rfsrc.Rd
Fast OpenMP parallel computing of random forests (Breiman 2001) for regression, classification, survival analysis (Ishwaran et al. 2008), competing risks (Ishwaran et al. 2012), multivariate (Segal and Xiao 2011), unsupervised (Mantero and Ishwaran 2020), quantile regression (Meinhausen 2006, Zhang et al. 2019, GreenwaldKhanna 2001), and class imbalanced qclassification (O'Brien and Ishwaran 2019). Different splitting rules invoked under deterministic or random splitting (Geurts et al. 2006, Ishwaran 2015) are available for all families. Different types of variable importance (VIMP), holdout VIMP, as well as confidence regions (Ishwaran and Lu 2019) can be calculated for single and grouped variables. Minimal depth variable selection (Ishwaran et al. 2010, 2011). Fast interface for missing data imputation using a variety of different random forest methods (Tang and Ishwaran 2017).
New items users should be aware of:
The default VIMP is no longer "permute" (BreimanCutler
permutation importance) and has been switched to "anti"
(importance="anti"
, importance=TRUE
). This calculates
VIMP by assigning OOB cases to the opposite (anti) split and is
considerably faster. Note in some situations, such as highly
imbalanced classification, permutation VIMP may perform better.
Users can always obtain permutation VIMP using
importance="permute"
.
Now available, Mahalanobis splitting for multivariate
regression with correlated youtcomes
(splitrule="mahalanobis"
).
Now available, visualize trees on your Safari or Google Chrome
browser (works for all families). See get.tree
.
This is the main entry point to the randomForestSRC
package. For more information about this package and OpenMP parallel
processing, use the command package?randomForestSRC
.
rfsrc(formula, data, ntree = 500, mtry = NULL, ytry = NULL, nodesize = NULL, nodedepth = NULL, splitrule = NULL, nsplit = 10, importance = c(FALSE, TRUE, "none", "anti", "permute", "random"), block.size = if (any(is.element(as.character(importance), c("none", "FALSE")))) NULL else 10, bootstrap = c("by.root", "none", "by.user"), samptype = c("swor", "swr"), samp = NULL, membership = FALSE, sampsize = if (samptype == "swor") function(x){x * .632} else function(x){x}, na.action = c("na.omit", "na.impute"), nimpute = 1, ntime = 150, cause, proximity = FALSE, distance = FALSE, forest.wt = FALSE, xvar.wt = NULL, yvar.wt = NULL, split.wt = NULL, case.wt = NULL, forest = TRUE, var.used = c(FALSE, "all.trees", "by.tree"), split.depth = c(FALSE, "all.trees", "by.tree"), seed = NULL, do.trace = FALSE, statistics = FALSE, ...) ## convenient interface for growing a CART tree rfsrc.cart(formula, data, ntree = 1, mtry = ncol(data), bootstrap = "none", ...)
formula  A symbolic description of the model to be fit. If missing, unsupervised splitting is implemented. 

data  Data frame containing the youtcome and xvariables. 
ntree  Number of trees. 
mtry  Number of variables randomly selected as candidates for
splitting a node. The default is 
ytry  For unsupervised forests, sets the number of randomly
selected pseudooutcomes (see below for more details).
The default is 
nodesize  Minumum size of terminal node.
The defaults are: survival (15), competing risk
(15), regression (5), classification (1), mixed outcomes (3),
unsupervised (3). It is recommended to experiment with different

nodedepth  Maximum depth to which a tree should be grown. The default behaviour is that this parameter is ignored. 
splitrule  Splitting rule (see below). 
nsplit  Nonnegative integer value for number of random splits to consider for each candidate splitting variable. This significantly increases speed. When zero or NULL, uses much slower deterministic splitting where all possible splits considered. 
importance  Method for computing variable importance (VIMP); see
below. Default action is 
block.size  Should the cumulative error rate be calculated on
every tree? When 
bootstrap  Bootstrap protocol. The default is 
samptype  Type of bootstrap when 
samp  Bootstrap specification when 
membership  Should terminal node membership and inbag information be returned? 
sampsize  Function specifying size of bootstrap data when

na.action  Action taken if the data contains 
nimpute  Number of iterations of the missing data algorithm.
