Package 'afttest'

Title: Model Diagnostics for Accelerated Failure Time Models
Description: A collection of model checking methods for semiparametric accelerated failure time (AFT) models under the rank-based approach. For the (computational) efficiency, Gehan's weight is used. It provides functions to verify whether the observed data fit the specific model assumptions such as a functional form of each covariate, a link function, and an omnibus test. The p-value offered in this package is based on the Kolmogorov-type supremum test and the variance of the proposed test statistics is estimated through the re-sampling method. Furthermore, a graphical technique to compare the shape of the observed residual to a number of the approximated realizations is provided. See the following references; A general model-checking procedure for semiparametric accelerated failure time models, Statistics and Computing, 34 (3), 117 <doi:10.1007/s11222-024-10431-7>; Diagnostics for semiparametric accelerated failure time models with R package 'afttest', Journal of Statistical Software, to appear, <doi:10.48550/arXiv.2511.09823>.
Authors: Woojung Bae [aut, cre] (ORCID: <https://orcid.org/0000-0001-6760-9900>), Dongrak Choi [aut] (ORCID: <https://orcid.org/0000-0003-3280-3329>), Jun Yan [aut] (ORCID: <https://orcid.org/0000-0003-4401-7296>), Sangwook Kang [aut] (ORCID: <https://orcid.org/0000-0003-2658-481X>)
Maintainer: Woojung Bae <matt.woojung@gmail.com>
License: GPL (>= 3)
Version: 4.6.2
Built: 2026-10-11 07:42:33 UTC
Source: https://github.com/woojungbae/afttest

Help Index

Model Diagnostics for Semiparametric AFT Models

Description

Performs model-checking procedures for a semiparametric AFT model. This is a generic function with methods for formulas and fitted objects from the aftgee package.

Usage

afttest(object, ...)

Arguments

object

A formula or a fitted model object (e.g., from aftsrr or aftgee).
...

Other arguments passed to methods. See the documentation for afttest.formula, afttest.aftsrr, and afttest.aftgee for details.

Value

An object of class afttest or htest. An object is a list containing at least the following components:

beta

a vector of beta estimates based on estMethod

hypothesis

null hypothesis for each testType

SE_process

estimated standard error of the observed process

obs_process

observed process

apprx_process

approximated process

obs_std_process

standardized observed process

apprx_std_process

standardized approximated processes

p_value

finite-resampling Monte Carlo p-value for the unstandardized test

p_std_value

finite-resampling Monte Carlo p-value for the standardized test

DF

a data frame of observed failure time, right censoring indicator, covariates (scaled), time-transformed residual based on beta estimates

npath

the number of sample paths

testType

testType

eqType

eqType

estMethod

estMethod

npathsave

npathsave

For an omnibus test, the observed process and the realizations are composed of the n by n matrix where rows represent the t and columns represent the x in the time-transformed residual order. The observed process and the simulated processesfor checking a functional form and a link function are given by the n by 1 vectorwhich is a function of x in the time-transformed residual order.

Examples

library(survival)
library(aftgee)
library(afttest)

datgen <- function(n = 100) {
  z1 <- rbinom(n, 1, 0.5)
  z2 <- rnorm(n)
  e <- rnorm(n)
  tt <- exp(2 + z1 + z2 + 0.5 * z2^2 + e)
  cen <- runif(n, 0, 100)
  data.frame(Time = pmin(tt, cen), status = 1 * (tt < cen),
             z1 = z1, z2 = z2, id = 1:n)
}
set.seed(1)
simdata <- datgen(300)

# --------------------------------------------------
# Method 1: Formula (Runs quickly for CRAN tests)
# --------------------------------------------------
result_form <- afttest(Surv(Time, status) ~ z1 + z2, data = simdata,
                       npath = 50, testType = "covForm", estMethod = "rr",
                       eqType = "ns", covTested = "z2", npathsave = 50,
                       linApprox = TRUE, seed = 1)
print(result_form)
plot(result_form, std = TRUE)


# --------------------------------------------------
# Method 2: Fitted aftsrr object (Induced Smoothing)
# --------------------------------------------------
fit_srr <- aftsrr(Surv(Time, status) ~ z1 + z2, data = simdata, 
                  eqType = "is", rankWeights = "gehan")
result_srr <- afttest(fit_srr, data = simdata, npath = 100, testType = "covForm", 
                      covTested = "z2", npathsave = 50, 
                      linApprox = TRUE, seed = 1)
summary(result_srr)
plot(result_srr, std = FALSE)

# --------------------------------------------------
# Method 3: Fitted aftgee object (Least Squares)
# --------------------------------------------------
fit_gee <- aftgee(Surv(Time, status) ~ z1 + z2, data = simdata)
result_gee <- afttest(fit_gee, data = simdata, npath = 100, testType = "covForm", 
                      covTested = "z2", npathsave = 50, 
                      linApprox = TRUE, seed = 1)
print(result_gee)

