Package 'CoxAalenCR'

Title: Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks
Description: Implements the flexible additive-multiplicative Cox-Aalen subdistribution hazard regression model for competing risks data as proposed by Li and Long (2019) <doi:10.1007/s11424-019-7281-6>. The framework accommodates both time-varying non-parametric additive covariate effects through an Aalen (1980) additive model and constant multiplicative effects via a Cox proportional hazards structure, generalizing Scheike and Zhang (2002) <doi:10.1111/1467-9469.00065> and Martinussen and Scheike (2002) <doi:10.1093/biomet/89.2.283>. Includes inverse probability of censoring weighting (IPCW) with both Kaplan-Meier weights (Fine and Gray, 1999 <doi:10.1080/01621459.1999.10474144>) and covariate-dependent Cox censoring weights (He et al., 2016 <doi:10.1111/sjos.12172>; Li and Long, 2019 <doi:10.1007/s11424-019-7281-6>). Provides simultaneous estimating equations based on Huffer and McKeague (1991) <doi:10.1080/01621459.1991.10475010>, asymptotic sandwich variance estimation with censoring-weight martingale corrections, cumulative incidence function (CIF) prediction with pointwise confidence intervals, supremum-type goodness-of-fit tests for time-varying covariate effects, and Monte Carlo competing risks data simulation.
Authors: Shikhar Tyagi [aut, cre] (ORCID: <https://orcid.org/0000-0003-1606-0844>), Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer: Shikhar Tyagi <[email protected]>
License: GPL (>= 3)
Version: 0.1.0
Built: 2026-09-21 09:41:27 UTC
Source: https://github.com/cran/CoxAalenCR

Help Index

Akaike Information Criterion for Cox-Aalen Model

Description

AIC placeholder for semiparametric estimating equations.

Usage

## S3 method for class 'cox_aalen_fit'
AIC(object, ..., k = 2)

Arguments

object

an object of class "cox_aalen_fit".
...

further arguments.
k

numeric penalty per parameter (default 2).

Value

Numeric NA.

Predict Cumulative Incidence Functions for Cox-Aalen Model

Description

Computes predicted cumulative incidence functions (CIF) for specified covariate profiles under the additive-multiplicative Cox-Aalen model with analytical pointwise standard errors and confidence intervals as derived in Theorem 4.3 of Li and Long (2019) <doi:10.1007/s11424-019-7281-6>.

Usage

cif_predict(
  object,
  newdata = NULL,
  newZ = NULL,
  newtime = NULL,
  se.fit = TRUE,
  conf.level = 0.95,
  ...
)

Arguments

object

an object of class "cox_aalen_fit" or "cox_aalen".
newdata

matrix or data frame of new additive covariates XX. If NULL, uses the design matrix from the fitted object.
newZ

matrix or data frame of new multiplicative covariates ZZ. If NULL and object$n_mult > 0, uses the multiplicative covariates from the fitted object.
newtime

numeric vector of time points for prediction. If NULL, predictions are evaluated at all event times object$A_times.
se.fit

logical indicating whether standard errors and confidence intervals should be computed (TRUE or FALSE). Default is TRUE.
conf.level

numeric confidence level for pointwise confidence intervals (default 0.95).
...

additional arguments (currently unused).

Value

A list of class "cif_predict" containing:

cif

Numeric matrix of predicted CIF values (dimension nnew×ntimesn_{new} \times n_{times}).

se

Numeric matrix of pointwise standard errors (or NULL if se.fit = FALSE).

lower

Numeric matrix of lower confidence bounds clamped to [0,1][0, 1].

upper

Numeric matrix of upper confidence bounds clamped to [0,1][0, 1].

time

Numeric vector of time points where predictions are evaluated.

conf.level

Confidence level used.

