Package {coxmnar}

Title:	Cox Regression with Missing not at Random Failure Indicators
Version:	0.1.0
Description:	Implements estimation for the Cox (1972, 1975) <doi:10.1111/j.2517-6161.1972.tb00899.x> <doi:10.1093/biomet/62.2.269> 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) <doi:10.1007/s11222-026-10857-1>. Also provided for comparison are the full-data partial-likelihood estimator of Andersen and Gill (1982) <doi:10.1214/aos/1176345976>, 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) <doi:10.1007/s11425-012-4492-x>, and a Nadaraya-Watson kernel-smoothed estimator of the missingness propensity is constructed following Qiu, Chen, and Zhou (2015) <doi:10.1016/j.spl.2014.12.006>. 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.
License:	GPL (≥ 3)
Encoding:	UTF-8
Language:	en-US
Depends:	R (≥ 4.1.0)
Imports:	survival (≥ 3.5-0), stats, Rdpack
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown, covr
RoxygenNote:	7.3.3
VignetteBuilder:	knitr
RdMacros:	Rdpack
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-07-22 23:23:20 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-07-31 15:10:02 UTC

coxmnar: Cox Regression with Missing Not at Random Failure Indicators

Description

Implements estimation for the Cox proportional hazards model when failure indicators are missing not at random (MNAR) following the methodology of Liu and Liu (2026).

Author(s)

Maintainer: Shikhar Tyagi shikhar1093tyagi@gmail.com (ORCID)

Authors:

• Arvind Pandey arvindmzu@gmail.com

• Bhupendra Singh bhupendra.rana@gmail.com

• Vrijesh Tripathi vrijesh.tripathi@uwi.edu

References

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.

Asymptotic and Nonparametric Bootstrap Variance Estimation

Description

Asymptotic and Nonparametric Bootstrap Variance Estimation

Usage

asymptotic_variance(
  val_data,
  beta_hat,
  theta_hat,
  alpha_hat,
  m_formula,
  pi_formula,
  w,
  method,
  control = coxmnar_control()
)

Breslow Baseline Cumulative Hazard and Survival Functions

Description

Breslow Baseline Cumulative Hazard and Survival Functions

Usage

breslow_baseline_hazard(Z, time, w, beta)

Fit probability models m(w, theta) and pi(w, alpha) jointly by maximum likelihood

Description

Fit probability models m(w, theta) and pi(w, alpha) jointly by maximum likelihood

Usage

build_design_matrix(formula, data)

References

Byrd RH, Lu P, Nocedal J, Zhu C (1995). “A limited memory algorithm for bound constrained optimization.” SIAM Journal on Scientific Computing, 16(5), 1190–1208. doi:10.1137/0916069.

Sun Z, Xie T, Liang H (2013). “Statistical inference for right-censored data with nonignorable missing censoring indicators.” Science China Mathematics, 56(6), 1263–1278. doi:10.1007/s11425-012-4492-x.

Reverse cumulative risk set calculations, Cox score, Hessian, and Newton-Raphson solver

Description

Reverse cumulative risk set calculations, Cox score, Hessian, and Newton-Raphson solver

Usage

compute_cox_risk_sums(Z, time, beta)

References

Cox DR (1972). “Regression models and life-tables.” Journal of the Royal Statistical Society, Series B, 34(2), 187–220. doi:10.1111/j.2517-6161.1972.tb00899.x.

Cox DR (1975). “Partial likelihood.” Biometrika, 62(2), 269–276. doi:10.1093/biomet/62.2.269.

Cox Regression with Missing Not At Random Failure Indicators

Description

Fits the Cox proportional hazards model when failure indicators (causes of failure) are missing not at random (MNAR), using the adjusted imputation estimators of Liu and Liu (2026). Also supports complete-case, missing-at-random (MAR), and benchmark full-data estimation.

Usage

coxmnar(
  formula,
  time,
  cause = NULL,
  observed = NULL,
  data,
  method = c("ai", "ac", "mar", "cc", "full"),
  m_formula = NULL,
  pi_formula = NULL,
  kernel = c("gaussian", "triangular", "epanechnikov", "quartic", "triweight"),
  bandwidth = NULL,
  se_method = c("bootstrap", "asymptotic", "both", "none"),
  B = 500L,
  control = coxmnar_control(),
  ties = c("efron", "breslow"),
  x = FALSE,
  seed = NULL
)

Arguments

Value

An object of S3 class "coxmnar", containing estimated coefficients, variance-covariance matrix, standard errors, z-scores, p-values, fitted probability models, baseline hazard, and model diagnostics.

References

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.

Andersen PK, Gill RD (1982). “Cox's regression model for counting processes: a large sample study.” The Annals of Statistics, 10(4), 1100–1120. doi:10.1214/aos/1176345976.

Liu C, Wang Q (2010). “Semiparametric estimation for regression coefficients in the Cox model with failure indicators missing at random.” Statistica Sinica, 20(3), 1125–1142.