# --------------------------------------------------
# Method 4: Standard Resampling (linApprox = FALSE)
# --------------------------------------------------
result_resamp <- afttest(Surv(Time, status) ~ z1 + z2, data = simdata,
                         npath = 100, testType = "covForm", estMethod = "rr",
                         eqType = "ns", covTested = "z2", npathsave = 50,
                         linApprox = FALSE, seed = 1)
summary(result_resamp)

Model Diagnostics for Generalized Estimating Equation (aftgee) Objects

Description

Model Diagnostics for Generalized Estimating Equation (aftgee) Objects

Usage

## S3 method for class 'aftgee'
afttest(
  object,
  data,
  npath = 200,
  testType = "omnibus",
  eqType = "ls",
  covTested = 1,
  npathsave = 50,
  linApprox = TRUE,
  seed = NULL,
  ...
)

Arguments

object

A fitted model object of class aftgee from the aftgee package.
data

An optional data frame in which to interpret the variables occurring in the formula.
npath

An integer value specifying the number of approximated processes. The default is given by 200.
testType

A character string specifying the type of the test. The following are permitted:

omnibus

an omnibus test

link

a link function test

covForm

a functional form of a covariate
eqType

The estimating-equation type used for the diagnostic procedure. For a fitted aftgee object, this is fixed to "ls". Any other supplied value is ignored with a warning.
covTested

A single design-matrix column to test when testType is covForm, supplied by position or name.
npathsave

An integer value specifying the number of simulated paths retained in the returned object. The default is 50.
linApprox

A logical value. If TRUE, the multiplier bootstrap is computed using the asymptotic linear approximation, which is significantly faster. If FALSE, the estimating equations are solved numerically for each bootstrap replication. Defaults to TRUE.
seed

An optional integer specifying the random seed for reproducibility.
...

Other arguments passed to methods.

Model Diagnostics for Smooth Rank Regression (aftsrr) Objects

Description

Model Diagnostics for Smooth Rank Regression (aftsrr) Objects

Usage

## S3 method for class 'aftsrr'
afttest(
  object,
  data,
  npath = 200,
  testType = "omnibus",
  eqType = NULL,
  covTested = 1,
  npathsave = 50,
  linApprox = TRUE,
  seed = NULL,
  ...
)

Arguments

object

A fitted model object of class aftsrr from the aftgee package.
data

An optional data frame in which to interpret the variables occurring in the formula.
npath

An integer value specifying the number of approximated processes. The default is given by 200.
testType

A character string specifying the type of the test. The following are permitted:

omnibus

an omnibus test

link

a link function test

covForm

a functional form of a covariate
eqType

An optional character string specifying the type of the estimating equation. For a fitted aftsrr object, the estimating equation used in the fitted object is retained. If it cannot be identified from the fitted object, "ns" is used. The permitted values are "ns" and "is". If a different value from that used in the fitted object is supplied, it is ignored with a warning.
covTested

A single design-matrix column to test when testType is covForm, supplied by position or name.
npathsave

An integer value specifying the number of simulated paths retained in the returned object. The default is 50.
linApprox

A logical value. If TRUE, the multiplier bootstrap is computed using the asymptotic linear approximation, which is significantly faster. If FALSE, the estimating equations are solved numerically for each bootstrap replication. Defaults to TRUE.
seed

An optional integer specifying the random seed for reproducibility.
...

Other arguments passed to methods.

Model Diagnostics for AFT Models using Formulas

Description

Model Diagnostics for AFT Models using Formulas

Usage

## S3 method for class 'formula'
afttest(
  object,
  data,
  npath = 200,
  testType = "omnibus",
  estMethod = "rr",
  eqType = "ns",
  covTested = 1,
  npathsave = 50,
  linApprox = TRUE,
  seed = NULL,
  ...
)

Arguments

object

A formula expression, of the form response ~ predictors. The response is a Surv object with right censoring. See the documentation of lm, coxph and formula for details.
data

An optional data frame in which to interpret the variables occurring in the formula.
npath

An integer value specifying the number of approximated processes. The default is given by 200.
testType

A character string specifying the type of the test. The following are permitted:

omnibus

an omnibus test

link

a link function test

covForm

a functional form of a covariate
estMethod

A character string specifying the type of the estimator used. The readers are referred to the aftgee package for details. The following are permitted:

ls

Least-Squares Approach for Accelerated Failure Time with Generalized Estimating Equation

rr

Accelerated Failure Time with Smooth Rank Regression
eqType

A character string specifying the type of the estimating equation used to obtain the regression parameters. The readers are referred to the aftgee package for details. The following are permitted:

ns

Regression parameters are estimated by directly solving the nonsmooth estimating equations.