References

Li, W. and Long, Y. (2019). An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data. Journal of Systems Science and Complexity, 32(6), 1727-1746. doi:10.1007/s11424-019-7281-6

Examples

set.seed(123)
dat <- simulate_coxaalen(n = 60, p = 0.3, censoring = "cox", cens_rate = 0.20)
fit <- cox_aalen_fit(
  time = dat$time,
  status = dat$status,
  X = cbind(Intercept = 1, X = dat$X),
  Z = matrix(dat$Z, ncol = 1, dimnames = list(NULL, "Z")),
  W = dat$W
)
pred <- cif_predict(fit, newdata = cbind(1, c(0.2, 0.8)), newZ = matrix(c(0.5, 0.5), ncol = 1))
print(pred$time[1:5])
print(pred$cif[, 1:5])

Extract Coefficients from Cox-Aalen Model

Description

Extracts multiplicative regression coefficients β\beta.

Usage

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

Arguments

object

an object of class "cox_aalen_fit".
...

further arguments.

Value

Named numeric vector of multiplicative regression coefficients.

Confidence Intervals for Cox-Aalen Multiplicative Parameters

Description

Computes Wald confidence intervals for multiplicative parameters β\beta.

Usage

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

Arguments

object

an object of class "cox_aalen_fit".
parm

a specification of which parameters are to be given confidence intervals.
level

confidence level (default 0.95).
...

further arguments.

Value

A matrix with columns for the lower and upper confidence limits.

Formula Interface for Additive-Multiplicative Cox-Aalen Model

Description

Fits the additive-multiplicative Cox-Aalen subdistribution hazard model for competing risks data using a formula specification.

Usage

cox_aalen(
  formula,
  data,
  W = NULL,
  weight_type = c("cox", "km"),
  tau = NULL,
  control = list()
)

Arguments

formula

a two-part formula of the form Surv(time, status) ~ X1 + X2 | Z1 + Z2 where terms before | represent additive (time-varying) covariates XX, and terms after | represent multiplicative (constant) covariates ZZ. If | is omitted, all RHS covariates are treated as additive.
data

a data frame containing the variables named in formula and W.
W

optional formula (e.g. ~ W1 + W2) or numeric matrix specifying covariates for the censoring distribution model.
weight_type

character string specifying the IPCW weighting scheme: "cox" (default) or "km".
tau

optional numeric value specifying the maximum follow-up time.
control

list of control parameters forwarded to cox_aalen_fit.

Value

An object of class c("cox_aalen", "cox_aalen_fit") containing the fitted model components, formula, and matched call. See cox_aalen_fit for full details.

References

Li, W. and Long, Y. (2019). An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data. Journal of Systems Science and Complexity, 32(6), 1727-1746. doi:10.1007/s11424-019-7281-6

Examples

set.seed(123)
dat <- simulate_coxaalen(n = 60, p = 0.3, censoring = "cox", cens_rate = 0.20)
fit <- cox_aalen(
  formula = survival::Surv(time, status) ~ X | Z,
  data = dat,
  W = ~ W,
  weight_type = "cox"
)
print(fit)
summary(fit)

Fit Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model

Description

Fits the flexible additive-multiplicative Cox-Aalen subdistribution hazard regression model for competing risks data via the estimating equations approach of Li and Long (2019) <doi:10.1007/s11424-019-7281-6>.

Usage

cox_aalen_fit(
  time,
  status,
  X,
  Z = NULL,
  W = NULL,
  weight_type = c("cox", "km"),
  tau = NULL,
  control = list()
)

Arguments

time

numeric vector of observed follow-up times Ti=min⁡(T~i,Ci)T_i = \min(\tilde{T}_i, C_i). Missing values are not allowed.
status

integer vector of event status indicators: 1 = event of interest (cause 1), 0 = censored, 2 = competing risk event. Missing values are not allowed.
X

matrix or data frame of covariates for the additive (time-varying) component. Must have nn rows.
Z

matrix or data frame of covariates for the multiplicative (constant) component. If NULL, a purely additive Aalen subdistribution model is fitted.
W

matrix or data frame of covariates for the censoring distribution model. Used when weight_type = "cox".
weight_type

character string specifying the IPCW weighting scheme: "cox" for covariate-dependent Cox censoring weights (default), or "km" for univariate Kaplan-Meier weights.
tau

numeric value specifying the maximum follow-up time. Default is the maximum observed time for cause 1 events.
control

a list of control parameters for the Newton-Raphson solver:

max_iter

integer maximum number of iterations (default 50).

tol

numeric convergence tolerance on parameter change and score norm (default 1e-6).