Performance measures such as outofbag (OOB) error rates tend to
become optimistic if 
ntime  Integer value used for survival to constrain ensemble
calculations to an 
cause  Integer value between 1 and 
proximity  Proximity of cases as measured by the frequency of
sharing the same terminal node. This is an 
distance  Distance between cases as measured by the ratio of the
sum of the count of edges from each case to their immediate common
ancestor node to the sum of the count of edges from each case to the
root node. If the cases are coterminal for a tree, this measure is
zero and reduces to 1  the proximity measure for these cases in a
tree. This is an 
forest.wt  Should the forest weight matrix be
calculated? Creates an 
xvar.wt  Vector of nonnegative weights (does not have to sum to 1) representing the probability of selecting a variable for splitting. Default is to use uniform weights. 
yvar.wt  NOT YET IMPLEMENTED: Vector of nonnegative weights (does not have to sum to 1) representing the probability of selecting a outcome as a candidate for the split statistic in unsupervised settings. Default is to use uniform weights. 
split.wt  Vector of nonnegative weights used for multiplying the split statistic for a variable. A large value encourages the node to split on a specific variable. Default is to use uniform weights. 
case.wt  Vector of nonnegative weights (does not have to sum to 1) for sampling cases. Observations with larger weights will be selected with higher probability in the bootstrap (or subsampled) samples. It is generally better to use real weights rather than integers. See the example below for the breast data set for an illustration of its use for class imbalanced data. 
forest  Should the forest object be returned? Used for prediction on new data and required by many of the package functions. 
var.used  Return variables used for splitting? Default is

split.depth  Records the minimal depth for each variable.
Default is 
seed  Negative integer specifying seed for the random number generator. 
do.trace  Number of seconds between updates to the user on approximate time to completion. 
statistics  Should split statistics be returned? Values can be
parsed using 
...  Further arguments passed to or from other methods. 
Types of forests
There is no need to set the type of forest as the package automagically determines the underlying random forest requested from the type of outcome and the formula supplied. There are several possible scenarios:
Regression forests for continuous outcomes.
Classification forests for factor outcomes.
Multivariate forests for continuous and/or factor outcomes and for mixed (both type) of outcomes.
Unsupervised forests when there is no outcome.
Survival forests for rightcensored survival.
Competing risk survival forests for competing risk.
Splitting
Splitting rules are specified by the option splitrule
.
For all families, pure random splitting can be invoked by setting
splitrule="random"
.
For all families, computational speed can be increased using
randomized splitting invoked by the option nsplit
.
See Improving Computational Speed.
Available splitting rules
Regression analysis:
splitrule="mse"
: default split rule implements weighted
meansquared error splitting (Breiman et al. 1984, Chapter 8.4).
splitrule="quantile.regr"
: quantile regression splitting via
the "checkloss" function. Requires specifying the target
quantiles. See quantreg.rfsrc
for further details.
la.quantile.regr
: local adaptive quantile
regression splitting. See quantreg.rfsrc
.
Classification analysis:
splitrule="gini"
: default splitrule implements Gini
index splitting (Breiman et al. 1984, Chapter 4.3).
splitrule="auc"
: AUC (area under the ROC curve) splitting
for both twoclass and multiclass setttings. AUC splitting is
appropriate for imbalanced data. See imbalanced
for
more information.
splitrule="entropy"
: entropy splitting (Breiman et
al. 1984, Chapter 2.5, 4.3).
Survival analysis:
splitrule="logrank"
: default splitrule implements
logrank splitting (Segal, 1988; Leblanc and Crowley, 1993).
splitrule="bs.gradient"
: gradientbased (global nonquantile)
brier score splitting. The time horizon used for the Brier
score is set to the 90th percentile of the observed event times.
This can be overridden by the option prob
, which must be
a value between 0 and 1 (set to .90 by default).
splitrule="logrankscore"
: logrank score splitting (Hothorn and
Lausen, 2003).
Competing risk analysis (for details see Ishwaran et al., 2014):
splitrule="logrankCR"
: default splitrule implements a modified
weighted logrank splitting rule modeled after Gray's test
(Gray, 1988). Use this to find *all* variables
that are informative and when the goal is long term
prediction.
splitrule="logrank"
: weighted logrank splitting where each
event type is treated as the event of interest and all
other events are treated as censored. The split rule is
the weighted value of each of logrank statistics,
standardized by the variance. Use this to find variables
that affect a *specific* cause of interest and when
the goal is a targeted analysis of a specific cause.
However in order for this to be effective, remember to set
the cause
option to the targeted cause of interest.
See examples below.
Multivariate analysis:
When one or both regression and classification outcomes are detected, a multivariate normalized composite split rule of meansquared error and Gini index splitting is invoked. See Tang and Ishwaran (2017).
splitrule="mahalanobis"
: Mahalanobis splitting
that adjusts for correlation can be specified in the special
case of multivariate regression (all outcomes must be real).
Unsupervised analysis: In settings where there is no
outcome, unsupervised splitting is invoked. In this case,
the mixed outcome splitting rule (above) is applied. Also
see sidClustering
for a more sophisticated method for
unsupervised analysis (Mantero and Ishwaran, 2020).
