MTAFT: Data-Driven Estimation for Multi-Threshold Accelerate Failure Time Model

Description

Developed a data-driven estimation framework for the multi-threshold accelerate failure time (MTAFT) model. The MTAFT model features different linear forms in different subdomains, and one of the major challenges is determining the number of threshold effects. The package introduces a data-driven approach that utilizes a Schwarz' information criterion, which demonstrates consistency under mild conditions. Additionally, a cross-validation (CV) criterion with an order-preserved sample-splitting scheme is proposed to achieve consistent estimation, without the need for additional parameters. The package establishes the asymptotic properties of the parameter estimates and includes an efficient score-type test to examine the existence of threshold effects. The methodologies are supported by numerical experiments and theoretical results, showcasing their reliable performance in finite-sample cases.

Author(s)

Maintainer: Chuang WAN wanchuang@nankai.edu.cn

Authors:

• Hao ZENG zenghao@stu.xmu.edu.cn

• Wei ZHONG wzhong@xmu.edu.cn

• Changliang ZOU nk.chlzou@gmail.com

MTAFT_CV: Cross-Validation for Multiple Thresholds Accelerated Failure Time Model

Description

This function implements a cross-validation method for the multiple thresholds accelerated failure time (AFT) model using either the "WBS" (Wild Binary Segmentation) or "DP" (Dynamic Programming) algorithm. It determines the optimal number of thresholds by evaluating the cross-validation (CV) values.

Usage

MTAFT_CV(
  Y,
  X,
  delta,
  Tq,
  algorithm,
  dist_min = 50,
  ncps_max = 4,
  wbs_nintervals = 200
)

Arguments

Value

A list with the following components:

params

the subgroup-specific slope estimates and variance estimates.

thres

the threshold estimates.

CV_vals

the CV values for all candidate number of thresholds.

Examples

# Generate simulated data with 500 samples and normal error distribution
dataset <- MTAFT_simdata(n = 500, err = "normal")

Y <- dataset[, 1]
delta <- dataset[, 2]
Tq <- dataset[, 3]
X <- dataset[, -c(1:3)]

# Run mAFT_CV with WBS algorithm
maft_cv_result <- MTAFT_CV(Y, X, delta, Tq, algorithm = "WBS")
maft_cv_result$params
maft_cv_result$thres
maft_cv_result$CV_vals

MTAFT_IC: Multiple Thresholds Accelerated Failure Time Model with Information Criteria

Description

This function implements a method for multiple thresholds accelerated failure time (AFT) model with information criteria. It estimates the subgroup-specific slope coefficients and variance estimates, as well as the threshold estimates using either the "WBS" (Wild Binary Segmentation) or "DP" (Dynamic Programming) algorithm.

Usage

MTAFT_IC(
  Y,
  X,
  delta,
  Tq,
  c0 = 0.299,
  delta0 = 2.01,
  algorithm = c("WBS", "DP"),
  dist_min = 50,
  ncps_max = 4,
  wbs_nintervals = 200
)

Arguments

Value

A list with the following components:

params

the subgroup-specific slope estimates and variance estimates.

thres

the threshold estimates.

IC_val

the IC values for all candidate number of thresholds.

References

(Add relevant references here)

Examples

# Generate simulated data with 500 samples and normal error distribution
dataset <- MTAFT_simdata(n = 500, err = "normal")
Y <- dataset[, 1]
delta <- dataset[, 2]
Tq <- dataset[, 3]
X <- dataset[, -c(1:3)]

# Run MTAFT_IC with WBS algorithm
mtaft_ic_result <- MTAFT_IC(Y, X, delta, Tq, algorithm = 'WBS')
mtaft_ic_result$params
mtaft_ic_result$thres
mtaft_ic_result$IC_val

Generate simulated data for MTAFT analysis.

Description

This function generates simulated data for the MTAFT (Multi-Threshold Accelerated Failure Time) analysis based on a simple simulation procedure described in the article.

Usage

MTAFT_simdata(n, err = c("normal", "t3"))

Arguments

Value

A dataset containing the simulated data for MTAFT analysis.

Examples

# Generate simulated data with 500 samples and normal error distribution
dataset <- MTAFT_simdata(n = 500, err = "normal")
Y <- dataset[, 1]
delta <- dataset[, 2]
Tq <- dataset[, 3]
X <- dataset[, -c(1:3)]

# Generate simulated data with 200 samples and t3 error distribution
dataset <- MTAFT_simdata(n = 200, err = "t3")
Y <- dataset[, 1]
delta <- dataset[, 2]
Tq <- dataset[, 3]
X <- dataset[, -c(1:3)]

Perform score-type test for the presence of threshold effect in multi-threshold situations.

Description

This function performs a score-type test statistics for the presence of threshold effect in multi-threshold situations.

Usage

MTAFT_test(Y, X, Tq, delta, nboots)

Arguments

Value

p-value result indicating the presence of threshold effect.

Examples

# Generate simulated data with 500 samples and normal error distribution
dataset <- MTAFT_simdata(n = 500, err = "normal")
Y <- dataset[, 1]
delta <- dataset[, 2]
Tq <- dataset[, 3]
X <- dataset[, -c(1:3)]

# Perform score-type test with 500 bootstraps
pval <- MTAFT_test(Y, X, Tq, delta, nboots = 500)

# Perform score-type test with 1000 bootstraps
pval <- MTAFT_test(Y, X, Tq, delta, nboots = 1000)

TSMCP: Two stage multiple change points detection for AFT model.

Description

This function first formulates the threshold problem as a group model selection problem so that a concave 2-norm group selection method can be applied using the 'grpreg' package in R, and then finalizes it via a refining method.

Usage

TSMCP(Y, X, delta, c, penalty = "scad")

Arguments

Value

An object with the following components:

cp

the change points.

coef

the estimated coefficients.

sigma

the variance of the error.

residuals

the residuals.

Yn

weighted Y by Kaplan-Meier weight.

Xn

weighted Xn by Kaplan-Meier weight.

References

Li, Jialiang, and Baisuo Jin. 2018. “Multi-Threshold Accelerated Failure Time Model.” The Annals of Statistics 46 (6A): 2657–82.

See Also

grpreg

Examples

library(grpreg)
# Generate simulated data with 500 samples and normal error distribution
dataset <- MTAFT_simdata(n = 500, err = "normal")
Y <- dataset[, 1]
delta <- dataset[, 2]
Tq <- dataset[, 3]
X <- dataset[, -c(1:3)]
n1 = sum(delta)
c=seq(0.5,1.5,0.1)
m=ceiling(c*sqrt(n1))
bicy= rep(NA,length(c))
tsmc=NULL
p = ncol(X)
for(i in 1:length(c)){
    tsm=try(TSMCP(Y,X,delta,c[i],penalty = "scad"),silent=TRUE)
    if(is(tsm,"try-error")) next()
    bicy[i]=log(n)*((length(tsm[[1]])+1)*(p+1))+n*log(tsm[[3]])
    tsmc[[i]]=tsm
}

if((any(!is.na(bicy)))){
    tsmcp=tsmc[[which(bicy==min(bicy))[1]]]
    thre.LJ = Tq[tsmcp[[1]]]
    thre.num.Lj = length(thre.LJ)
    thre.LJ
    thre.num.Lj
}