Proximal Weighting Estimation for Dependent Left Truncation

Implements proximal weighting estimators for the expectation of an arbitrarily transformed event time under dependent left truncation, with optional inverse probability of censoring weighting to handle right censoring. The methods leverage proxy variables to handle dependent left truncation in settings where dependence-inducing factors are not fully observed.

truncProxy

truncProxy implements proximal weighting estimators for the expectation of an arbitrarily transformed event time under dependent left truncation, with optional inverse probability of censoring weighting to handle right censoring.

The current package exports:

• PQB_estimator()
• PQB_IPCW_estimator()

The associated paper is available at https://arxiv.org/pdf/2512.21283.

Installation

Once the package is published on CRAN, it can be installed with:

install.packages("truncProxy")

During development, it can also be installed from GitHub with:

devtools::install_github("wangyuyao98/truncProxy_weighting", subdir = "pkg/truncProxy")

During development from this repository root, it can be installed with:

devtools::install("pkg/truncProxy")

Simulation-Based Example

library(truncProxy)

simulate_truncproxy_data <- function(n = 300, multi = 20) {
  para_set <- list(
    mu_Z = 0.6,
    sigma_Z = 0.45,
    mu_U = 0.6,
    sigma_U = 0.45,
    mu_W1 = c(1.4, 0.3, -0.9),
    sigma_W1 = 0.25,
    mu_W2 = c(0.6, -0.2, 0.5),
    sigma_W2 = 0.25,
    mu_Q = c(0.1, 0.25, 1),
    mu_TT = c(0.25, 0.3, 0.6),
    T.min = 0,
    Q.max = 2,
    shape_D = 2,
    scale_D = 2
  )

  Z <- pmax(0, para_set$mu_Z + rnorm(multi * n, 0, para_set$sigma_Z))
  U <- pmax(0, para_set$mu_U + rnorm(multi * n, 0, para_set$sigma_U))
  W1 <- cbind(1, Z, U) %*% para_set$mu_W1 + rnorm(multi * n, 0, para_set$sigma_W1)
  W2 <- cbind(1, Z, U) %*% para_set$mu_W2 + rnorm(multi * n, 0, para_set$sigma_W2)
  TT <- para_set$T.min + rexp(multi * n, cbind(1, Z, U) %*% para_set$mu_TT)

  tau <- para_set$Q.max
  Q2 <- rexp(multi * n, cbind(1, Z, U) %*% para_set$mu_Q)
  Q2 <- pmin(Q2, tau)
  Q <- tau - Q2

  D <- rweibull(n, shape = para_set$shape_D, scale = para_set$scale_D)
  C <- Q + D
  X <- pmin(TT, C)
  delta <- as.integer(TT < C)

  dat_full <- data.frame(X = X, TT = TT, delta = delta, Q = Q, W1 = W1, W2 = W2, Z = Z)
  dat_obs <- dat_full[dat_full$Q < dat_full$TT, , drop = FALSE]
  dat_obs[seq_len(n), , drop = FALSE]
}

set.seed(1)
dat <- simulate_truncproxy_data()
nu <- function(t) as.numeric(t > 1)

PQB_estimator(
  nu = nu,
  dat = dat,
  time.name = "TT",
  Q.name = "Q",
  W1.name = "W1",
  W2.name = "W2",
  Z.name = "Z"
)

PQB_IPCW_estimator(
  nu = nu,
  t0 = 1,
  dat = dat,
  time.name = "X",
  Q.name = "Q",
  event.name = "delta",
  W1.name = "W1",
  W2.name = "W2",
  Z.name = "Z",
  IPCW_time_varying = TRUE
)

Notes

In the current implementation, the IPCW weights are computed from a weighted Kaplan-Meier estimator on the residual time scale time - Q.