R: Buckley-James Regression

bujar {bujar}

R Documentation

Buckley-James Regression

Description

Usage

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)
## S3 method for class 'bujar'
print(x, ...)
## S3 method for class 'bujar'
predict(object, newx=NULL, ...)
## S3 method for class 'bujar'
plot(x, ...)
## S3 method for class 'bujar'
coef(object, ...)
## S3 method for class 'bujar'
summary(object, ...)

Arguments

`y`	survival time
`cens`	censoring indicator, must be 0 or 1 with 0=alive, 1=dead
`x`	covariate matrix
`object`	an object of class `"bujar"`
`newx`	covariate matrix for prediction
`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
`...`	additional arguments used in estimation methods, for instance, trees.

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 convergency
`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

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)

[Package bujar version 0.2-11 Index]