Value

An object of class "cox_aalen_fit" containing:

beta

Estimated regression coefficient vector for multiplicative covariates ZZ.

beta_se

Standard error vector for beta.

beta_names

Character vector of variable names for beta.

A

Matrix of cumulative additive coefficient estimates A^(t)\hat{A}(t) across event times.

A_times

Numeric vector of unique event times corresponding to rows of A.

A_se

Matrix of pointwise standard errors for A.

vcov

Estimated asymptotic variance-covariance matrix for beta.

var_A

3D array of variance-covariance matrices for A^(t)\hat{A}(t) across event times.

gamma

Estimated coefficient vector for the censoring model (if Cox weights used).

gamma_se

Standard error vector for gamma.

weight_type

Character string of weight type used.

psi1

Matrix of influence function values ψ^1i\hat{\psi}_{1i} for beta.

psi2

3D array of influence function values ψ^2i(t)\hat{\psi}_{2i}(t) for A.

n

Integer sample size.

n_add

Integer number of additive covariates.

n_mult

Integer number of multiplicative covariates.

converged

Logical indicating whether the optimization converged (TRUE or FALSE).

iterations

Integer number of iterations performed.

tau

Maximum follow-up time used.

call

Matched call.

References

Fine, J. P. and Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94(446), 496-509. doi:10.1080/01621459.1999.10474144

He, P., Ewell, M. and Scheike, T. H. (2016). A proportional hazards regression model for the subdistribution with covariates-adjusted censoring weight for competing risks data. Scandinavian Journal of Statistics, 43(1), 103-122. doi:10.1111/sjos.12172

Li, W. and Long, Y. (2019). An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data. Journal of Systems Science and Complexity, 32(6), 1727-1746. doi:10.1007/s11424-019-7281-6

Examples

set.seed(123)
dat <- simulate_coxaalen(n = 60, p = 0.3, censoring = "cox", cens_rate = 0.20)
fit <- cox_aalen_fit(
  time = dat$time,
  status = dat$status,
  X = cbind(Intercept = 1, X = dat$X),
  Z = matrix(dat$Z, ncol = 1, dimnames = list(NULL, "Z")),
  W = dat$W,
  weight_type = "cox"
)
print(fit)

Covariate-Dependent Cox IPCW Weights for Competing Risks

Description

Fits a Cox proportional hazards model for the censoring distribution conditional on censoring covariates WW and computes covariate-adjusted IPCW weights as proposed by He et al. (2016) <doi:10.1111/sjos.12172> and Li and Long (2019) <doi:10.1007/s11424-019-7281-6>.

Usage

cox_weights(time, status, W = NULL)

Arguments

time

numeric vector of observed follow-up times Ti=min⁡(T~i,Ci)T_i = \min(\tilde{T}_i, C_i). Missing values are not permitted.
status

integer vector of event status indicators: 1 = event of interest, 0 = censored, 2 = competing risk event. Missing values are not permitted.
W

matrix or data frame of covariates associated with the censoring distribution. Must have nn rows matching time. If NULL or empty, falls back to Kaplan-Meier weights.

Value

A list of class "cox_weights" containing:

gamma

Estimated regression coefficient vector for the censoring Cox model.

gamma_se

Standard error vector for gamma.

cox_fit

The fitted coxph model object for censoring.

baseline_haz

Data frame containing the Breslow cumulative baseline hazard estimate with columns time and hazard.

weights_obs

Numeric vector of censoring survival probabilities G^(Ti;Wi)\hat{G}(T_i; W_i) evaluated at each subject's observed time.

n

Integer sample size.

n_covariates

Integer number of censoring covariates.