is

Regression parameters are estimated by directly solving the induced-smoothing estimating equations.
covTested

A single design-matrix column to test when testType is covForm, supplied by position or name. In formulas containing factors, a factor can expand to several columns; use one of the expanded column names returned by model.matrix().
npathsave

An integer value specifying the number of simulated paths retained in the returned object. The default is 50. Retaining paths can require substantial memory for omnibus tests.
linApprox

A logical value. If TRUE, the multiplier bootstrap is computed using the asymptotic linear approximation, which is significantly faster. If FALSE, the estimating equations are solved numerically for each bootstrap replication. Defaults to TRUE.
seed

An optional integer specifying the random seed for reproducibility.
...

Other arguments passed to methods.

Plotting Method for Semiparametric AFT Model Diagnostics

Description

Plotting Method for Semiparametric AFT Model Diagnostics

Usage

## S3 method for class 'afttest'
plot(x, npath = 50, std = TRUE, quantile = NULL, ...)

Arguments

x

An object of class afttest.
npath

A numeric value specifying the number of approximated processes to plot. The default is set to 50.
std

A logical value specifying if the graph is based on the standardized test statistics (TRUE) or unstandardized (FALSE). The default is TRUE.
quantile

A numeric vector specifying 5 quantiles within the range [0,1]. The default is set to c(0.1, 0.25, 0.5, 0.75, 0.9).
...

Other arguments passed to methods for future extension.

Value

plot.afttest returns a plot based on the testType:

omnibus

an x of the omnibus test is the form of n by n matrix, some quantiles of x, which are used in weight, are plotted for graphs, i.e. 10%, 25%, 50%, 75%, and 90% are used by default.

link

an x of the link function test is the form of n by 1 matrix

covForm

an x of the functional form test is the form of n by 1 matrix

See the documentation of ggplot2 and gridExtra for details.

Examples

library(survival)
library(aftgee)
library(afttest)

datgen <- function(n = 100) {
  z1 <- rbinom(n, 1, 0.5)
  z2 <- rnorm(n)
  e <- rnorm(n)
  tt <- exp(2 + z1 + z2 + 0.5 * z2^2 + e)
  cen <- runif(n, 0, 100)
  data.frame(Time = pmin(tt, cen), status = 1 * (tt < cen),
             z1 = z1, z2 = z2, id = 1:n)
}
set.seed(1)
simdata <- datgen(300)

# --------------------------------------------------
# Method 1: Formula (Runs quickly for CRAN tests)
# --------------------------------------------------
result_form <- afttest(Surv(Time, status) ~ z1 + z2, data = simdata,
                       npath = 50, testType = "covForm", estMethod = "rr",
                       eqType = "ns", covTested = "z2", npathsave = 50,
                       linApprox = TRUE, seed = 1)
print(result_form)
plot(result_form, std = TRUE)


# --------------------------------------------------
# Method 2: Fitted aftsrr object (Induced Smoothing)
# --------------------------------------------------
fit_srr <- aftsrr(Surv(Time, status) ~ z1 + z2, data = simdata, 
                  eqType = "is", rankWeights = "gehan")
result_srr <- afttest(fit_srr, data = simdata, npath = 100, testType = "covForm", 
                      covTested = "z2", npathsave = 50, 
                      linApprox = TRUE, seed = 1)
summary(result_srr)
plot(result_srr, std = FALSE)

# --------------------------------------------------
# Method 3: Fitted aftgee object (Least Squares)
# --------------------------------------------------
fit_gee <- aftgee(Surv(Time, status) ~ z1 + z2, data = simdata)
result_gee <- afttest(fit_gee, data = simdata, npath = 100, testType = "covForm", 
                      covTested = "z2", npathsave = 50, 
                      linApprox = TRUE, seed = 1)
print(result_gee)

# --------------------------------------------------
# Method 4: Standard Resampling (linApprox = FALSE)
# --------------------------------------------------
result_resamp <- afttest(Surv(Time, status) ~ z1 + z2, data = simdata,
                         npath = 100, testType = "covForm", estMethod = "rr",
                         eqType = "ns", covTested = "z2", npathsave = 50,
                         linApprox = FALSE, seed = 1)
summary(result_resamp)

Print Method for Semiparametric AFT Model Diagnostics

Description

Print Method for Semiparametric AFT Model Diagnostics

Usage

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

Arguments

x

An object of class afttest.
...

Other arguments passed to methods.

Value

print.afttest returns a summary of an afttest fit.

