A Pairwise Likelihood Augmented Cox Estimator for Left-Truncated Data

A semi-parametric estimation method for the Cox model with left-truncated data using augmented information from the marginal of truncation times.

plac

This R package implements a semi-parametric estimation method for the Cox model introduced in the paper A Pairwise Likelihood Augmented Cox Estimator for Left-truncated data by Wu et al. (2018). It gives more efficient estimate for left-truncated survival data using the marginal survival information up to the start of follow-up (when the subject enters the risk set). The independence between the underlying truncation time distribution and the covariates is the only additional assumption, which holds true for most applications of length-biased sampling problem and beyond.

Installation

The package can be installed from CRAN:

install.packages("plac")

You can also install the development version of it from GitHub with:

# install.packages("devtools")
devtools::install_github("942kid/plac")

Example

The main wrapper function PLAC() calls the appropriate working function according to the covariate types in the dataset. For example,

library(plac)
#> Loading required package: survival

# When only time-invariant covariates are involved
dat1 <- sim.ltrc(n = 50)$dat
PLAC(
  ltrc.formula = Surv(As, Ys, Ds) ~ Z1 + Z2,
  ltrc.data = dat1,
  td.type = "none"
)
#> Calling PLAC_TI()...
#> 12 Iterations
#> Coefficient Estimates:
#>    est.Cox se.Cox p.Cox est.PLAC se.PLAC p.PLAC
#> Z1   2.055  0.431 0.000    1.804   0.357  0.000
#> Z2   0.919  0.347 0.008    0.804   0.259  0.002

# When there is a time-dependent covariate that is independent of the truncation time
dat2 <- sim.ltrc(n = 50, time.dep = TRUE, distr.A = "binomial", p.A = 0.8, Cmax = 5)$dat
PLAC(
  ltrc.formula = Surv(As, Ys, Ds) ~ Z,
  ltrc.data = dat2, td.type = "independent",
  td.var = "Zv", t.jump = "zeta"
)
#> Calling PLAC_TD()...
#> 100 Iterations
#> 
#> Coefficient Estimates:
#>    est.Cox se.Cox p.Cox est.PLAC se.PLAC p.PLAC
#> Z    0.866  0.330 0.009    0.795   0.224      0
#> Zv   0.877  0.355 0.014    0.864   0.214      0

# When there is a time-dependent covariate that depends on the truncation time
dat3 <- sim.ltrc(n = 50, time.dep = TRUE, Zv.depA = TRUE, Cmax = 5)$dat
PLAC(
  ltrc.formula = Surv(As, Ys, Ds) ~ Z,
  ltrc.data = dat3, td.type = "post-trunc",
  td.var = "Zv", t.jump = "zeta"
)
#> Calling PLAC_TDR()...
#> 8 Iterations
#> 
#> Coefficient Estimates:
#>    est.Cox se.Cox p.Cox est.PLAC se.PLAC p.PLAC
#> Z    0.668  0.301 0.027    0.487   0.246  0.047
#> Zv   0.915  0.327 0.005    0.938   0.301  0.002

For computation details, please refer to the document of the main wrapper function:

help(PLAC)

References

Wu, F., Kim, S., Qin, J., Saran, R., & Li, Y. (2018). A pairwise likelihood augmented Cox estimator for left‐truncated data. Biometrics, 74(1), 100-108.