jointCox.Weibull.reg {joint.Cox} | R Documentation |
Weibull-based Likelihood Estimation under the Joint Cox Models Between Tumour Progression and Death for Meta-Analysis
Description
Perform Weibull regression analyses under a copula-based joint Cox proportional hazards model between tumour progression and death for meta-analysis, which is proposed by Wu et al. (2020).
Usage
jointCox.Weibull.reg(t.event, event, t.death, death, Z1, Z2, group, alpha = 1,
Randomize_num = 10, u.min = 0.001, u.max = 10, Adj = 500,convergence.par=FALSE)
Arguments
t.event |
a vector for time-to-tumour progression (TTP) |
event |
a vector for progression indicator (=1 if progression; =0 if not progression) |
t.death |
a vector for overall survival (OS), i.e., time-to-death |
death |
a vector for death indicator(=1 if death; =0 if not death) |
Z1 |
a matrix for covariates associated with TTP; ncol(Z1)=the number of covariates |
Z2 |
a matrix for covariates associated with OS; ncol(Z2)=the number of covariates |
group |
a vector for group identification numbers, like 1,2,3.... |
alpha |
A value related to the frailty (e.g., alpha=0 or =1); alpha=1 is default |
Randomize_num |
The number of randomizations for the ititial p0 |
u.min |
the lower bound of the numerical integration for the frailty term |
u.max |
the upper bound of the numerical integration for the frailty term |
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) |
Details
We employ "nlm" routine to maximize the penalized likelihood function with the initial value described in Wu et al. (2020). If "nlm" does not converge, then we randomize the initial value by adding uniform random variables (Hu and Emura, 2015).
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 |
tau |
Kendall's tau corresponding to the copula parameter |
scale1 |
Scale parameter for the Weibull model of TTP |
shape1 |
Shape parameter for the Weibull model of TTP |
scale2 |
Scale parameter for the Weibull model of OS |
shape2 |
Shape parameter for the Weibull model of OS |
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).
Author(s)
Takeshi Emura
References
Wu BH, Michimae H, Emura T (2020), Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty-copula model. Comp Stat 35(4):1525-52
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
Hu YH, Emura T (2015), Maximum likelihood estimation for a special exponential family under random double-truncation, Comp Stat 30 (4): 1199-1229
Examples
data(dataOvarian)
t.event=dataOvarian$t.event
event=dataOvarian$event
t.death=dataOvarian$t.death
death=dataOvarian$death
Z1=dataOvarian$CXCL12
group=dataOvarian$group
alpha_given=0
#set.seed(1)
#jointCox.Weibull.reg(t.event=t.event,event=event,t.death=t.death,death=death,
# Z1=Z1,Z2=Z1,group=group,alpha=alpha_given,Adj=500)