By Ruilin Li
This package provide functions that solve the Regularized Cox proportional hazard model with time-varying covariate
See DESCRIPTION and vignettes to use this package.
There are a few ways to represent time-varying covariates. In this example I will use the Stanford Heart Transplant data to demonstrate how to use this package when the time-varying covariate is specified by a operation (such as a surgery). Another form of time-varying covariate are same variables measured over time, which is easier to specify with this package.
library(survival)
library(dplyr)
N = nrow(jasa)
jasa$ID = 1:N
jasa$y = pmax(0.5, as.numeric(jasa$fu.date - jasa$accept.dt))
jasa$age = jasa$age - 48
jasa$year = as.numeric(jasa$accept.dt - as.Date("1967-10-01"))/365.25
jasa$txtime= with(jasa, ifelse(tx.date== fu.date,
(tx.date -accept.dt) -.5,
(tx.date - accept.dt)))
jasa$status = jasa$fustat
Notice that:
- The response variable y here is the time from accept date to last followup, which is possibly adeath time.
- The status variable is 1 if death happend before last followup, 0 otherwise.
- txtime is the waiting time of heart transplant after the patient us accepted.
- In this example, the time varying covariates are the transplant indicator, and the interaction between transplant and age.
The jasa data frame can be readily fed into the coxtv function. Now we put the time varying covariates into a format suitable for this package.
# at the beginning no-one has transplant
tv_trans = data.frame(ID=1:N, time=0, value = 0)
tmp = jasa %>% select(c(ID, txtime)) %>% filter(!is.na(txtime))
tmp$time = tmp$txtime
tmp$value = 1
tmp = select(tmp, c(ID, time, value))
# At the transplant, the transplant indicator becomes 1
tv_trans = rbind(tv_trans, tmp)
# The interaction between age and transplant
tv_inter = tv_trans
tv_inter$value = tv_inter$value * jasa$age[match(tv_inter$ID, jasa$ID)]
tv_list = list(transplant = tv_trans, transplant_age = tv_inter)
Now we can fit a model
library(coxtv)
result = coxtv(jasa, tv_list,c('surgery', 'year', 'age'),c(0.01, 0.0))
result
#> [[1]]
#> transplant transplant_age surgery year age
#> 0.00000000 0.02674333 -0.50728342 -0.13635015 0.01582830
#>
#> [[2]]
#> transplant transplant_age surgery year age
#> 0.04449054 0.02702202 -0.62291877 -0.13600685 0.01528013
Compute the training C-index:
cindex_tv(jasa, tv_list,c('surgery', 'year', 'age'), result[[1]])
#> [1] 0.6837927
cindex_tv(jasa, tv_list,c('surgery', 'year', 'age'), result[[2]])
#> [1] 0.6813671
We can also draw a Kaplan-Meier curve based on a time varying covariate. We use the definition defined in section four of this paper.
KM_curve_tv(jasa, tv_list[[1]], ngroup=2)
