Variable selection using minimal depth.

var.select(formula,
data,
object,
cause,
m.target,
method = c("md", "vh", "vh.vimp"),
conservative = c("medium", "low", "high"),
ntree = (if (method == "md") 1000 else 500),
mvars = (if (method != "md") ceiling(ncol(data)/5) else NULL),
mtry = (if (method == "md") ceiling(ncol(data)/3) else NULL),
nodesize = 2, splitrule = NULL, nsplit = 10, xvar.wt = NULL,
refit = (method != "md"), fast = FALSE,
na.action = c("na.omit", "na.impute"),
always.use = NULL, nrep = 50, K = 5, nstep = 1,
prefit =  list(action = (method != "md"), ntree = 100,
mtry = 500, nodesize = 3, nsplit = 1),
verbose = TRUE, ...)

## Arguments

formula

A symbolic description of the model to be fit. Must be specified unless object is given.

data

Data frame containing the y-outcome and x-variables in the model. Must be specified unless object is given.

object

An object of class (rfsrc, grow). Not required when formula and data are supplied.

cause

Integer value between 1 and J indicating the event of interest for competing risks, where J is the number of event types (this option applies only to competing risk families). The default is to use the first event type.

m.target

Character value for multivariate families specifying the target outcome to be used. If left unspecified, the algorithm will choose a default target.

method

Variable selection method:

md:

minimal depth (default).

vh:

variable hunting.

vh.vimp:

variable hunting with VIMP (variable importance).

conservative

Level of conservativeness of the thresholding rule used in minimal depth selection:

high:

Use the most conservative threshold.

medium:

Use the default less conservative tree-averaged threshold.

low:

Use the more liberal one standard error rule.

ntree

Number of trees to grow.

mvars

Number of randomly selected variables used in the variable hunting algorithm (ignored when method="md").

mtry

The mtry value used.

nodesize

Forest average terminal node size.

splitrule

Splitting rule used.

nsplit

If non-zero, the specified tree splitting rule is randomized which significantly increases speed.

xvar.wt

Vector of non-negative weights specifying the probability of selecting a variable for splitting a node. Must be of dimension equal to the number of variables. Default (NULL) invokes uniform weighting or a data-adaptive method depending on prefit$action. refit Should a forest be refit using the selected variables? fast Speeds up the cross-validation used for variable hunting for a faster analysis. See miscellanea below. na.action Action to be taken if the data contains NA values. always.use Character vector of variable names to always be included in the model selection procedure and in the final selected model. nrep Number of Monte Carlo iterations of the variable hunting algorithm. K Integer value specifying the K-fold size used in the variable hunting algorithm. nstep Integer value controlling the step size used in the forward selection process of the variable hunting algorithm. Increasing this will encourage more variables to be selected. prefit List containing parameters used in preliminary forest analysis for determining weight selection of variables. Users can set all or some of the following parameters: action: Determines how (or if) the preliminary forest is fit. See details below. ntree: Number of trees used in the preliminary analysis. mtry: mtry used in the preliminary analysis. nodesize: nodesize used in the preliminary analysis. nsplit: nsplit value used in the preliminary analysis. verbose Set to TRUE for verbose output. ... Further arguments passed to forest grow call. ## Details This function implements random forest variable selection using tree minimal depth methodology (Ishwaran et al., 2010). The option method allows for two different approaches: 1. method="md" Invokes minimal depth variable selection. Variables are selected using minimal depth variable selection. Uses all data and all variables simultaneously. This is basically a front-end to the max.subtree wrapper. Users should consult the max.subtree help file for details. Set mtry to larger values in high-dimensional problems. 2. method="vh" or method="vh.vimp" Invokes variable hunting. Variable hunting is used for problems where the number of variables is substantially larger than the sample size (e.g., p/n is greater than 10). It is always prefered to use method="md", but to find more variables, or when computations are high, variable hunting may be preferred. When method="vh": Using training data from a stratified K-fold subsampling (stratification based on the y-outcomes), a forest is fit using mvars randomly selected variables (variables are chosen with probability proportional to weights determined using an initial forest fit; see below for more details). The mvars variables are ordered by increasing minimal depth and added sequentially (starting from an initial model determined using minimal depth selection) until joint VIMP no longer increases (signifying the final model). A forest is refit to the final model and applied to test data to estimate prediction error. The process is repeated nrep times. Final selected variables are the top P ranked variables, where P is the average model size (rounded up to the nearest integer) and variables are ranked by frequency of occurrence. The same algorithm is used when method="vh.vimp", but variables are ordered using VIMP. This is faster, but not as accurate. Miscellanea 1. When variable hunting is used, a preliminary forest is run and its VIMP is used to define the probability of selecting a variable for splitting a node. Thus, instead of randomly selecting mvars at random, variables are selected with probability proportional to their VIMP (the probability is zero if VIMP is negative). A preliminary forest is run once prior to the analysis if prefit$action=TRUE, otherwise it is run prior to each iteration (this latter scenario can be slow). When method="md", a preliminary forest is fit only if prefit$action=TRUE. Then instead of randomly selecting mtry variables at random, mtry variables are selected with probability proportional to their VIMP. In all cases, the entire option is overridden if xvar.wt is non-null. 2. If object is supplied and method="md", the grow forest from object is parsed for minimal depth information. While this avoids fitting another forest, thus saving computational time, certain options no longer apply. In particular, the value of cause plays no role in the final selected variables as minimal depth is extracted from the grow forest, which has already been grown under a preselected cause specification. Users wishing to specify cause should instead use the formula and data interface. Also, if the user requests a prefitted forest via prefit$action=TRUE, then object is not used and a refitted forest is used in its place for variable selection. Thus, the effort spent to construct the original grow forest is not used in this case.