Custom splitting: All families except unsupervised are
available for user defined custom splitting. Some basic
Cprogramming skills are required. The harness for defining
these rules is in splitCustom.c
. In this file we
give examples of how to code rules for regression,
classification, survival, and competing risk. Each family
can support up to sixteen custom split rules. Specifying
splitrule="custom"
or splitrule="custom1"
will
trigger the first split rule for the family defined by the
training data set. Multivariate families will need a custom
split rule for both regression and classification. In the
examples, we demonstrate how the user is presented with the
node specific membership. The task is then to define a
split statistic based on that membership. Take note of the
instructions in splitCustom.c
on how to
register the custom split rules. It is suggested
that the existing custom split rules be kept in place for
reference and that the user proceed to develop
splitrule="custom2"
and so on. The package must be
recompiled and installed for the custom split rules to
become available.
Improving computational speed
See the function rfsrc.fast
for a fast
implementation of rfsrc
. In general, the key methods for
increasing speed are as follows:
Randomized splitting rules
Computational speed can be significantly improved with randomized
splitting invoked by the option nsplit
. When nsplit
is set to a nonzero positive integer, a maximum of nsplit
split points are chosen randomly for each of the candidate
splitting variables when splitting a tree node, thus significantly
reducing the cost from having to consider all possible splitvalues.
To revert to traditional deterministic splitting (all split
values considered) use nsplit
=0.
Randomized splitting for trees has a long history. See for
example, Loh and Shih (1997), Dietterich (2000), and Lin and Jeon
(2006). Geurts et al. (2006) recently introduced extremely
randomized trees using what they call the extratrees algorithm.
We can see that this algorithm essentially corresponds to
randomized splitting with nsplit
=1. In our experience
however this is not always the optimal value for nsplit
and
may often be too low. See Ishwaran (2015).
Finally, for completely randomized (pure random) splitting use
splitrule="random"
. In pure splitting, nodes are split by
randomly selecting a variable and randomly selecting its split
point (Cutler and Zhao, 2001).
Subsampling
Subsampling can be used to reduce the size of the insample data
used to grow a tree and therefore can greatly reduce computational
load. Subsampling is implemented using options sampsize
and samptype
. See rfsrc.fast
for a fast forest
implementation using subsampling.
Unique time points
Setting ntime
to a reasonably small value such as
150 (the default) constrains survival ensemble calculations to a
restricted grid of time points and significantly improves
computational times.
Large number of variables
The default setting importance="none"
turns off variable
importance (VIMP) calculations and considerably reduces
computational times. Variable importance can always
be recovered later using functions vimp
or
predict
. Also consider using max.subtree
which calculates minimal depth, a measure of the depth that a
variable splits, and yields fast variable selection (Ishwaran,
2010).
Prediction Error
Prediction error is calculated using OOB data. Performance is
measured in terms of meansquarederror for regression, and
misclassification error for classification. A normalized Brier
score (relative to a cointoss) and the AUC (area under the ROC
curve) is also provided upon printing a classification forest.
Performance for Brier score can be specified using
perf.type="brier"
. Gmean performance is also available, see
the function imbalanced
for more details.
For survival, prediction error is measured by 1C, where C is Harrell's (Harrell et al., 1982) concordance index. Prediction error is between 0 and 1, and measures how well the predictor correctly ranks (classifies) two random individuals in terms of survival. A value of 0.5 is no better than random guessing. A value of 0 is perfect.
When bootstrapping is by none
, a coherent OOB subset is not
available to assess prediction error. Thus, all outputs dependent
on this are suppressed. In such cases, prediction error is only
available via classical crossvalidation (the user will need to use
the predict.rfsrc
function).
Variable Importance (VIMP)
By default, importance=FALSE
and VIMP is not calculated
unless requested.
The option importance="permute"
returns permutation VIMP by
permuting OOB cases (classical BreimanCutler importance). The
option importance="random"
returns importance by random
daughter assignment of OOB cases whenever a split is encountered for
the target variable. The default is importance="anti"
(equivalent to importance=TRUE
) which assigns OOB cases to
the anti (opposite) split.
VIMP depends upon block.size
, an integer value between 1 and
ntree
, specifying number of trees in a block used for VIMP.
When block.size
=1, VIMP is calculated for each tree. When
block.size="ntree"
, VIMP is calculated for the entire forest
by comparing the perturbed OOB forest ensemble (using all trees) to
the unperturbed OOB forest ensemble (using all trees). This yields
ensemble VIMP, which does not measure the tree average effect of a
variable, but rather its overall forest effect.
