trReg: Fitting regression model via structural transformation model

In tranSurv: Transformation-Based Regression under Dependent Truncation

Fitting regression model via structural transformation model

Description

trReg fits transformation model under dependent truncation and independent censoring via a structural transformation model.

Usage

trReg(
  formula,
  data,
  subset,
  tFun = "linear",
  method = c("kendall", "adjust"),
  B = 0,
  control = list()
)

Arguments

formula	a formula expression, of the form response ~ predictors. The response is assumed to be a survival::Surv object with both left truncation and right censoring. When there is no covariates, e.g., when the right hand side of the formula is ~ 1, the trReg() function returns a trSurvfit object. See ?survival::Surv for more details.
data	an optional data frame in which to interpret the variables occurring in the formula.
subset	an optional vector specifying a subset of observations to be used in the fitting process.
tFun	a character string specifying the transformation function or a user specified function indicating the relationship between X, T, and a. When tFun is a character, the following are permitted: linear linear transformation structure, log log-linear transformation structure, exp exponential transformation structure.
method	a character string specifying how the transformation parameter is estimated. The available options are "kendall" and "adjust". See Details.
B	a numerical value specifies the bootstrap size for estimating the standard error. When B = 0 (default), the bootstrap standard errors will not be computed.
control	a list of control parameters. The following arguments are allowed: lower The lower bound to search for the transformation parameter; default at -1. upper The upper bound to search for the transformation parameter; default at 20. tol The tolerance used in the search for the transformation parameter; default at 0.01. G The number of grids used in the search for the transformation parameter; default is 50. A smaller G could results in faster search, but might be inaccurate. Q The number of cutpoints for the truncation time used when method = "adjust". The default is 0. P The number of breakpoints to divide the event times into equally spaced segments. When P > 1, the latent truncation time, T'(a) will be computed in each subset. The transformation model is then applied to the aggregated data. a The transformation parameter. When this is specified, the transformation model is applied based on the specified a. When this is not specified, an optimized a will be determined by optimization one of the quasi-independence measure. See Details. parallel an logical value indicating whether parallel computation will be applied when B > 0. parCl an integer value specifying the number of CPU cores to be used when parallel = TRUE. The default value is half the CPU cores on the current host.

Details

The main assumption on the structural transformation model is that it assumes there is a latent, quasi-independent truncation time that is associated with the observed dependent truncation time, the event time, and an unknown dependence parameter through a specified function. The structure of the transformation model is of the form:

h(U) = (1 + a)^{-1} \times (h(T) + ah(X)),

where T is the truncation time, X is the observed failure time, U is the transformed truncation time that is quasi-independent from X and h(\cdot) is a monotonic transformation function. The condition, T < X, is assumed to be satisfied. The quasi-independent truncation time, U, is obtained by inverting the test for quasi-independence by one of the following methods:

method = "kendall"

by minimizing the absolute value of the restricted inverse probability weighted Kendall's tau or maximize the corresponding p-value. This is the same procedure used in the trSUrvfit() function.

method = "adjust"

includes a function of latent truncation time, U, as a covariate. A piece-wise function is constructed based on (Q + 1) indicator functions on whether U falls in the Qth and the (Q+1)th percentile, where Q is the number of cutpoints used. See control for details. The transformation parameter, a, is then chosen to minimize the significance of the coefficient parameter.

Value

A trReg object containing the following components:

PE

A named numeric matrix of point estimates and related statistics (e.g., coefficient, exponentiated coefficient, standard error, z-score, and p-value).

varNames

Character string giving the name(s) of the covariates.

SE

A numeric vector contains the bootstrap standard error.

a

Estimated transformation parameter.

Call

The matched call to the fitting function.

B, Q, P

Model parameters; B is the bootstrap sapmle, Q is the number of cutpoints, and P is the number of break points. See Details.

tFun

A function defining the transformation model.

vNames

Character vector of covariate names.

method

Character string specifying the estimation method (e.g., "kendall" or "adjust").

.data

A data frame used in fitting.

See Also

trSurvfit

Examples

data(channing, package = "boot")
chan <- subset(channing, entry < exit)
trReg(Surv(entry, exit, cens) ~ sex, data = chan)

tranSurv documentation built on Nov. 6, 2025, 1:08 a.m.