Package 'aftgee' reference manual

Title:	Accelerated Failure Time Model with Generalized Estimating Equations
Description:	A collection of methods for both the rank-based estimates and least-square estimates to the Accelerated Failure Time (AFT) model. For rank-based estimation, it provides approaches that include the computationally efficient Gehan's weight and the general's weight such as the logrank weight. Details of the rank-based estimation can be found in Chiou et al. (2014) <doi:10.1007/s11222-013-9388-2> and Chiou et al. (2015) <doi:10.1002/sim.6415>. For the least-square estimation, the estimating equation is solved with generalized estimating equations (GEE). Moreover, in multivariate cases, the dependence working correlation structure can be specified in GEE's setting. Details on the least-squares estimation can be found in Chiou et al. (2014) <doi:10.1007/s10985-014-9292-x>.
Authors:	Sy Han Chiou [aut, cre], Sangwook Kang [aut], Jun Yan [aut]
Maintainer:	Sy Han Chiou <[email protected]>
License:	GPL (>= 3)
Version:	1.2.1
Built:	2024-11-07 06:14:22 UTC
Source:	CRAN

aftgee: Accelerated Failure Time with Generalized Estimating Equation

Description

A package that uses Generalized Estimating Equations (GEE) to estimate Multivariate Accelerated Failure Time Model (AFT). This package implements recently developed inference procedures for AFT models with both the rank-based approach and the least squares approach. For the rank-based approach, the package allows various weight choices and uses an induced smoothing procedure that leads to much more efficient computation than the linear programming method. With the rank-based estimator as an initial value, the generalized estimating equation approach is used as an extension of the least squares approach to the multivariate case. Additional sampling weights are incorporated to handle missing data needed as in case-cohort studies or general sampling schemes.

Author(s)

Maintainer: Sy Han Chiou [email protected]

Authors:

Sangwook Kang
Jun Yan

References

Chiou, S., Kim, J. and Yan, J. (2014) Marginal Semiparametric Multivariate Accelerated Failure Time Model with Generalized Estimating Equation. Life Time Data, 20(4): 599–618.

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.

Jin, Z. and Lin, D. Y. and Ying, Z. (2006) On Least-squares Regression with Censored Data. Biometrika, 90, 341–353.

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.

Zeng, D. and Lin, D. Y. (2008) Efficient Resampling Methods for Nonsmooth Estimating Functions. Biostatistics, 9, 355–363

Least-Squares Approach for Accelerated Failure Time with Generalized Estimating Equation

Description

Fits a semiparametric accelerated failure time (AFT) model with least-squares approach. Generalized estimating equation is generalized to multivariate AFT modeling to account for multivariate dependence through working correlation structures to improve efficiency.

Usage

aftgee(
  formula,
  data,
  subset,
  id = NULL,
  contrasts = NULL,
  weights = NULL,
  margin = NULL,
  corstr = c("independence", "exchangeable", "ar1", "unstructured", "userdefined",
    "fixed"),
  binit = "srrgehan",
  B = 100,
  control = aftgee.control()
)
aftgee(
  formula,
  data,
  subset,
  id = NULL,
  contrasts = NULL,
  weights = NULL,
  margin = NULL,
  corstr = c("independence", "exchangeable", "ar1", "unstructured", "userdefined",
    "fixed"),
  binit = "srrgehan",
  B = 100,
  control = aftgee.control()
)

Arguments

`formula`	a formula expression, of the form `response ~ predictors`. The `response` is a `Surv` object with right censoring. In the case of no censoring, `aftgee` will return an ordinary least estimate when `corstr = "independence"`. 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`.
`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 `data` is presumed to represent a distinct subject. The length of `id` should be the same as the number of observations.
`contrasts`	an optional list.
`weights`	an optional vector of observation weights.
`margin`	a `sformula` vector; default at 1.
`corstr`	a character string specifying the correlation structure. The following are permitted: `independence` `exchangeable` `ar1` `unstructured` `userdefined` `fixed`
`binit`	an optional vector can be either a numeric vector or a character string specifying the initial slope estimator. When `binit` is a vector, its length should be the same as the dimension of covariates. When `binit` is a character string, it should be either `lm` for simple linear regression, or `srrgehan` for smoothed Gehan weight estimator. The default value is "srrgehan".
`B`	a numeric value specifies the resampling number. When B = 0, only the beta estimate will be displayed.
`control`	controls maxiter and tolerance.