A useful compromise between tree VIMP and ensemble VIMP can be
obtained by setting block.size
to a value between 1 and
ntree
. Smaller values generally gives better accuracy,
however computational times will be higher because VIMP is
calculated over more blocks. However, see imbalanced
for
imbalanced classification data where larger block.size
often works better (O'Brien and Ishwaran, 2019).
See vimp
for a user interface for extracting VIMP and
subsampling
for calculating confidence intervals for VIMP.
Also see holdout.vimp
for holdout VIMP, which calculates
importance by holding out variables. This is more conservative, but
with good false discovery properties.
For classification, VIMP is returned as a matrix with with J+1 columns where J is the number of classes. The first column "all" is the unconditional VIMP, while the remaining columns are VIMP conditioned on cases corresponding to that class label.
Multivariate Forests
Multivariate forests can be specified in two ways:
rfsrc(Multivar(y1, y2, ..., yd) ~ . , my.data, ...)
rfsrc(cbind(y1, y2, ..., yd) ~ . , my.data, ...)
By default, a multivariate normalized composite splitting rule is used to split nodes (for multivariate regression, users have the option to use Mahalanobis splitting).
The nature of the outcomes informs the code as to what type of multivariate forest is grown; i.e. whether it is realvalued, categorical, or a combination of both (mixed). Performance measures (when requested) are returned for all outcomes.
Unsupervised Forests and sidClustering
See sidClustering sidClustering
for a more sophisticated
method for unsupervised analysis.
Otherwise a more direct (but naive) way to proceed is to use the unsupervised splitting rule. The following are equivalent ways to grow an unsupervised forest via unsupervised splitting:
rfsrc(data = my.data)
rfsrc(Unsupervised() ~ ., data = my.data)
In unsupervised mode, features take turns acting as target
youtcomes and xvariables for splitting. Specifically, mtry
xvariables are randomly selected for splitting the node. Then for
each mtry
feature, ytry
variables are selected
from the remaining features to act as the target pseduooutcomes.
Splitting uses the multivariate normalized composite splitting rule.
The default value of ytry
is 1 but can be increased. As
illustration, the following equivalent unsupervised calls set
mtry=10
and ytry
=5:
rfsrc(data = my.data, ytry = 5, mtry = 10)
rfsrc(Unsupervised(5) ~ ., my.data, mtry = 10)
Note that all performance values (error rates, VIMP, prediction) are turned off in unsupervised mode.
Survival, Competing Risks
Survival settings require a time and censoring variable which
should be identifed in the formula as the outcome using the standard
Surv
formula specification. A typical formula call looks like:
Surv(my.time, my.status) ~ .
where my.time
and my.status
are the variables names for
the event time and status variable in the users data set.
For survival forests (Ishwaran et al. 2008), the censoring variable must be coded as a nonnegative integer with 0 reserved for censoring and (usually) 1=death (event).
For competing risk forests (Ishwaran et al., 2013), the implementation is similar to survival, but with the following caveats:
Censoring must be coded as a nonnegative integer, where 0 indicates rightcensoring, and nonzero values indicate different event types. While 0,1,2,..,J is standard, and recommended, events can be coded nonsequentially, although 0 must always be used for censoring.
Setting the splitting rule to logrankscore
will result
in a survival analysis in which all events are treated as if they
are the same type (indeed, they will coerced as such).
Generally, competing risks requires a larger nodesize
than
survival settings.
Missing data imputation
Set na.action="na.impute"
to impute missing data (both x and
yvariables) using the missing data algorithm of Ishwaran et
al. (2008). However, see the function impute
for an
alternate way to do fast and accurate imputation.
The missing data algorithm can be iterated by setting nimpute
to a positive integer greater than 1. When iterated, at the
completion of each iteration, missing data is imputed using OOB
nonmissing terminal node data which is then used as input to grow a
new forest. A side effect of iteration is that missing values in
the returned objects xvar
, yvar
are replaced by
imputed values. In other words the incoming data is overlaid with
the missing data. Also, performance measures such as error rates
and VIMP become optimistically biased.
Records in which all outcome and xvariable information are missing are removed from the forest analysis. Variables having all missing values are also removed.
Allowable data types and factors
Data types must be real valued, integer, factor or logical 
however all except factors are coerced and treated as if real
valued. For ordered xvariable factors, splits are similar to real
valued variables. For unordered factors, a split will move a subset
of the levels in the parent node to the left daughter, and the
complementary subset to the right daughter. All possible
complementary pairs are considered and apply to factors with an
unlimited number of levels. However, there is an optimization check
to ensure number of splits attempted is not greater than number of
cases in a node or the value of nsplit
.
