Buckley-James Regression

Description

Buckley-James regression for right-censoring survival data with high-dimensional covariates. Including L_2 boosting with componentwise linear least squares, componentwise P-splines, regression trees. Other Buckley-James methods including elastic net, MCP, SCAD, MARS and ACOSSO (ACOSSO not supported for the current version).

Usage

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bujar(y, cens, x, valdata = NULL, degree = 1, learner = "linear.regression",
center=TRUE, mimpu = NULL, iter.bj = 20, max.cycle = 5, nu = 0.1, mstop = 50, 
twin = FALSE, mstop2= 100, tuning = TRUE, cv = FALSE, nfold = 5, method = "corrected", 
vimpint = TRUE,gamma = 3, lambda=NULL, whichlambda=NULL, lamb = 0, s = 0.5, nk = 4, 
wt.pow = 1, theta = NULL, rel.inf = FALSE, tol = .Machine$double.eps, n.cores= 2, 
rng=123, trace = FALSE)

Arguments

y

survival time

cens

censoring indicator, must be 0 or 1 with 0=alive, 1=dead

x

covariate matrix

valdata

test data, which must have the first column as survival time, second column as censoring indicator, and the remaining columns similar to same x.

degree

mars/tree/linear regression degree of interaction; if 2, second-order interaction, if degree=1, additive model;

learner

methods used for BJ regression.

center

center covariates

mimpu

initial estimate. If TRUE, mean-imputation; FALSE, imputed with the marginal best variable linear regression; if NULL, 0.

iter.bj

number of B-J iteration

max.cycle

max cycle allowed

nu

step-size boosting parameter

mstop

boosting tuning parameters. It can be one number or have the length iter.bj+max.cycle. If cv=TRUE, then mstop is the maximum number of tuning parameter

twin

logical, if TRUE, twin boosting

mstop2

twin boosting tuning parameter

tuning

logical value. if TRUE, the tuning parameter will be selected by cv or AIC/BIC methods. Ignored if twin=TRUE for which no tuning parameter selection is implemented

cv

logical value. if TRUE, cross-validation for tuning parameter, only used if tuning=TRUE. If tuning=FALSE or twin=TRUE, then ignored

nfold

number of fold of cv

method

boosting tuning parameter selection method in AIC

vimpint

logical value. If TRUE, compute variable importance and interaction measures for MARS if learner="mars" and degree > 1.

gamma

MCP, or SCAD gamma tuning parameter

lambda

MCP, or SCAD lambda tuning parameter

whichlambda

which lambda used for MCP or SCAD lambda tuning parameter

lamb

elastic net lambda tuning parameter, only used if learner="enet"

s

the second enet tuning parameter, which is a fraction between (0, 1), only used if learne="enet"

nk

number of basis function for learner="mars"

wt.pow

not used but kept for historical reasons, only for learner=ACOSSO. This is a parameter (power of weight). It might be chosen by CV from c(0, 1.0, 1.5, 2.0, 2.5, 3.0). If wt.pow=0, then this is COSSO method

theta

For learner="acosso", not used now. A numerical vector with 0 or 1. 0 means the variable not included and 1 means included. See Storlie et al. (2009).

rel.inf

logical value. if TRUE, variable importance measure and interaction importance measure computed

tol

convergency criteria

n.cores

The number of CPU cores to use. The cross-validation loop will attempt to send different CV folds off to different cores. Used for learner="tree"

rng

a number to be used for random number generation in boosting trees

trace

logical value. If TRUE, print out interim computing results

Details

Buckley-James regression for right-censoring survival data with high-dimensional covariates. Including L_2 boosting with componentwise linear least squares, componentwise P-splines, regression trees. Other Buckley-James methods including elastic net, SCAD and MCP. learner="enet" and learner="enet2" use two different implementations of LASSO. Some of these methods are discussed in Wang and Wang (2010) and the references therein. Also see the references below.