References

He, P., Ewell, M. and Scheike, T. H. (2016). A proportional hazards regression model for the subdistribution with covariates-adjusted censoring weight for competing risks data. Scandinavian Journal of Statistics, 43(1), 103-122. doi:10.1111/sjos.12172

Li, W. and Long, Y. (2019). An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data. Journal of Systems Science and Complexity, 32(6), 1727-1746. doi:10.1007/s11424-019-7281-6

Examples

set.seed(123)
dat <- simulate_coxaalen(n = 60, p = 0.3, censoring = "cox", cens_rate = 0.20)
cw_res <- cox_weights(time = dat$time, status = dat$status, W = dat$W)
print(cw_res$gamma)

Kaplan-Meier IPCW Weights for Competing Risks

Description

Computes inverse probability of censoring weighting (IPCW) using the univariate Kaplan-Meier estimator for the censoring distribution as proposed by Fine and Gray (1999) <doi:10.1080/01621459.1999.10474144>.

Usage

km_weights(time, status)

Arguments

time

numeric vector of observed follow-up times Ti=min⁡(T~i,Ci)T_i = \min(\tilde{T}_i, C_i). Missing values (NA, NaN) are not permitted.
status

integer vector of event status indicators: 1 = event of interest (cause 1), 0 = censored, 2 = competing risk event. Missing values are not permitted.

Value

A list of class "km_weights" containing:

surv_fit

The fitted survfit object for censoring.

weights_obs

Numeric vector of censoring survival probabilities G^(Ti)\hat{G}(T_i) evaluated at each subject's observed time.

n

Integer sample size.

n_events

Integer count of events of interest.

n_censored

Integer count of censored observations.

n_competing

Integer count of competing risk events.

References

Fine, J. P. and Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94(446), 496-509. doi:10.1080/01621459.1999.10474144

Examples

set.seed(123)
dat <- simulate_coxaalen(n = 50, p = 0.3, censoring = "independent", cens_rate = 0.20)
km_res <- km_weights(time = dat$time, status = dat$status)
print(head(km_res$weights_obs))

Log-Likelihood Method for Cox-Aalen Model

Description

Pseudo log-likelihood for estimating equation models.

Usage

## S3 method for class 'cox_aalen_fit'
logLik(object, ...)

Arguments

object

an object of class "cox_aalen_fit".
...

further arguments.

Value

An object of class "logLik" (evaluates to NA with df and nobs attributes).

Number of Observations in Cox-Aalen Model

Description

Returns the number of observations used in model fitting.

Usage

## S3 method for class 'cox_aalen_fit'
nobs(object, ...)

Arguments

object

an object of class "cox_aalen_fit".
...

further arguments.

Value

An integer representing the number of observations.

Plot Predicted Cumulative Incidence Functions

Description

Displays predicted cumulative incidence functions (CIF) with optional confidence bands.

Usage

plot_cif(
  fit,
  newdata = NULL,
  newZ = NULL,
  conf_level = 0.95,
  xlab = "Time",
  ylab = "Cumulative Incidence",
  main = "Predicted Cumulative Incidence Function",
  col = NULL,
  ...
)

Arguments

fit

a fitted object of class "cox_aalen_fit" or "cox_aalen".
newdata

optional matrix or data frame of new additive covariates XX.
newZ

optional matrix or data frame of new multiplicative covariates ZZ.
conf_level

numeric confidence level for confidence bands (default 0.95).
xlab

character label for the x-axis (default "Time").
ylab

character label for the y-axis (default "Cumulative Incidence").
main

character title for the plot (default "Predicted Cumulative Incidence Function").
col

optional vector of colors for the predicted curves.
...

additional graphical parameters passed to plot.

Value

No return value, called for side effects.

Plot Cumulative Additive Regression Functions

Description

Plots the estimated non-parametric cumulative additive coefficient curves A^j(t)\hat{A}_j(t) over time along with 95% pointwise confidence bands.