For coherence, an immutable map is applied to each factor that ensures factor levels in the training data are consistent with the factor levels in any subsequent test data. This map is applied to each factor before and after the native C library is executed. Because of this, if all xvariables all factors, then computational time will be long in high dimensional problems. Consider converting factors to real if this is the case.
An object of class (rfsrc, grow)
with the following
components:
The original call to rfsrc
.
The family used in the analysis.
Sample size of the data (depends upon NA
's, see na.action
).
Number of trees grown.
Number of variables randomly selected for splitting at each node.
Minimum size of terminal nodes.
Maximum depth allowed for a tree.
Splitting rule used.
Number of randomly selected split points.
youtcome values.
A character vector of the youtcome names.
Data frame of xvariables.
A character vector of the xvariable names.
Vector of nonnegative weights specifying the probability used to select a variable for splitting a node.
Vector of nonnegative weights specifying multiplier by which the split statistic for a covariate is adjusted.
Vector of weights used for the composite competing risk splitting rule.
Number of terminal nodes for each tree in the
forest. Vector of length ntree
. A value of zero indicates
a rejected tree (can occur when imputing missing data).
Values of one indicate tree stumps.
Proximity matrix recording the frequency of pairs of data points occur within the same terminal node.
If forest=TRUE
, the forest object is returned.
This object is used for prediction with new test data
sets and is required for other Rwrappers.
Forest weight matrix.
Matrix recording terminal node membership where each column records node mebership for a case for a tree (rows).
Splitting rule used.
Matrix recording inbag membership where each column contains the number of times that a case appears in the bootstrap sample for a tree (rows).
Count of the number of times a variable is used in growing the forest.
Vector of indices for cases with missing values.
Data frame of the imputed data. The first column(s) are reserved for the youtcomes, after which the xvariables are listed.
Matrix (i,j) or array (i,j,k) recording the minimal depth for variable j for case i, either averaged over the forest, or by tree k.
Split statistics returned when
statistics=TRUE
which can be parsed using stat.split
.
Tree cumulative OOB error rate.
When importance=TRUE
, vector of the
cumulative error rate for each ensemble block comprised of
block.size
trees. So with block.size = 10
, entries are
the cumulative error rate for the first 10 trees, the first 20 trees,
30 trees, and so on. As another exmple, if block.size = 1
,
entries are the error rate for each tree.
Variable importance (VIMP) for each xvariable.
Inbag predicted value.
OOB predicted value.
for classification settings, additionally ++++++++
Inbag predicted class labels.
OOB predicted class labels.
for multivariate settings, additionally ++++++++
List containing performance values for multivariate regression outcomes (applies only in multivariate settings).
List containing performance values for multivariate categorical (factor) outcomes (applies only in multivariate settings).
for survival settings, additionally ++++++++
Inbag survival function.
OOB survival function.
Inbag cumulative hazard function (CHF).
OOB CHF.
Ordered unique death times.
Number of deaths.
for competing risks, additionally ++++++++
Inbag causespecific cumulative hazard function (CSCHF) for each event.
OOB CSCHF.
Inbag cumulative incidence function (CIF) for each event.
OOB CIF.
Ordered unique event times.
Number of events.
Values returned depend heavily on the family. In particular,
predicted values from the forest (predicted
and
predicted.oob
) are as follows:
For regression, a vector of predicted youtcomes.
For classification, a matrix with columns containing the estimated class probability for each class. Performance values and VIMP for classification are reported as a matrix with J+1 columns where J is the number of classes. The first column "all" is the unconditional value for performance (VIMP), while the remaining columns are performance (VIMP) conditioned on cases corresponding to that class label.
For survival, a vector of mortality values (Ishwaran et al.,
2008) representing estimated risk for each individual calibrated
to the scale of the number of events (as a specific example, if
i has a mortality value of 100, then if all individuals had
the same xvalues as i, we would expect an average of 100
events). Also returned are matrices containing
the CHF and survival function. Each row corresponds to an
individual's ensemble CHF or survival function evaluated at each
time point in time.interest
.
For competing risks, a matrix with one column for each event
recording the expected number of life years lost due to the event
specific cause up to the maximum follow up (Ishwaran et al.,
2013). Also returned are the causespecific cumulative hazard
function (CSCHF) and the cumulative incidence function (CIF) for
each event type. These are encoded as a threedimensional array,
with the third dimension used for the event type, each time point
in time.interest
making up the second dimension (columns),
and the case (individual) being the first dimension (rows).
For multivariate families, predicted values (and other
performance values such as VIMP and error rates) are stored in the
lists regrOutput
and clasOutput
which can be
extracted using functions get.mv.error
,
get.mv.predicted
and get.mv.vimp
.