Examples

library(survival)
library(aftgee)
library(afttest)

datgen <- function(n = 100) {
  z1 <- rbinom(n, 1, 0.5)
  z2 <- rnorm(n)
  e <- rnorm(n)
  tt <- exp(2 + z1 + z2 + 0.5 * z2^2 + e)
  cen <- runif(n, 0, 100)
  data.frame(Time = pmin(tt, cen), status = 1 * (tt < cen),
             z1 = z1, z2 = z2, id = 1:n)
}
set.seed(1)
simdata <- datgen(300)

# --------------------------------------------------
# Method 1: Formula (Runs quickly for CRAN tests)
# --------------------------------------------------
result_form <- afttest(Surv(Time, status) ~ z1 + z2, data = simdata,
                       npath = 50, testType = "covForm", estMethod = "rr",
                       eqType = "ns", covTested = "z2", npathsave = 50,
                       linApprox = TRUE, seed = 1)
print(result_form)
plot(result_form, std = TRUE)


# --------------------------------------------------
# Method 2: Fitted aftsrr object (Induced Smoothing)
# --------------------------------------------------
fit_srr <- aftsrr(Surv(Time, status) ~ z1 + z2, data = simdata, 
                  eqType = "is", rankWeights = "gehan")
result_srr <- afttest(fit_srr, data = simdata, npath = 100, testType = "covForm", 
                      covTested = "z2", npathsave = 50, 
                      linApprox = TRUE, seed = 1)
summary(result_srr)
plot(result_srr, std = FALSE)

# --------------------------------------------------
# Method 3: Fitted aftgee object (Least Squares)
# --------------------------------------------------
fit_gee <- aftgee(Surv(Time, status) ~ z1 + z2, data = simdata)
result_gee <- afttest(fit_gee, data = simdata, npath = 100, testType = "covForm", 
                      covTested = "z2", npathsave = 50, 
                      linApprox = TRUE, seed = 1)
print(result_gee)

# --------------------------------------------------
# Method 4: Standard Resampling (linApprox = FALSE)
# --------------------------------------------------
result_resamp <- afttest(Surv(Time, status) ~ z1 + z2, data = simdata,
                         npath = 100, testType = "covForm", estMethod = "rr",
                         eqType = "ns", covTested = "z2", npathsave = 50,
                         linApprox = FALSE, seed = 1)
summary(result_resamp)

Summary Method for Semiparametric AFT Model Diagnostics

Description

Summary Method for Semiparametric AFT Model Diagnostics

Usage

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

Arguments

object

An object of class afttest.
...

Other arguments passed to methods.

Value

summary.afttest returns a detailed summary of an afttest fit.

Examples

library(survival)
library(aftgee)
library(afttest)

datgen <- function(n = 100) {
  z1 <- rbinom(n, 1, 0.5)
  z2 <- rnorm(n)
  e <- rnorm(n)
  tt <- exp(2 + z1 + z2 + 0.5 * z2^2 + e)
  cen <- runif(n, 0, 100)
  data.frame(Time = pmin(tt, cen), status = 1 * (tt < cen),
             z1 = z1, z2 = z2, id = 1:n)
}
set.seed(1)
simdata <- datgen(300)

# --------------------------------------------------
# Method 1: Formula (Runs quickly for CRAN tests)
# --------------------------------------------------
result_form <- afttest(Surv(Time, status) ~ z1 + z2, data = simdata,
                       npath = 50, testType = "covForm", estMethod = "rr",
                       eqType = "ns", covTested = "z2", npathsave = 50,
                       linApprox = TRUE, seed = 1)
print(result_form)
plot(result_form, std = TRUE)


# --------------------------------------------------
# Method 2: Fitted aftsrr object (Induced Smoothing)
# --------------------------------------------------
fit_srr <- aftsrr(Surv(Time, status) ~ z1 + z2, data = simdata, 
                  eqType = "is", rankWeights = "gehan")
result_srr <- afttest(fit_srr, data = simdata, npath = 100, testType = "covForm", 
                      covTested = "z2", npathsave = 50, 
                      linApprox = TRUE, seed = 1)
summary(result_srr)
plot(result_srr, std = FALSE)

# --------------------------------------------------
# Method 3: Fitted aftgee object (Least Squares)
# --------------------------------------------------
fit_gee <- aftgee(Surv(Time, status) ~ z1 + z2, data = simdata)
result_gee <- afttest(fit_gee, data = simdata, npath = 100, testType = "covForm", 
                      covTested = "z2", npathsave = 50, 
                      linApprox = TRUE, seed = 1)
print(result_gee)

# --------------------------------------------------
# Method 4: Standard Resampling (linApprox = FALSE)
# --------------------------------------------------
result_resamp <- afttest(Surv(Time, status) ~ z1 + z2, data = simdata,
                         npath = 100, testType = "covForm", estMethod = "rr",
                         eqType = "ns", covTested = "z2", npathsave = 50,
                         linApprox = FALSE, seed = 1)
summary(result_resamp)