I.spline {joint.Cox}

I-spline basis function

Description

Calculate the I-spline basis functions (the integrals of the M-spline basis functions).

Usage

I.spline(time, xi1, xi3)

Arguments

time

a vector of time points

xi1

lower bound of time points

xi3

upper bound of time points

Details

The output shows the values of the 5 basis functions at "time", giving a matrix with nrow=length(time) and ncol=5. The five basis functions were originally given in the Supplementary Material of Emura et al. (2017). More details can be found in Emura and Chen (2018), Emura et al. (2019), and Shih and Emura (2021). The "time" argument should be a vector satisfying the contraints xi1<=time<=xi3. If "time" does not meet the constraints, error messages are shown.

Value

NULL

A matrix with nrow=length(time) and ncol=5, containing the values of the 5 I-spline basis functions at "time".

Author(s)

Takeshi Emura

References

Emura T, Chen YH (2018). Analysis of Survival Data with Dependent Censoring, Copula-Based Approaches, JSS Research Series in Statistics, Springer, Singapore.

Emura T, Matsui S, Rondeau V (2019), Survival Analysis with Correlated Endpoints; Joint Frailty-Copula Models, JSS Research Series in Statistics, Springer

Emura T, Nakatochi M, Murotani K, Rondeau V (2017), A joint frailty-copula model between tumour progression and death for meta-analysis, Stat Methods Med Res 26(6): 2649-66: Supplementary Material.

Shih JH, Emura T (2021) Penalized Cox regression with a five-parameter spline model, Commun Stat-Theor 50(16):3749-68

Examples

I.spline(time=c(1,2,3),xi1=1,xi3=3)