Value

An object of class "aftgee" representing the fit. The aftgee object is a list containing at least the following components:

coefficients: a vector of initial value and a vector of point estimates
coef.res: a vector of point estimates
var.res: estimated covariance matrix
coef.init: a vector of initial value
var.init.mat: estimated initial covariance matrix
binit: a character string specifying the initial estimator.
conv: An integer code indicating type of convergence after GEE iteration. 0 indicates successful convergence; 1 indicates that the iteration limit maxit has been reached
ini.conv: An integer code indicating type of convergence for initial value. 0 indicates successful convergence; 1 indicates that the iteration limit maxit has been reached
conv.step: An integer code indicating the step until convergence

References

Chiou, S., Kim, J. and Yan, J. (2014) Marginal Semiparametric Multivariate Accelerated Failure Time Model with Generalized Estimating Equation. Lifetime Data Analysis, 20(4): 599–618.

Jin, Z. and Lin, D. Y. and Ying, Z. (2006) On Least-squares Regression with Censored Data. Biometrika, 90, 341–353.

Examples

## Simulate data from an AFT model with possible depended response
datgen <- function(n = 100, tau = 0.3, dim = 2) {
    x1 <- rbinom(dim * n, 1, 0.5)
    x2 <- rnorm(dim * n)
    e <- c(t(exp(MASS::mvrnorm(n = n, mu = rep(0, dim), Sigma = tau + (1 - tau) * diag(dim)))))
    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 = rep(1:n, each = dim))
}
set.seed(1); dat <- datgen(n = 50, dim = 2)
fm <- Surv(Time, status) ~ x1 + x2
fit1 <- aftgee(fm, data = dat, id = id, corstr = "ind")
fit2 <- aftgee(fm, data = dat, id = id, corstr = "ex")
summary(fit1)
summary(fit2)

confint(fit1)
confint(fit2)
## Simulate data from an AFT model with possible depended response
datgen <- function(n = 100, tau = 0.3, dim = 2) {
    x1 <- rbinom(dim * n, 1, 0.5)
    x2 <- rnorm(dim * n)
    e <- c(t(exp(MASS::mvrnorm(n = n, mu = rep(0, dim), Sigma = tau + (1 - tau) * diag(dim)))))
    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 = rep(1:n, each = dim))
}
set.seed(1); dat <- datgen(n = 50, dim = 2)
fm <- Surv(Time, status) ~ x1 + x2
fit1 <- aftgee(fm, data = dat, id = id, corstr = "ind")
fit2 <- aftgee(fm, data = dat, id = id, corstr = "ex")
summary(fit1)
summary(fit2)

confint(fit1)
confint(fit2)

Auxiliary for Controlling AFTGEE Fitting

Description

Auxiliary function as user interface for aftgee and aftsrr fitting.

Usage

aftgee.control(
  maxiter = 50,
  reltol = 0.001,
  trace = FALSE,
  seIni = FALSE,
  parallel = FALSE,
  parCl = parallel::detectCores()/2,
  gp.pwr = -999
)
aftgee.control(
  maxiter = 50,
  reltol = 0.001,
  trace = FALSE,
  seIni = FALSE,
  parallel = FALSE,
  parCl = parallel::detectCores()/2,
  gp.pwr = -999
)

Arguments

`maxiter`	max number of iteration.
`reltol`	relative error tolerance.
`trace`	a binary variable, determine whether to display output for each iteration.
`seIni`	a logical value indicating whether a new rank-based initial value is computed for each resampling sample in variance estimation.
`parallel`	an logical value indicating whether parallel computing is used for resampling and bootstrap.
`parCl`	an integer value indicating the number of CPU cores used when `parallel = TRUE`.
`gp.pwr`	an numerical value indicating the GP parameter when `rankWeights = GP`. The default value is half the CPU cores on the current host.

Details

When trace is TRUE, output for each iteration is printed to the screen.

Value

A list with the arguments as components.

