cphGM function

CoxPH model with parametric baseline and frailty terms

Function for estimating the parameters of coxPH model with frailty terms

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

Returns

Estimates obtained from coxph model with the frailty terms.

Details

The hazard model is as follows:

where baseline survival distribution could be Weibull distribution and the hazard function is:

. 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

The method argument allows the user to select suitable optimisation method available in optim function.

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
##

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

dscore ,simfdata

Author(s)

Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra K. Vishwakarma