Hemant Ishwaran and Udaya B. Kogalur
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Loh W.Y and Shih Y.S (1997). Split selection methods for classification trees, Statist. Sinica, 7:815840.
Mantero A. and Ishwaran H. (2021). Unsupervised random forests. Statistical Analysis and Data Mining, 14(2):144167.
Meinshausen N. (2006) Quantile regression forests, Journal of Machine Learning Research, 7:983999.
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imbalanced.rfsrc
,
impute.rfsrc
,
partial.rfsrc
,
plot.competing.risk.rfsrc
,
plot.rfsrc
,
plot.survival.rfsrc
,
plot.variable.rfsrc
,
predict.rfsrc
,
print.rfsrc
,
rfsrc
,
rfsrc.cart
,
rfsrc.fast
,
## ## survival analysis ## ## veteran data ## randomized trial of two treatment regimens for lung cancer data(veteran, package = "randomForestSRC") v.obj < rfsrc(Surv(time, status) ~ ., data = veteran, ntree = 100, block.size = 1) ## print tree number 3 plot(get.tree(v.obj, 3)) ## print the grow object and plot various useful details print(v.obj) plot(v.obj) ## plot survival curves for first 10 individuals  direct way matplot(v.obj$time.interest, 100 * t(v.obj$survival.oob[1:10, ]), xlab = "Time", ylab = "Survival", type = "l", lty = 1) ## plot survival curves for first 10 individuals ## using function "plot.survival" plot.survival(v.obj, subset = 1:10) # \donttest{ ## fast nodesize optimization for veteran data ## optimal nodesize in survival is larger than other families ## see the function "tune" for more examples tune.nodesize(Surv(time,status) ~ ., veteran) ## Primary biliary cirrhosis (PBC) of the liver data(pbc, package = "randomForestSRC") pbc.obj < rfsrc(Surv(days, status) ~ ., pbc) print(pbc.obj) ## ## trees can be plotted for any family ## see get.tree for details and more examples ## ## survival where factors have many levels data(veteran, package = "randomForestSRC") vd < veteran vd$celltype=factor(vd$celltype) vd$diagtime=factor(vd$diagtime) vd.obj < rfsrc(Surv(time,status)~., vd, ntree = 100, nodesize = 5) plot(get.tree(vd.obj, 3)) ## classification iris.obj < rfsrc(Species ~., data = iris) plot(get.tree(iris.obj, 25, class.type = "bayes")) plot(get.tree(iris.obj, 25, target = "setosa")) plot(get.tree(iris.obj, 25, target = "versicolor")) plot(get.tree(iris.obj, 25, target = "virginica")) ##  ## simple example of VIMP using iris classification ##  ## directly from grow call print(rfsrc(Species~.,iris,importance=TRUE)$importance) ## note by default VIMP (and performance) uses misclassification error, ## but brier prediction error can be specified print(rfsrc(Species~.,iris,importance=TRUE,perf.type="brier")$importance) ## using vimp function (see vimp help file for details) iris.obj < rfsrc(Species ~., data = iris) print(vimp(iris.obj)$importance) print(vimp(iris.obj,perf.type="brier")$importance) ## hold out vimp (see holdout.vimp help file for details) print(holdout.vimp(Species~.,iris)$importance) print(holdout.vimp(Species~.,iris,perf.type="brier")$importance) ##  ## confidence interval for vimp using subsampling ## compare with holdout vimp ##  ## new York air quality measurements o < rfsrc(Ozone ~ ., data = airquality) so < subsample(o) plot(so) ## compare with holdout vimp print(holdout.vimp(Ozone ~ ., data = airquality)$importance) ## ## example of imputation in survival analysis ## data(pbc, package = "randomForestSRC") pbc.obj2 < rfsrc(Surv(days, status) ~ ., pbc, nsplit = 10, na.action = "na.impute") ## same as above but we iterate the missing data algorithm pbc.obj3 < rfsrc(Surv(days, status) ~ ., pbc, na.action = "na.impute", nimpute = 3) ## fast way to impute the data (no inference is done) ## see impute for more details pbc.imp < impute(Surv(days, status) ~ ., pbc, splitrule = "random") ## ## compare RFSRC to Cox regression ## Illustrates Cindex and Brier score measures of performance ## assumes "pec" and "survival" libraries are loaded ## if (library("survival", logical.return = TRUE) & library("pec", logical.return = TRUE) & library("prodlim", logical.return = TRUE)) { ##prediction function required for pec predictSurvProb.rfsrc < function(object, newdata, times, ...){ ptemp < predict(object,newdata=newdata,...)