Sun Z, Xie T, Liang H (2013). “Statistical inference for right-censored data with nonignorable missing censoring indicators.” Science China Mathematics, 56(6), 1263–1278. doi:10.1007/s11425-012-4492-x.

Qiu Z, Chen X, Zhou Y (2015). “A kernel-assisted imputation estimating method for the additive hazards model with missing censoring indicator.” Statistics & Probability Letters, 98, 89–97. doi:10.1016/j.spl.2014.12.006.

Examples

set.seed(123)
sim_data <- simulate_coxmnar_data(n = 100, beta0 = 0.2, mechanism = "mnar", seed = 123)
fit <- coxmnar(cause ~ Z, time = "time", data = sim_data, method = "ai", B = 10L, seed = 123)
print(fit)
summary(fit)

S3 Methods for coxmnar Objects

Description

Print, summary, prediction, confidence intervals, survival curves, and plotting for coxmnar objects.

Usage

## S3 method for class 'coxmnar'
print(x, ...)

## S3 method for class 'coxmnar'
summary(object, conf.level = 0.95, ...)

## S3 method for class 'summary.coxmnar'
print(x, ...)

## S3 method for class 'coxmnar'
coef(object, ...)

## S3 method for class 'coxmnar'
vcov(object, ...)

## S3 method for class 'coxmnar'
confint(object, parm, level = 0.95, ...)

## S3 method for class 'coxmnar'
predict(
  object,
  newdata = NULL,
  type = c("lp", "risk", "survival", "cumhaz"),
  times = NULL,
  ...
)

## S3 method for class 'coxmnar'
survfit(formula, newdata = NULL, ...)

## S3 method for class 'coxmnar'
plot(x, compare_km = TRUE, ...)

## S3 method for class 'coxmnar_compare'
summary(object, ...)

## S3 method for class 'summary.coxmnar_compare'
print(x, ...)

Arguments

Value

Various objects depending on the method called.

Compare Multiple Coxmnar Estimation Methods

Description

Convenience wrapper to fit and compare multiple estimation methods on the same dataset.

Usage

coxmnar_compare(
  formula,
  time,
  data,
  methods = c("ai", "ac", "mar", "cc", "full"),
  ...
)

Arguments

Value

An object of class "coxmnar_compare", containing a list of fits and a comparison table.

Examples

set.seed(123)
sim_data <- simulate_coxmnar_data(n = 100, beta0 = 0.2, mechanism = "mnar", seed = 123)
comp <- coxmnar_compare(cause ~ Z, time = "time", data = sim_data, B = 10L, seed = 123)
summary(comp)

Control Parameters for coxmnar

Description

Specifies numerical optimization, tolerance, and control parameters for coxmnar.

Usage

coxmnar_control(
  maxit = 200L,
  tol = 1e-08,
  eps = 1e-06,
  nn_fallback_k = NULL,
  boot_max_attempts_factor = 10L,
  optim_method = "L-BFGS-B",
  step_halving_max = 20L,
  on_failure = c("error", "warn"),
  verbose = FALSE
)

Arguments

Value

A validated control list.

Examples

ctrl <- coxmnar_control(maxit = 100L, tol = 1e-6)

Evaluate kernel functions

Description

Computes the kernel function value for 1D inputs. Supported kernels: '"gaussian"', '"triangular"', '"epanechnikov"', '"quartic"' (biweight), '"triweight"'.

Usage

eval_kernel(
  u,
  kernel = c("gaussian", "triangular", "epanechnikov", "quartic", "triweight")
)

Arguments

Value

Numeric array of same dimension as 'u'.

Nadaraya-Watson kernel propensity estimator u_hat_n(w)

Description

Nadaraya-Watson kernel propensity estimator u_hat_n(w)

Usage

nadaraya_watson(
  W_df,
  xi,
  eval_W_df = W_df,
  kernel = "gaussian",
  bandwidth = NULL,
  control = coxmnar_control()
)

References

Qiu Z, Chen X, Zhou Y (2015). “A kernel-assisted imputation estimating method for the additive hazards model with missing censoring indicator.” Statistics & Probability Letters, 98, 89–97. doi:10.1016/j.spl.2014.12.006.

Simulate Survival Data with MNAR or MAR Failure Indicators

Description

Generates synthetic survival data following the Cox proportional hazards model and missingness data-generating processes (DGPs) described in Sections 3.1-3.3 of Liu and Liu (2026).

Usage

simulate_coxmnar_data(
  n,
  beta0 = 0.2,
  mechanism = c("mnar", "mar"),
  covariate_dist = function(n) stats::runif(n, 0, 15),
  censoring_rate = 0.2,
  missing_rate = 0.2,
  conditionally_independent_censoring = FALSE,
  extended_missingness = FALSE,
  seed = NULL
)

Arguments

Value

A data frame with columns 'time', 'cause' (with 'NA' where 'xi=0'), 'Z' (or 'Z1'), and attributes recording ground truth parameters.

References

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.

Examples

set.seed(123)
sim_df <- simulate_coxmnar_data(n = 200, beta0 = 0.2, mechanism = "mnar", seed = 123)
head(sim_df)