aftsrr {aftgee} | R Documentation |
Accelerated Failure Time with Smooth Rank Regression
Description
Fits a semiparametric accelerated failure time (AFT) model with rank-based approach.
General weights, additional sampling weights and fast sandwich variance estimations
are also incorporated.
Estimating equations are solved with Barzilar-Borwein spectral method implemented as
BBsolve
in package BB.
Usage
aftsrr(
formula,
data,
subset,
id = NULL,
contrasts = NULL,
weights = NULL,
B = 100,
rankWeights = c("gehan", "logrank", "PW", "GP", "userdefined"),
eqType = c("is", "ns", "mis", "mns"),
se = c("NULL", "bootstrap", "MB", "ZLCF", "ZLMB", "sHCF", "sHMB", "ISCF", "ISMB"),
control = list()
)
Arguments
formula |
a formula expression, of the form |
data |
an optional data frame in which to interpret the variables
occurring in the |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
id |
an optional vector used to identify the clusters.
If missing, then each individual row of |
contrasts |
an optional list. |
weights |
an optional vector of observation weights. |
B |
a numeric value specifies the resampling number.
When |
rankWeights |
a character string specifying the type of general weights. The following are permitted:
|
eqType |
a character string specifying the type of the estimating equation used to obtain the regression parameters. The following are permitted:
|
se |
a character string specifying the estimating method for the variance-covariance matrix. The following are permitted:
|
control |
controls equation solver, maxiter, tolerance, and resampling variance estimation.
The available equation solvers are
.
The readers are refered to the BB package for details.
Instead of searching for the zero crossing, options including |
Details
When se = "bootstrap"
or se = "MB"
, the variance-covariance matrix
is estimated through a bootstrap fashion.
Bootstrap samples that failed to converge are removed when computing the empirical variance matrix.
When bootstrap is not called, we assume the variance-covariance matrix has a sandwich form
\Sigma = A^{-1}V(A^{-1})^T,
where V
is the asymptotic variance of the estimating function and
A
is the slope matrix.
In this package, we provide seveal methods to estimate the variance-covariance
matrix via this sandwich form, depending on how V
and A
are estimated.
Specifically, the asymptotic variance, V
, can be estimated by either a
closed-form formulation (CF
) or through bootstrap the estimating equations (MB
).
On the other hand, the methods to estimate the slope matrix A
are
the inducing smoothing approach (IS
), Zeng and Lin's approach (ZL
),
and the smoothed Huang's approach (sH
).
Value
aftsrr
returns an object of class "aftsrr
" representing the fit.
An object of class "aftsrr
" is a list containing at least the following components:
- beta
A vector of beta estimates
- covmat
A list of covariance estimates
- convergence
An integer code indicating type of convergence.
- 0
indicates successful convergence.
- 1
indicates that the iteration limit
maxit
has been reached.- 2
indicates failure due to stagnation.
- 3
indicates error in function evaluation.
- 4
is failure due to exceeding 100 step length reductions in line-search.
- 5
indicates lack of improvement in objective function.
- bhist
When
variance = "MB"
,bhist
gives the bootstrap samples.
References
Chiou, S., Kang, S. and Yan, J. (2014) Fast Accelerated Failure Time Modeling for Case-Cohort Data. Statistics and Computing, 24(4): 559–568.
Chiou, S., Kang, S. and Yan, J. (2014) Fitting Accelerated Failure Time Model in Routine Survival Analysis with R Package Aftgee. Journal of Statistical Software, 61(11): 1–23.
Huang, Y. (2002) Calibration Regression of Censored Lifetime Medical Cost. Journal of American Statistical Association, 97, 318–327.
Johnson, L. M. and Strawderman, R. L. (2009) Induced Smoothing for the Semiparametric Accelerated Failure Time Model: Asymptotic and Extensions to Clustered Data. Biometrika, 96, 577 – 590.
Varadhan, R. and Gilbert, P. (2009) BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function. Journal of Statistical Software, 32(4): 1–26
Zeng, D. and Lin, D. Y. (2008) Efficient Resampling Methods for Nonsmooth Estimating Functions. Biostatistics, 9, 355–363
Examples
## Simulate data from an AFT model
datgen <- function(n = 100) {
x1 <- rbinom(n, 1, 0.5)
x2 <- rnorm(n)
e <- rnorm(n)
tt <- exp(2 + x1 + x2 + e)
cen <- runif(n, 0, 100)
data.frame(Time = pmin(tt, cen), status = 1 * (tt < cen),
x1 = x1, x2 = x2, id = 1:n)
}
set.seed(1); dat <- datgen(n = 50)
summary(aftsrr(Surv(Time, status) ~ x1 + x2, data = dat, se = c("ISMB", "ZLMB"), B = 10))
## Data set with sampling weights
data(nwtco, package = "survival")
subinx <- sample(1:nrow(nwtco), 668, replace = FALSE)
nwtco$subcohort <- 0
nwtco$subcohort[subinx] <- 1
pn <- mean(nwtco$subcohort)
nwtco$hi <- nwtco$rel + ( 1 - nwtco$rel) * nwtco$subcohort / pn
nwtco$age12 <- nwtco$age / 12
nwtco$study <- factor(nwtco$study)
nwtco$histol <- factor(nwtco$histol)
sub <- nwtco[subinx,]
fit <- aftsrr(Surv(edrel, rel) ~ histol + age12 + study, id = seqno,
weights = hi, data = sub, B = 10, se = c("ISMB", "ZLMB"),
subset = stage == 4)
summary(fit)
confint(fit)