Package coxerr performs the functional modeling methods
of Huang and Wang (2018) to accommodate dependent error in covariates of
the proportional hazards model. The adopted measurement error model has
minimal assumptions on the dependence structure, and an instrumental
variable is supposed to be available.
Simulate a dataset for the purpose of illustration, following Scenario 1 of Table 1 in Huang and Wang (2018):
size <- 300
bt0 <- 1
## true covariate
x <- rnorm(size)
## survival time, censoring time, follow-up time, censoring indicator
s <- rexp(size) * exp(-bt0 * x)
c <- runif(size) * ifelse(x <= 0, 4.3, 8.6)
t <- pmin(s, c)
dlt <- as.numeric(s <= c)
## mismeasured covariate with heterogeneous error, IV
w <- x + rnorm(size) * sqrt(pnorm(x) * 2) * 0.5 + 1
u <- x * 0.8 + rnorm(size) * 0.6
wuz <- cbind(w, u)Run the two proposed methods:
library(coxerr)
## estimation using PROP1
fit1 <- coxerr(t, dlt, wuz, 1)
fit1
#> $bt
#> [1] 1.068322
#>
#> $va
#> [,1]
#> [1,] 0.029144
#>
#> $succ
#> [1] TRUE
## estimation using PROP2
fit2 <- coxerr(t, dlt, wuz, 2)
fit2
#> $bt
#> [1] 1.067537
#>
#> $va
#> [,1]
#> [1,] 0.02456402
#>
#> $succ
#> [1] TRUEHuang, Y. and Wang, C. Y. (2018) Cox Regression with dependent error in covariates, Biometrics 74, 118–126.