Usage

plot_cumulative_coef(
  fit,
  conf_level = 0.95,
  xlab = "Time",
  ylab = "Cumulative Coefficient",
  main = NULL,
  ...
)

Arguments

fit

a fitted object of class "cox_aalen_fit" or "cox_aalen".
conf_level

numeric confidence level for confidence bands (default 0.95).
xlab

character label for the x-axis (default "Time").
ylab

character label for the y-axis (default "Cumulative Coefficient").
main

optional main title prefix.
...

additional graphical parameters.

Value

No return value, called for side effects.

Plot Method for Cox-Aalen Objects

Description

Plots predicted cumulative incidence functions or cumulative additive coefficient paths.

Usage

## S3 method for class 'cox_aalen'
plot(x, which = c("cif", "cumulative_coef"), ...)

Arguments

x

an object of class "cox_aalen" or "cox_aalen_fit".
which

character string specifying which plot to produce: "cif" or "cumulative_coef".
...

further arguments passed to plot_cif or plot_cumulative_coef.

Value

No return value, called for side effects.

Plot Method for Cox-Aalen Fit Objects

Description

S3 plot method for objects of class "cox_aalen_fit".

Usage

## S3 method for class 'cox_aalen_fit'
plot(x, which = c("cif", "cumulative_coef"), ...)

Arguments

x

an object of class "cox_aalen_fit".
which

character string specifying which plot to produce: "cif" or "cumulative_coef".
...

further arguments passed to plotting routines.

Value

No return value, called for side effects.

Predict Method for Cox-Aalen Objects

Description

Predicts cumulative incidence functions using fitted model.

Usage

## S3 method for class 'cox_aalen'
predict(
  object,
  newdata = NULL,
  newtime = NULL,
  se.fit = TRUE,
  conf.level = 0.95,
  ...
)

Arguments

object

an object of class "cox_aalen".
newdata

optional data frame of new observation profiles.
newtime

optional numeric vector of prediction times.
se.fit

logical indicating whether standard errors should be computed.
conf.level

numeric confidence level (default 0.95).
...

further arguments.

Value

An object of class "cif_predict".

Print Method for Cox-Aalen Formula Object

Description

Prints the matched call and model summary.

Usage

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

Arguments

x

an object of class "cox_aalen".
...

further arguments passed to or from other methods.

Value

No return value, called for side effects.

Print Method for Cox-Aalen Fitted Models

Description

Prints a concise summary of the fitted additive-multiplicative Cox-Aalen model.

Usage

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

Arguments

x

an object of class "cox_aalen_fit" or "cox_aalen".
...

further arguments passed to or from other methods.

Value

No return value, called for side effects.

Print Method for Simulation Study Results

Description

Prints the formatted simulation study performance metrics.

Usage

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

Arguments

x

an object of class "simulation_study".
...

further arguments.

Value

No return value, called for side effects.

Print Method for Summary of Cox-Aalen Model

Description

Prints the formatted summary table.

Usage

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

Arguments

x

an object of class "summary.cox_aalen_fit".
...

further arguments passed to or from other methods.

Value

No return value, called for side effects.

Print Method for Goodness-of-Fit Test

Description

Prints the summary of time-varying effect goodness-of-fit tests.

Usage

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

Arguments

x

an object of class "time_varying_test".
...

further arguments.

Value

No return value, called for side effects.

Simulate Competing Risks Data under Cox-Aalen Model

Description

Generates competing risks survival data exactly following the simulation design in Section 5 of Li and Long (2019) <doi:10.1007/s11424-019-7281-6>.

