cphGM {dscoreMSM} | R Documentation |
CoxPH model with parametric baseline and frailty terms
Description
Function for estimating the parameters of coxPH model with frailty terms
Usage
cphGM(
formula,
fterm,
Time,
status,
id,
data,
bhdist,
method = "L-BFGS-B",
maxit = 200
)
Arguments
formula |
survival model formula like Surv(time,status)~x1+x2 |
fterm |
frailty term like c('gamma','center'). Currently we have the option for gamma distribution. |
Time |
survival time column |
status |
survival status column |
id |
id column |
data |
dataset |
bhdist |
distribution of survival time at baseline. Available option 'weibull','exponential','gompertz', |
method |
options are 'LFGS','L-BFGS-G','CG' etc. for more details see optim |
maxit |
maximum number of iteration |
Details
The hazard model is as follows:
h_i(t)=z_ih_0(t)exp(\textbf{x}_i\beta)\;;i=1,2,3,...,n
where baseline survival distribution could be Weibull distribution and the hazard function is:
h_0(t)=\rho \lambda t^{\rho-1}
. Similarly we can have Expoenetial, log logistic distribution. The following are the formula for hazard and cummulative hazard function
For exponential: h_0(t)=\lambda
and H_0(t)=\lambda t
\;\lambda>0
Gompertz: h_0(t)=\lambda exp(\gamma t)
and H_0(t)=\frac{\lambda}{\gamma}(exp(\gamma t)-1)
;\lambda,\gamma>0
The frailty term z_i
follows Gamma distribution with parameter \theta
. The parameter estimates are obtained by maximising the log likelihood
\prod_{i=1}^{n}l_i(\beta,\theta,\lambda,\rho)
The method argument allows the user to select suitable optimisation method available in optim
function.
Value
Estimates obtained from coxph model with the frailty terms.
Author(s)
Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra K. Vishwakarma
References
Vishwakarma, G. K., Bhattacherjee, A., Rajbongshi, B. K., & Tripathy, A. (2024). Censored imputation of time to event outcome through survival proximity score method. Journal of Computational and Applied Mathematics, 116103;
Bhattacharjee, A., Vishwakarma, G. K., Tripathy, A., & Rajbongshi, B. K. (2024). Competing risk multistate censored data modeling by propensity score matching method. Scientific Reports, 14(1), 4368.
See Also
Examples
##
X1<-matrix(rnorm(1000*2),1000,2)
simulated_data<-simfdata(n=1000,beta=c(0.5,0.5),fvar=0.5,
X=X1)
model1<-cphGM(formula=Surv(time,status)~X1+X2,
fterm<-c('gamma','id'),Time="time",status="status",
id="id",data=simulated_data,bhdist='weibull')
model1
##