R: Fitting regression model via structural transformation model

trReg {tranSurv}

R Documentation

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 segmenets. 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 funciton. 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.

Examples

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