Accelerated Failure Time with Smooth Rank Regression

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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

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aftsrr(formula, data, subset, id = NULL, contrasts = NULL,
       strata = NULL, weights = NULL, rankWeights = "gehan",
       method = "sm", variance = "ISMB", B = 100, SigmaInit = NULL, 
       control = aftgee.control())
       

Arguments

formula

a formula expression, of the form response ~ predictors. The response is a Surv object object with right censoring. See the documentation of lm, coxph and formula for details.

data

an optional data frame in which to interpret the variables occurring in the formula.

id

an optional vector used to identify the clusters. If missing, then each individual row of data is presumed to represent a distinct subject. The length of id should be the same as the number of observation.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

contrasts

an optional list.

strata

a vector which identifies strata. This can also be used to distinct case-cohort sampling and stratified sampling.

weights

an optional vector of observation weights.

rankWeights

a character string specifying the type of general weights. The following are permitted: logrank: logrank weight, gehan: Gehan's weight, PW: Prentice-Wilcoxon weight, GP: GP class weight.

method

a character string specifying the methods to estimate the regression parameter. The following are permitted: nonsm: Regression parameters are estimated by directly solving the nonsmooth estimating equations. sm: Regression parameters are estimated by directly solving the smoothed estimating equations. monosm:Regression parameters are estimated by iterating the monotonic smoothed estimating equations. This is typical when rankWeights = "PW" and rankWeights = "GP".

variance

a character string specifying the covariance estimating method. The following are permitted: MB: multiplier resampling, ZLCF: Zeng and Lin's approach with closed form Si, ZLMB: Zeng and Lin's approach with empirical Si, sHCF: Huang's approach with closed form Si, sHMB: Huang's approach with empirical Si, ISCF: Johnson and Strwderman's sandwich variance estimates with closed form Si, ISMB: Johnson and Strwderman's sandwich variance estimates with empirical Si, js: Johnson and Strwderman's iterating approach.

B

a numeric value specifies the resampling number. When B = 0, only the beta estimate will be displayed.

SigmaInit

the initial covariance matrix; default at identity matrix.

control

controls maxiter and tolerance.

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. Error codes are 1 indicates that the iteration limit maxit has been reached; 2 is failure due to stagnation; 3 indicates error in function evaluation; 4 is failure due to exceeding 100 step length reductions in line-search; and 5 indicates lack of improvement in objective function.

bhist

When variance = "MB", bhist gives the bootstrap samples.

Author(s)

Sy Han Chiou, Sangwook Kang, Jun Yan.

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

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#### kidney data
library(survival)
data(kidney)
foo <- aftsrr(Surv(time, status) ~ age + sex - 1, id = id,
                data = kidney, variance = c("ISMB", "ZLMB"), B = 10)
foo

#### nwtco data
library(survival)
data(nwtco)
subinx <- sample(1:nrow(nwtco), 668, replace = FALSE)
nwtco$subcohort <- 0
nwtco$subcohort[subinx] <- 1
pn <- table(nwtco$subcohort)[[2]] / sum(table(nwtco$subcohort))
nwtco$hi <- nwtco$rel + ( 1 - nwtco$rel) * nwtco$subcohort / pn
nwtco$age12 <- nwtco$age / 12
nwtco$study <- nwtco$study - 3
nwtco$histol = nwtco$histol - 1
sub <- nwtco[subinx,]
fit <- aftsrr(Surv(edrel, rel) ~ histol + age12 + study, id = seqno,
       weights = hi, data = sub, B = 10, variance = c("ISMB", "ZLMB"),
       subset = stage == 4)
summary(fit)