Usage

simulate_coxaalen(
  n,
  p = 0.3,
  alpha = 1,
  beta1 = 1,
  beta2 = 1,
  censoring = c("independent", "cox", "threshold_uniform"),
  cens_rate = c(0.2, 0.4)
)

Arguments

n

integer sample size.
p

numeric baseline subdistribution probability p=F1(∞;0,0)∈(0,1)p = F_1(\infty; 0, 0) \in (0, 1). Default is 0.3.
alpha

numeric parameter α\alpha for time-varying effect α2(t)=αe−t\alpha_2(t) = \alpha e^{-t}. Default is 1.0.
beta1

numeric true coefficient β1\beta_1 for the event of interest. Default is 1.0.
beta2

numeric true coefficient β2\beta_2 for the competing risk event. Default is 1.0.
censoring

character string specifying the censoring scenario: "independent" (C∼U(0,a)C \sim U(0, a)), "cox" (λC(t;W)=λCeγW\lambda_C(t; W) = \lambda_C e^{\gamma W}), or "threshold_uniform" (piecewise uniform depending on WW).
cens_rate

numeric target censoring rate: 0.20 (20%) or 0.40 (40%).

Value

A data frame with nn rows and columns:

time

Observed follow-up time Ti=min⁡(T~i,Ci)T_i = \min(\tilde{T}_i, C_i).

status

Event status indicator: 1 = cause 1 (event of interest), 2 = cause 2 (competing risk), 0 = censored.

X

Additive covariate generated from U(0,1)U(0, 1).

Z

Multiplicative covariate generated from U(0,1)U(0, 1).

W

Censoring-dependent covariate (equals ZZ).

References

Li, W. and Long, Y. (2019). An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data. Journal of Systems Science and Complexity, 32(6), 1727-1746. doi:10.1007/s11424-019-7281-6

Examples

set.seed(123)
dat <- simulate_coxaalen(n = 100, p = 0.3, censoring = "cox", cens_rate = 0.20)
head(dat)
table(dat$status)

Monte Carlo Simulation Study for Cox-Aalen Model

Description

Conducts a Monte Carlo simulation study to evaluate the empirical bias, standard errors, and 95% coverage probability of the Cox-Aalen model estimators under various censoring scenarios.

Usage

simulation_study(
  n_sim = 50L,
  n = 100L,
  p = 0.3,
  alpha = 1,
  beta1 = 1,
  beta2 = 1,
  censoring = c("independent", "cox", "threshold_uniform"),
  cens_rate = 0.2,
  weight_type = c("cox", "km")
)

Arguments

n_sim

integer number of simulation replications (default 50).
n

integer sample size per replication (default 100).
p

numeric baseline subdistribution parameter (default 0.3).
alpha

numeric time-varying parameter (default 1.0).
beta1

numeric true multiplicative coefficient (default 1.0).
beta2

numeric true competing risk coefficient (default 1.0).
censoring

character string: "independent", "cox", or "threshold_uniform".
cens_rate

numeric target censoring rate (0.20 or 0.40).
weight_type

character string: "cox" or "km".

Value

An object of class "simulation_study" containing:

results

Data frame with columns Parameter, True, Bias, Empirical_SE, Average_SE, and Coverage_95.

settings

List of simulation configuration parameters.

References

Li, W. and Long, Y. (2019). An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data. Journal of Systems Science and Complexity, 32(6), 1727-1746. doi:10.1007/s11424-019-7281-6

Examples

set.seed(123)
sim_res <- simulation_study(n_sim = 5, n = 40, p = 0.3, censoring = "independent")
print(sim_res)

Summary Method for Cox-Aalen Formula Object

Description

Summary method for formula-fitted Cox-Aalen model.

Usage

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

Arguments

object

an object of class "cox_aalen".
...

further arguments passed to or from other methods.

Value

An object of class "summary.cox_aalen".

Summary Method for Cox-Aalen Fitted Models

Description

Produces a detailed summary of the fitted model parameters, standard errors, z-values, p-values, and cumulative additive functions.

Usage

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

Arguments

object

an object of class "cox_aalen_fit" or "cox_aalen".
...

further arguments passed to or from other methods.

Value

An object of class "summary.cox_aalen_fit" containing summary tables and fit statistics.

