splineCox.reg {joint.Cox}

Fitting the Cox model for survival data using a penalized spline model

Description

Fitting the Cox proportional hazards model when the baseline hazard function is specified by a five-parameter spline model.

Usage

splineCox.reg(t.event, event, Z, xi1 = min(t.event), xi3 = max(t.event), 
kappa = c(seq(10, 1e+17, length = 30)), LCV.plot = TRUE,p0=rep(0,5+p))

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)

kappa

a vector for candidate smoothing parameters. Only positive values are allowed. Values too close to zero may yeild errors (see below).

LCV.plot

Plot the LCV curves if "TRUE". This plot is used to find the optimal value from the candidate smoothing parameters given by "kappa".

p0

Initial values to maximize the penalized likelihood (5+p parameters; five M-spline coefficients and p regression coefficients)

Details

One can perform Cox-type regression for censored survival data with covariates. The method is essentially the same as as Cox regression (Cox 1972) expect for the models of the baseline hazard function. Unlike the nonparametric model of Cox (1972), the method applies a five-parameter spline model as originally proposed by Emura et al. (2017). The method is detailed in Section 2.4 of Emura et al. (2019). See also Shih and Emura (2021) for more details. This method is also used as a subroutine for computing the optimal smoothing parameter (kappa1 and kappa2) for many advanced functions, such as "jointCox.reg", "cmprskCox.reg", and "condCox.reg". The definition of LCV is given in Section 3.7 of Emura et al. (2019). See also Shih and Emura (2021). The error message "Error in nlm(l.func, p = rep(0, 5 + p), hessian = TRUE):non-finite value supplied by 'nlm'" may imply that some candidate parameters for kappa are too close to zero; please exclude such values from kappa. The output values are usually similar to those given by "coxph(Surv(t.event,event)~Z)". Unreasonable output values are usually caused by a wrong choice of "kappa" and occasionary caused by a wrong choice of p0.

Value

beta

Regression coefficient for Z

h

M-spline coefficients

h_var

Variance of M-spline coefficients

kappa

smoothing parameter at the optimal LCV

DF

degree of freedom at the optimal LCV

LCV

the optimal LCV(=logL-DF)

Author(s)

Takeshi Emura

References

Cox DR (1972), Regression models and life-tables, JRSS(B) 34(2):187-202.

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

data(dataOvarian)
t.event=dataOvarian$t.event
event=dataOvarian$event
t.death=dataOvarian$t.death
death=dataOvarian$death
Z=dataOvarian$CXCL12
#splineCox.reg(t.event,event,Z,kappa=c(seq(10,1e+17,length=30)))