Value

x

original covariates

y

survival time

cens

censoring indicator

ynew

imputed y

yhat

estimated y from ynew

pred.bj

estimated y from the testing sample

res.fit

model fitted with the learner

learner

original learner used

degree

=1, additive model, degree=2, second-order interaction

mse

MSE at each BJ iteration, only available in simulations, or when valdata provided

mse.bj

MSE from training data at the BJ termination

mse.bj.val

MSE with valdata

mse.all

a vector of MSE for uncensoring data at BJ iteration

nz.bj.iter

number of selected covariates at each BJ iteration

nz.bj

number of selected covariates at the claimed BJ termination

xselect

a vector of dimension of covariates, either 1 (covariate selected) or 0 (not selected)

coef.bj

estimated coefficients with linear model

vim

a vector of length of number of column of x, variable importance, between 0 to 100

interactions

measure of strength of interactions

ybstdiff

largest absolute difference of estimated y. Useful to monitor convergency

ybstcon

a vector with length of BJ iteration each is a convergency measure

cycleperiod

number of cycle of BJ iteration

cycle.coef.diff

within cycle of BJ, the maximum difference of coefficients for BJ boosting

nonconv

logical value. if TRUE, non-convergency

fnorm2

value of L_2 norm, can be useful to access convergencey

mselect

a vector of length of BJ iteration, each element is the tuning parameter mstop

contype

0 (converged), 1, not converged but cycle found, 2, not converged and max iteration reached.

Author(s)

Zhu Wang

References

Zhu Wang and C.Y. Wang (2010), Buckley-James Boosting for Survival Analysis with High-Dimensional Biomarker Data. Statistical Applications in Genetics and Molecular Biology, Vol. 9 : Iss. 1, Article 24.

Peter Buhlmann and Bin Yu (2003), Boosting with the L2 loss: regression and classification. Journal of the American Statistical Association, 98, 324–339.

Peter Buhlmann (2006), Boosting for high-dimensional linear models. The Annals of Statistics, 34(2), 559–583.

Peter Buhlmann and Torsten Hothorn (2007), Boosting algorithms: regularization, prediction and model fitting. Statistical Science, 22(4), 477–505.

J. Friedman (1991), Multivariate Adaptive Regression Splines (with discussion) . Annals of Statistics, 19/1, 1–141.

J.H. Friedman, T. Hastie and R. Tibshirani (2000), Additive Logistic Regression: a Statistical View of Boosting. Annals of Statistics 28(2):337-374.

C. Storlie, H. Bondell, B. Reich and H. H. Zhang (2009), Surface Estimation, Variable Selection, and the Nonparametric Oracle Property. Statistica Sinica, to appear.

Sijian Wang, Bin Nan, Ji Zhu, and David G. Beer (2008), Doubly penalized Buckley-James Method for Survival Data with High-Dimensional Covariates. Biometrics, 64:132-140.

H. Zou and T. Hastie (2005), Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B, 67, 301-320.

Examples

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data("wpbc", package = "TH.data")
wpbc2 <- wpbc[, 1:12]
wpbc2$status <- as.numeric(wpbc2$status) - 1
fit <- bujar(y=log(wpbc2$time),cens=wpbc2$status, x= wpbc2[, -(1:2)])
print(fit)
coef(fit)
pr <- predict(fit)
plot(fit)
fit <- bujar(y=log(wpbc2$time),cens=wpbc2$status, x= wpbc2[, -(1:2)], tuning = TRUE)
## Not run: 
fit <- bujar(y=log(wpbc2$time),cens=wpbc2$status, x=wpbc2[, -(1:2)], learner="pspline")
fit <- bujar(y=log(wpbc2$time),cens=wpbc2$status, x=wpbc2[, -(1:2)], 
 learner="tree", degree=2)
### select tuning parameter for "enet"
tmp <- gcv.enet(y=log(wpbc2$time), cens=wpbc2$status, x=wpbc2[, -(1:2)])
fit <- bujar(y=log(wpbc2$time),cens=wpbc2$status, x=wpbc2[, -(1:2)], learner="enet", 
lamb = tmp$lambda, s=tmp$s)

fit <- bujar(y=log(wpbc2$time),cens=wpbc2$status, x=wpbc2[, -(1:2)], learner="mars", 
degree=2)
summary(fit)

## End(Not run)