Tamoxifen Breast Cancer Competing Risks Clinical Trial Dataset

Description

Clinical trial dataset of 641 women aged 50 years or older with early breast cancer treated at Princess Margaret Hospital between 1992 and 2000, analyzing the effect of breast irradiation plus tamoxifen vs. tamoxifen alone under competing risks as analyzed in Li and Long (2019) <doi:10.1007/s11424-019-7281-6>, Fyles et al. (2004) <doi:10.1056/NEJMoa040595>, and Melania Pintilie (2006, ISBN:978-0-470-87068-6).

Usage

tamoxifen

Format

A data frame with 641 rows and 5 variables:

time

Follow-up time in years.

status

Event status: 1 = second malignancy (event of interest), 2 = death without second malignancy (competing risk), 0 = censored.

age

Patient age in years at study entry (mean 66.45, standard deviation 8.91).

pathsize

Pathological tumor size in centimeters (mean 1.55, standard deviation 0.77).

treatment

Treatment indicator: 1 = radiation plus tamoxifen, 0 = tamoxifen alone.

Source

Princess Margaret Hospital breast cancer study, published in Fyles et al. (2004) and analyzed in Li and Long (2019).

References

Fyles, A. W., McCready, D. R., Manchul, L. A., et al. (2004). Tamoxifen with or without breast irradiation in women 50 years of age or older with early breast cancer. New England Journal of Medicine, 351(10), 963-970. doi:10.1056/NEJMoa040595

Li, W. and Long, Y. (2019). An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data. Journal of Systems Science and Complexity, 32(6), 1727-1746. doi:10.1007/s11424-019-7281-6

Pintilie, M. (2006). Competing Risks: A Practical Perspective. John Wiley & Sons, Chichester. ISBN:978-0-470-87068-6.

Examples

data(tamoxifen)
head(tamoxifen)
table(tamoxifen$status)

Goodness-of-Fit Test for Time-Varying Effects in Cox-Aalen Model

Description

Performs supremum-type Kolmogorov-Smirnov and Cramer-von Mises goodness-of-fit tests to evaluate whether additive covariates have time-varying or constant effects, implementing Remark 4.4 of Li and Long (2019) <doi:10.1007/s11424-019-7281-6> using Gaussian multiplier resampling (Lin et al., 1993 <doi:10.1093/biomet/80.3.557>; Scheike and Zhang, 2002 <doi:10.1111/1467-9469.00065>).

Usage

time_varying_test(fit, B = 500L)

Arguments

fit

a fitted model object of class "cox_aalen_fit" or "cox_aalen".
B

integer number of Monte Carlo resampling iterations (default 500).

Value

A list of class "time_varying_test" containing:

test_results

A data frame with columns Covariate, Sup_Stat (supremum statistic), p_value_sup (resampling p-value for supremum test), CvM_Stat (Cramer-von Mises statistic), and p_value_cvm.

B

Integer number of resampling iterations used.

n_add

Number of additive covariates tested.

References

Li, W. and Long, Y. (2019). An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data. Journal of Systems Science and Complexity, 32(6), 1727-1746. doi:10.1007/s11424-019-7281-6

Lin, D. Y., Wei, L. J., Yang, I. and Ying, Z. (1993). Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika, 80(3), 557-572. doi:10.1093/biomet/80.3.557

Scheike, T. H. and Zhang, M. J. (2002). An additive-multiplicative Cox-Aalen regression model. Scandinavian Journal of Statistics, 29(1), 75-88. doi:10.1111/1467-9469.00065

Examples

set.seed(123)
dat <- simulate_coxaalen(n = 50, p = 0.3, censoring = "independent", cens_rate = 0.20)
fit <- cox_aalen_fit(
  time = dat$time,
  status = dat$status,
  X = cbind(Intercept = 1, X = dat$X),
  Z = matrix(dat$Z, ncol = 1, dimnames = list(NULL, "Z"))
)
test_res <- time_varying_test(fit, B = 100)
print(test_res)

Variance-Covariance Matrix for Cox-Aalen Model

Description

Extracts the asymptotic variance-covariance matrix of β\beta.

Usage

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

Arguments

object

an object of class "cox_aalen_fit".
...

further arguments.

Value

Matrix of variance-covariance estimates for multiplicative parameters.