Cox Regression with Missing not at Random Failure Indicators

Implements estimation for the Cox (1972, 1975) proportional hazards model when the failure indicator (cause of failure) is missing not at random (MNAR), following the two adjusted imputation-based estimating equations of Liu and Liu (2026) . Also provided for comparison are the full-data partial-likelihood estimator of Andersen and Gill (1982) , the complete-case estimator, and the missing-at-random imputation estimator of Liu and Wang (2010, Statistica Sinica, 20, 1125-1142). The probability models for the failure indicator and for the missingness mechanism are estimated jointly by maximum likelihood following Sun, Xie, and Liang (2013) , and a Nadaraya-Watson kernel-smoothed estimator of the missingness propensity is constructed following Qiu, Chen, and Zhou (2015) . Both an asymptotic (sandwich-type) variance estimator and a nonparametric bootstrap variance estimator are provided. When failure indicators are fully observed the estimators reduce algebraically to the classical Cox partial-likelihood estimator.

coxmnar: Cox Regression with Missing Not at Random Failure Indicators

coxmnar implements estimation for the Cox proportional hazards model when the failure indicator (cause of failure) is missing not at random (MNAR), following the methodology of Liu and Liu (2026) (Statistics and Computing, 36, 112).

Features

• Adjusted Imputation (AI) ($\hat{\beta}_n^{AI}$) and Adjusted Complete (AC) ($\hat{\beta}_n^{AC}$) estimators under MNAR.
• Benchmark estimators: Complete-Case (CC), Missing-at-Random (MAR), and Full-Data (full).
• Joint maximum likelihood estimation of outcome and missingness propensity models via L-BFGS-B.
• Nadaraya-Watson kernel propensity smoothing with 5 kernel choices and automatic bandwidth selection.
• Nonparametric bootstrap and asymptotic sandwich variance estimators.
• Data simulator simulate_coxmnar_data() implementing paper simulation DGPs.

Installation

You can install the development version of coxmnar from GitHub:

# install.packages("devtools")
devtools::install_github("shikhartyagi/coxmnar")

Quick Start

library(coxmnar)

# Simulate survival data with MNAR missing failure indicators
set.seed(123)
sim_data <- simulate_coxmnar_data(n = 200, beta0 = 0.2, mechanism = "mnar", seed = 123)

# Fit Adjusted-Imputation MNAR estimator
fit <- coxmnar(
  cause ~ Z,
  time = "time",
  data = sim_data,
  method = "ai",
  B = 100L,
  seed = 123
)

summary(fit)

Citation

To cite coxmnar in publications:

citation("coxmnar")

Reference

• Liu, Y., & Liu, K. (2026). Estimation in the Cox proportional hazards model with missing not at random failure indicators. Statistics and Computing, 36, 112. doi:10.1007/s11222-026-10857-1