joint.Cox (version 3.16)

cmprskCox.reg: The Competing Risks Version of Penalized Likelihood Estimation under the Joint Cox Models Between Tumour Progression and Death for Meta-Analysis

Description

Perform regression analyses under a copula-based joint Cox proportional hazards model between tumour progression and death for meta-analysis, which is proposed in Section 6.2 of Emura et al. (2017) and Section 5.1 of Emura et al. (2020). This is the competing risks version of "jointCox.reg". To avoid the indentifiability problem, the copula parameter (theta) should be given by user, e.g., theta=2. The method is applicable for meta-analysis combining several studies or for cluster survival data.

Usage

cmprskCox.reg(t.event, event1, event2, Z1, Z2, group, theta, alpha = 1,
 kappa1 = c(seq(10, 1e+17, length = 30)), kappa2 = c(seq(10, 1e+17, length = 30)),
 LCV.plot = TRUE, Randomize_num = 10, Adj = 500,convergence.par=FALSE)

Arguments

t.event

a vector for event tims

event1

a vector for event-type 1 indicators (=1 with event; =0 without event)

event2

a vector for event-type 2 indicators (=1 with event; =0 without event)

Z1

a matrix for covariates associated with event-type 1; ncol(Z1)=the number of covariates

Z2

a matrix for covariates associated with event-type 2; ncol(Z2)=the number of covariates

group

a vector for a group identification number, like 1,2,3....

theta

A copula parameter under the Clayton copula (theta > 0)

alpha

A value related to the frailty (e.g., alpha=0 or =1); alpha=1 is default

kappa1

a vector for candidate smoothing parameters

kappa2

a vector for candidate smoothing parameters

LCV.plot

Plot the LCV curves if "TRUE"

Randomize_num

The number of randomizations for the ititial p0

Adj

Numerical adjustment to prevent overflow; Adj=500 is recommended

convergence.par

If TRUE, the converged estimate, gradient, and Hessian matrix are given (log-transformed)

Value

count

Count for event occurences

beta1

Regression coefficient for Z1

beta2

Regression coefficient for Z2

eta

Frailty parameter (variance)

theta

Copula parameter under the Clayton copula (fixed by user)

tau

Kendall's tau corresponding to the copula parameter

LCV1

Likelihood cross-validation for event-type 1

LCV2

Likelihood cross-validation for event-type 2

g

M-spline coefficients for event-type 1

h

M-spline coefficients for event-type 2

g_var

Variance of M-spline coefficients for event-type 1

h_var

Variance of M-spline coefficients for event-type 2

convergence

convergence results for maximizing penalized likelihood

convergence.parameters

converged estimate, gradient, and Hessian matrix (log-transformed)

Error

"Error in integrate(func1, 0.001, 10, stop.on.error = FALSE):non-finite function value", an error occurring when the penalized likelihood is maximizad by "nlm". The error may frequently occur during the iterations for maximizing the penalized likelihood, but is not crucial (can simply be ignored).

Warning

"NA/Inf replaced by maximum positive value", an error occurring when the penalized likelihood is maximizad by "nlm". The error frequently occurs during the iterations for maximizing the penalized likelihood, but is not crucial (can simply be ignored).

Details

We employ "nlm" routine to maximize the penalized likelihood function with the initial value described in Emura et al. (2015). If "nlm" does not converge, then we randomize the initial value by adding uniform random variables (Hu and Emura, 2015).

References

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

Emura T, Shih JH, Ha ID, Wilke RA (2020), Comparison of the marginal hazard model and the sub-distribution hazard model for competing risks under an assumed copula, Stat Methods Med Res, 29(8): 2307-27

Hu YH, Emura T (2015), Maximum likelihood estimation for a special exponential family under random double-truncation, Compu Stat 30 (4): 1199-1229

Examples

# NOT RUN {
data(dataOvarian)
t.event=dataOvarian$t.event
t.death=dataOvarian$t.death
event=dataOvarian$event
death=dataOvarian$death
non.event=which(event==1 & death==1 & t.event==t.death)
non.death=which(event==1 & death==1 & t.event<t.death)
event[non.event]=0 ## relapse before death
death[non.death]=0 ## death before relapse (tie is counted as death)
Z=as.matrix(dataOvarian$CXCL12)
group=dataOvarian$group
alpha_given=0
theta=2.35
kappa_grid=seq(10,1e+17,length = 30)

#set.seed(1)
#cmprskCox.reg(t.event=t.event,event1=event,event2=death,
#              Z1=Z,Z2=Z,group=group,theta=theta,alpha=alpha_given,
#              kappa1=kappa_grid,kappa2=kappa_grid,LCV.plot=TRUE,Adj=500)
# }