aftsrr {aftgee}  R Documentation 
Accelerated Failure Time with Smooth Rank Regression
Description
Fits a semiparametric accelerated failure time (AFT) model with rankbased approach.
General weights, additional sampling weights and fast sandwich variance estimations
are also incorporated.
Estimating equations are solved with BarzilarBorwein 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 variancecovariance 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 variancecovariance 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 variancecovariance 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 variancecovariance
matrix via this sandwich form, depending on how V
and A
are estimated.
Specifically, the asymptotic variance, V
, can be estimated by either a
closedform 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 linesearch.
 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 CaseCohort 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 HighDimensional 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)