five-parameter spline Cox model for multiple specified shapes and selects the best-fitting model based on the maximization of the log-likelihood function. This function supports predefined model shapes and custom numeric vectors of length 5. If numeric vectors are provided, they 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 for the best-fitting model, along with its 95 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.reg2(
  t.event,
  event,
  Z,
  xi1 = min(t.event),
  xi3 = max(t.event),
  model = names(shape.list),
  p0 = rep(0, 1 + ncol(as.matrix(Z))),
  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 list of character strings and/or numeric vectors of length 5 specifying the shapes of the baseline hazard function to evaluate. Character options include: "increase", "constant", "decrease", "unimodal1", "unimodal2", "unimodal3", "bathtub1", "bathtub2", "bathtub3". Numeric vectors must be of length 5 and will be normalized to have an L1 norm of 1. Default is names(shape.list), which includes all predefined models.
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 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.

Value

A list containing the following components:

model	A character string indicating the shape of the baseline hazard function used.
parameter	A numeric vector of the parameters defining the baseline hazard shape.
beta	A named vector with the estimates, standard errors, and 95% confidence intervals for the regression coefficients.
gamma	A named vector with the estimate, standard error, and 95% confidence interval for the baseline hazard parameter.
loglik	A named vector containing the log-likelihood (LogLikelihood), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) for the best-fitting model.
other_models	A data frame containing the log-likelihood (LogLikelihood) for all other evaluated models, with model names as row names.
plot	A baseline hazard function plot for the best-fitting model (if plot = 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. \Sexpr[results=rd]{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

M = c("constant", "increase", "decrease")
reg2 <- splineCox.reg2(t.event, event, Z, model = M)
print(reg2)

splineCox documentation built on Aug. 8, 2025, 7:21 p.m.