$survival pos < sindex(jump.times = object$time.interest, eval.times = times) p < cbind(1,ptemp)[, pos + 1] if (NROW(p) != NROW(newdata)  NCOL(p) != length(times)) stop("Prediction failed") p } ## data, formula specifications data(pbc, package = "randomForestSRC") pbc.na < na.omit(pbc) ##remove NA's surv.f < as.formula(Surv(days, status) ~ .) pec.f < as.formula(Hist(days,status) ~ 1) ## run cox/rfsrc models ## for illustration we use a small number of trees cox.obj < coxph(surv.f, data = pbc.na, x = TRUE) rfsrc.obj < rfsrc(surv.f, pbc.na, ntree = 150) ## compute bootstrap crossvalidation estimate of expected Brier score ## see Mogensen, Ishwaran and Gerds (2012) Journal of Statistical Software set.seed(17743) prederror.pbc < pec(list(cox.obj,rfsrc.obj), data = pbc.na, formula = pec.f, splitMethod = "bootcv", B = 50) print(prederror.pbc) plot(prederror.pbc) ## compute outofbag Cindex for cox regression and compare to rfsrc rfsrc.obj < rfsrc(surv.f, pbc.na) cat("outofbag Cox Analysis ...", "\n") cox.err < sapply(1:100, function(b) { if (b%%10 == 0) cat("cox bootstrap:", b, "\n") train < sample(1:nrow(pbc.na), nrow(pbc.na), replace = TRUE) cox.obj < tryCatch({coxph(surv.f, pbc.na[train, ])}, error=function(ex){NULL}) if (!is.null(cox.obj)) { get.cindex(pbc.na$days[train], pbc.na$status[train], predict(cox.obj, pbc.na[train, ])) } else NA }) cat("\n\tOOB error rates\n\n") cat("\tRSF : ", rfsrc.obj$err.rate[rfsrc.obj$ntree], "\n") cat("\tCox regression : ", mean(cox.err, na.rm = TRUE), "\n") } ## ## competing risks ## ## WIHS analysis ## cumulative incidence function (CIF) for HAART and AIDS stratified by IDU data(wihs, package = "randomForestSRC") wihs.obj < rfsrc(Surv(time, status) ~ ., wihs, nsplit = 3, ntree = 100) plot.competing.risk(wihs.obj) cif < wihs.obj$cif.oob Time < wihs.obj$time.interest idu < wihs$idu cif.haart < cbind(apply(cif[,,1][idu == 0,], 2, mean), apply(cif[,,1][idu == 1,], 2, mean)) cif.aids < cbind(apply(cif[,,2][idu == 0,], 2, mean), apply(cif[,,2][idu == 1,], 2, mean)) matplot(Time, cbind(cif.haart, cif.aids), type = "l", lty = c(1,2,1,2), col = c(4, 4, 2, 2), lwd = 3, ylab = "Cumulative Incidence") legend("topleft", legend = c("HAART (NonIDU)", "HAART (IDU)", "AIDS (NonIDU)", "AIDS (IDU)"), lty = c(1,2,1,2), col = c(4, 4, 2, 2), lwd = 3, cex = 1.5) ## illustrates the various splitting rules ## illustrates event specific and nonevent specific variable selection if (library("survival", logical.return = TRUE)) { ## use the pbc data from the survival package ## events are transplant (1) and death (2) data(pbc, package = "survival") pbc$id < NULL ## modified Gray's weighted logrank splitting ## (equivalent to cause=c(1,1) and splitrule="logrankCR") pbc.cr < rfsrc(Surv(time, status) ~ ., pbc) ## logrank cause1 specific splitting and targeted VIMP for cause 1 pbc.log1 < rfsrc(Surv(time, status) ~ ., pbc, splitrule = "logrank", cause = c(1,0), importance = TRUE) ## logrank cause2 specific splitting and targeted VIMP for cause 2 pbc.log2 < rfsrc(Surv(time, status) ~ ., pbc, splitrule = "logrank", cause = c(0,1), importance = TRUE) ## extract VIMP from the logrank forests: eventspecific ## extract minimal depth from the Gray logrank forest: nonevent specific var.perf < data.frame(md = max.subtree(pbc.cr)$order[, 1], vimp1 = 100 * pbc.log1$importance[ ,1], vimp2 = 100 * pbc.log2$importance[ ,2]) print(var.perf[order(var.perf$md), ], digits = 2) } ##  ## regression analysis ##  ## new York air quality measurements airq.obj < rfsrc(Ozone ~ ., data = airquality, na.action = "na.impute") # partial plot of variables (see plot.variable for more details) plot.variable(airq.obj, partial = TRUE, smooth.lines = TRUE) ## motor trend cars mtcars.obj < rfsrc(mpg ~ ., data = mtcars) ##  ## regression