3. If fast=TRUE, and variable hunting is used, the training data is chosen to be of size n/K, where n=sample size (i.e., the size of the training data is swapped with the test data). This speeds up the algorithm. Increasing K also helps.

4. Can be used for competing risk data. When method="vh.vimp", variable selection based on VIMP is confined to an event specific cause specified by cause. However, this can be unreliable as not all y-outcomes can be guaranteed when subsampling (this is true even when stratifed subsampling is used as done here).

## Value

Invisibly, a list with the following components:

err.rate

Prediction error for the forest (a vector of length nrep if variable hunting is used).

modelsize

Number of variables selected.

topvars

Character vector of names of the final selected variables.

varselect

Useful output summarizing the final selected variables.

rfsrc.refit.obj

Refitted forest using the final set of selected variables (requires refit=TRUE).

md.obj

Minimal depth object. NULL unless method="md".

## Author

Hemant Ishwaran and Udaya B. Kogalur

## References

Ishwaran H., Kogalur U.B., Gorodeski E.Z, Minn A.J. and Lauer M.S. (2010). High-dimensional variable selection for survival data. J. Amer. Statist. Assoc., 105:205-217.

Ishwaran H., Kogalur U.B., Chen X. and Minn A.J. (2011). Random survival forests for high-dimensional data. Statist. Anal. Data Mining, 4:115-132.

find.interaction.rfsrc, holdout.vimp.rfsrc, max.subtree.rfsrc, vimp.rfsrc

## Examples

# \donttest{
## ------------------------------------------------------------
## Minimal depth variable selection
## survival analysis
## use larger node size which is better for minimal depth
## ------------------------------------------------------------

data(pbc, package = "randomForestSRC")
pbc.obj <- rfsrc(Surv(days, status) ~ ., pbc, nodesize = 20, importance = TRUE)

# default call corresponds to minimal depth selection
vs.pbc <- var.select(object = pbc.obj)
topvars <- vs.pbc$topvars # the above is equivalent to max.subtree(pbc.obj)$topvars

# different levels of conservativeness
var.select(object = pbc.obj, conservative = "low")
var.select(object = pbc.obj, conservative = "medium")
var.select(object = pbc.obj, conservative = "high")

## ------------------------------------------------------------
## Minimal depth variable selection
## competing risk analysis
## use larger node size which is better for minimal depth
## ------------------------------------------------------------

## competing risk data set involving AIDS in women
data(wihs, package = "randomForestSRC")
vs.wihs <- var.select(Surv(time, status) ~ ., wihs, nsplit = 3,
nodesize = 20, ntree = 100, importance = TRUE)

## competing risk analysis of pbc data from survival package
## implement cause-specific variable selection
if (library("survival", logical.return = TRUE)) {
data(pbc, package = "survival")
pbc$id <- NULL var.select(Surv(time, status) ~ ., pbc, cause = 1) var.select(Surv(time, status) ~ ., pbc, cause = 2) } ## ------------------------------------------------------------ ## Minimal depth variable selection ## classification analysis ## ------------------------------------------------------------ vs.iris <- var.select(Species ~ ., iris) ## ------------------------------------------------------------ ## Variable hunting high-dimensional example ## van de Vijver microarray breast cancer survival data ## nrep is small for illustration; typical values are nrep = 100 ## ------------------------------------------------------------ data(vdv, package = "randomForestSRC") vh.breast <- var.select(Surv(Time, Censoring) ~ ., vdv, method = "vh", nrep = 10, nstep = 5) # plot top 10 variables plot.variable(vh.breast$rfsrc.refit.obj,
xvar.names = vh.breast$topvars[1:10]) plot.variable(vh.breast$rfsrc.refit.obj,
xvar.names = vh.breast$topvars[1:10], partial = TRUE) ## similar analysis, but using weights from univarate cox p-values if (library("survival", logical.return = TRUE)) { cox.weights <- function(rfsrc.f, rfsrc.data) { event.names <- all.vars(rfsrc.f)[1:2] p <- ncol(rfsrc.data) - 2 event.pt <- match(event.names, names(rfsrc.data)) xvar.pt <- setdiff(1:ncol(rfsrc.data), event.pt) sapply(1:p, function(j) { cox.out <- coxph(rfsrc.f, rfsrc.data[, c(event.pt, xvar.pt[j])]) pvalue <- summary(cox.out)$coef[5]
if (is.na(pvalue)) 1.0 else 1/(pvalue + 1e-100)
})
}
data(vdv, package = "randomForestSRC")
rfsrc.f <- as.formula(Surv(Time, Censoring) ~ .)
cox.wts <- cox.weights(rfsrc.f, vdv)
vh.breast.cox <- var.select(rfsrc.f, vdv, method = "vh", nstep = 5,
nrep = 10, xvar.wt = cox.wts)
}

# }