Semiparametric Inference for AFT Models with Dependent Truncation

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Description

Regression estimation for AFT regression models based on left-truncated and right-censored data, which is proposed by Emura and Wang (2015). The dependency of truncation on lifetime is modeled through the AFT regression form.

Usage

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dependAFT.reg(t.trunc, y.trunc, d, x1.trunc, initial = c(0, 0), LY = FALSE, 
beta1_low = -0.2, beta1_up = 0.2, alpha = 1, epsilon = 1/50)

Arguments

t.trunc

vector of left-truncation variables satisfying t.trunc<=y.trunc

y.trunc

vector of lifetime variables satisfying t.trunc<=y.trunc

d

vector of censoring indicators

x1.trunc

vector of 1-dimensional covariates

initial

a pair of initial values for (beta, gamma)

LY

Lai and Ying's estimator for initial values

beta1_low

lower bound for beta

beta1_up

upper bound for beta

alpha

some tuning parameter for optimization, alpha=1 is default

epsilon

some tuning parameter for kernel methods

Details

Only the univariate regression (only one covariate) is allowed.

Value

beta

inference results for beta

gamma

inference results for gamma

beta_LY

the estimator of Lai & Ying (1991)

S2_Minimum

minimum of the objective function

detail

detailed results for minimizing the estimating objective function "optim"

Author(s)

Takeshi Emura

References

Emura T, Wang W (2015), Semiparametric Inference for an Accelerated Failure Time Model with Dependent Truncation, accepted, Annals of the Institute of Statistical Mathematics.

Lai TL, Ying Z (1991), Rank Regression Methods for Left-Truncated and Right-Censored Data. Annals of Statistics 19: 531-556.

Examples

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y.trunc=c(
  -0.52,  0.22, -1.42,  0.05,  0.32, -1.02, -0.47,  0.10, -0.38, -0.18,  0.97,  0.04, -0.10,
   0.50,  0.57, -0.80, -0.24,  0.07, -0.04,  0.88, -0.52, -0.28, -0.55,  0.53,  0.99, -0.52,
  -0.59, -0.48, -0.07,  0.20, -0.34,  1.00, -0.52)
t.trunc=c(
  -2.05, -0.25, -2.43, -0.32, -0.27, -1.06, -0.95, -0.82, -0.66, -0.28, -1.14, -0.32, -1.19,
  -2.18, -0.45, -1.71, -0.84, -1.93, -1.04, -2.58, -1.97, -2.15, -0.59, -0.74, -1.26, -2.57,
  -2.40, -2.22, -1.52, -0.21, -1.50, -1.99, -1.79)

d=c(1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
    0, 1, 1,1)

x1.trunc=c(
  0.27, 0.66, 0.77, 0.21, 0.48, 0.11, 0.69, 0.32, 0.33, 0.43, 0.12, 0.60, 0.13, 0.43, 0.99,
  0.21, 0.93, 0.60, 0.45, 0.41, 0.86, 0.90, 0.76, 0.93, 0.27, 0.13, 0.82, 0.17, 0.63, 0.31,
  0.13, 0.48, 0.32)

### Data analysis in Emura and Wang (2015) ###
# dependAFT.reg(t.trunc,y.trunc,d,x1.trunc,alpha=2,LY=TRUE,beta1_low=-5,beta1_up=5)
dependAFT.reg(t.trunc,y.trunc,d,x1.trunc,LY=FALSE,beta1_low=-5,beta1_up=5)

#### Channing hourse data analysis; Section 5 of Emura and Wang (2015) ##### 
# library(KMsurv)
# data(channing)
# y.trunc=log(channing$age)
# t.trunc=log(channing$ageentry)
# d=channing$death
# x1.trunc=as.numeric(channing$gender==1)

# dependAFT.reg(t.trunc,y.trunc,d,x1.trunc,beta1_low=-0.2,beta1_up=0.2)
# dependAFT.reg(t.trunc,y.trunc,d,x1.trunc,LY=TRUE,alpha=2,beta1_low=-0.2,beta1_up=0.2)