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()
)
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 `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`.
`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 `data` is presumed to represent a distinct subject. The length of `id` should be the same as the number of observation.
`contrasts`	an optional list.
`weights`	an optional vector of observation weights.
`B`	a numeric value specifies the resampling number. When `B = 0` or `se = NULL`, only the beta estimate will be displayed.
`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 `userdefined` a user defined weight provided as a vector with length equal to the number of subject. This argument is still under-development.
`eqType`	a character string specifying the type of the estimating equation used to obtain the regression parameters. The following are permitted: `is` Regression parameters are estimated by directly solving the induced-smoothing estimating equations. This is the default and recommended method. `ns` Regression parameters are estimated by directly solving the nonsmooth estimating equations. `mis` Regression parameters are estimated by iterating the monotonic smoothed Gehan-based estimating equations. This is typical when `rankWeights = "PW"` and `rankWeights = "GP"`. `mns` Regression parameters are estimated by iterating the monotonic non-smoothed Gehan-based estimating equations. This is typical when `rankWeights = "PW"` and `rankWeights = "GP"`.
`se`	a character string specifying the estimating method for the variance-covariance matrix. The following are permitted: `NULL` if `se` is specified as `NULL`, the variance-covariance matrix will not be computed. `bootstrap` nonparametric bootstrap. `MB` multiplier resampling. `ZLCF` Zeng and Lin's approach with closed form $V$ , see Details. `ZLMB` Zeng and Lin's approach with empirical $V$ , see Details. `sHCF` Huang's approach with closed form $V$ , see Details. `sHMB` Huang's approach with empirical $V$ , see Details. `ISCF` Johnson and Strawderman's sandwich variance estimates with closed form $V$ , see Details. `ISMB` Johnson and Strawderman's sandwich variance estimates with empirical $V$ , see Details.
`control`	controls equation solver, maxiter, tolerance, and resampling variance estimation. The available equation solvers are `BBsolve` and `dfsane` of the BB package. The default algorithm control parameters are used when these functions are called. However, the monotonicity parameter, `M`, can be specified by users via the control list. When `M` is specified, the merit parameter, `noimp`, is set at $10 * M$ . The readers are refered to the BB package for details. Instead of searching for the zero crossing, options including `BBoptim` and `optim` will return solution from maximizing the corresponding objective function. When `se = "bootstrap"` or `se = "MB"`, an additional argument `parallel = TRUE` can be specified to enable parallel computation. The number of CPU cores can be specified with `parCl`, the default number of CPU cores is the integer value of `detectCores() / 2`.

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)
## 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)

`is.Surv` function imported from `survival`

Description

This function is imported from the survival package. See is.Surv.

`Surv` function imported from `survival`

Description

This function is imported from the survival package. See Surv.

Quasi Information Criterion

Description

Implementation based on MES::QIC.geeglm

Usage

QIC(object)
QIC(object)

Arguments

object

is a aftgee fit

Examples

## Simulate data from an AFT model with possible depended response
datgen <- function(n = 100, tau = 0.3, dim = 2) {
    x1 <- rbinom(dim * n, 1, 0.5)
    x2 <- rnorm(dim * n)
    e <- c(t(exp(MASS::mvrnorm(n = n, mu = rep(0, dim), Sigma = tau + (1 - tau) * diag(dim)))))
    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 = rep(1:n, each = dim))
}
set.seed(1); dat <- datgen(n = 50, dim = 2)
fm <- Surv(Time, status) ~ x1 + x2
fit1 <- aftgee(fm, data = dat, id = id, corstr = "ind")
fit2 <- aftgee(fm, data = dat, id = id, corstr = "ex")

QIC(fit1)
QIC(fit2)
## Simulate data from an AFT model with possible depended response
datgen <- function(n = 100, tau = 0.3, dim = 2) {
    x1 <- rbinom(dim * n, 1, 0.5)
    x2 <- rnorm(dim * n)
    e <- c(t(exp(MASS::mvrnorm(n = n, mu = rep(0, dim), Sigma = tau + (1 - tau) * diag(dim)))))
    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 = rep(1:n, each = dim))
}
set.seed(1); dat <- datgen(n = 50, dim = 2)
fm <- Surv(Time, status) ~ x1 + x2
fit1 <- aftgee(fm, data = dat, id = id, corstr = "ind")
fit2 <- aftgee(fm, data = dat, id = id, corstr = "ex")

QIC(fit1)
QIC(fit2)

Package 'aftgee'

Help Index

aftgee: Accelerated Failure Time with Generalized Estimating Equation

Description

Author(s)

References

See Also

Least-Squares Approach for Accelerated Failure Time with Generalized Estimating Equation

Description

Usage

Arguments

Value

References

Examples

Auxiliary for Controlling AFTGEE Fitting

Description

Usage

Arguments

Details

Value

See Also

Accelerated Failure Time with Smooth Rank Regression

Description

Usage

Arguments

Details

Value

References

Examples

`is.Surv` function imported from `survival`

Description

`Surv` function imported from `survival`

Description

Quasi Information Criterion

Description

Usage

Arguments

Examples

Package 'aftgee'

Help Index

aftgee: Accelerated Failure Time with Generalized Estimating Equation

Description

Author(s)

References

See Also

Least-Squares Approach for Accelerated Failure Time with Generalized Estimating Equation

Description

Usage

Arguments

Value

References

Examples

Auxiliary for Controlling AFTGEE Fitting

Description

Usage

Arguments

Details

Value

See Also

Accelerated Failure Time with Smooth Rank Regression

Description

Usage

Arguments

Details

Value

References

Examples

is.Surv function imported from survival

Description

Surv function imported from survival

Description

Quasi Information Criterion

Description

Usage

Arguments

Examples

`is.Surv` function imported from `survival`

`Surv` function imported from `survival`