with custom bootstrap ##  ntree < 25 n < nrow(mtcars) s.size < n / 2 swr < TRUE samp < randomForestSRC:::make.sample(ntree, n, s.size, swr) o < rfsrc(mpg ~ ., mtcars, bootstrap = "by.user", samp = samp) ##  ## classification analysis ##  ## iris data iris.obj < rfsrc(Species ~., data = iris) ## wisconsin prognostic breast cancer data data(breast, package = "randomForestSRC") breast.obj < rfsrc(status ~ ., data = breast, block.size=1) plot(breast.obj) ##  ## big data set, reduce number of variables using simple method ##  ## use Iowa housing data set data(housing, package = "randomForestSRC") ## original data contains lots of missing data, use fast imputation ## however see impute for other methods housing2 < impute(data = housing, fast = TRUE) ## run shallow trees to find variables that split any tree xvar.used < rfsrc(SalePrice ~., housing2, ntree = 250, nodedepth = 4, var.used="all.trees", mtry = Inf, nsplit = 100)$var.used ## now fit forest using filtered variables xvar.keep < names(xvar.used)[xvar.used >= 1] o < rfsrc(SalePrice~., housing2[, c("SalePrice", xvar.keep)]) print(o) ##  ## imbalanced classification data ## see the "imbalanced" function for further details ## ## a) use balanced random forests with undersampling of the majority class ## Specifically let n0, n1 be sample sizes for majority, minority ## cases. We sample 2 x n1 cases with majority, minority cases chosen ## with probabilities n1/n, n0/n where n=n0+n1 ## ## b) balanced random forests using "imbalanced" ## ## c) qclassifier (RFQ) using "imbalanced" ## ##  ## Wisconsin breast cancer example data(breast, package = "randomForestSRC") breast < na.omit(breast) ## balanced random forests  brute force y < breast$status obdirect < rfsrc(status ~ ., data = breast, nsplit = 10, case.wt = randomForestSRC:::make.wt(y), sampsize = randomForestSRC:::make.size(y)) print(obdirect) print(get.imbalanced.performance(obdirect)) ## balanced random forests  using "imbalanced" ob < imbalanced(status ~ ., data = breast, method = "brf") print(ob) print(get.imbalanced.performance(ob)) ## qclassifier (RFQ)  using "imbalanced" oq < imbalanced(status ~ ., data = breast) print(oq) print(get.imbalanced.performance(oq)) ## qclassifier (RFQ)  with auc splitting oqauc < imbalanced(status ~ ., data = breast, splitrule = "auc") print(oqauc) print(get.imbalanced.performance(oqauc)) ##  ## unsupervised analysis ##  ## two equivalent ways to implement unsupervised forests mtcars.unspv < rfsrc(Unsupervised() ~., data = mtcars) mtcars2.unspv < rfsrc(data = mtcars) ## illustration of sidClustering for the mtcars data ## see sidClustering for more details mtcars.sid < sidClustering(mtcars, k = 1:10) print(split(mtcars, mtcars.sid$cl[, 3])) print(split(mtcars, mtcars.sid$cl[, 10])) ##  ## multivariate (bivariate) regression using Mahalanobis splitting ##  if (library("mlbench", logical.return = TRUE)) { ## load boston housing data, specify the bivariate regression data(BostonHousing) f < formula("Multivar(lstat, nox) ~.") ## Mahalanobis splitting bh.mreg < rfsrc(f, BostonHousing, importance = TRUE, splitrule = "mahal") ## performance error and vimp vmp < get.mv.vimp(bh.mreg) pred < get.mv.predicted(bh.mreg) ## standardized error and vimp err.std < get.mv.error(bh.mreg, standardize = TRUE) vmp.std < get.mv.vimp(bh.mreg, standardize = TRUE) } ##  ## multivariate mixed forests (nutrigenomic study) ## study effects of diet, lipids and gene expression for mice ## diet, genotype and lipids used as the multivariate y ## genes used for the x features ##  ## load the data (data is a list) data(nutrigenomic, package = "randomForestSRC") ## assemble the multivariate y data ydta < data.frame(diet = nutrigenomic$diet, genotype = nutrigenomic$genotype, nutrigenomic$lipids) ## multivariate mixed forest call ## uses "get.mv.formula" for conveniently setting formula mv.obj < rfsrc(get.mv.formula(colnames(ydta)), data.frame(ydta, nutrigenomic$genes), importance=TRUE, nsplit = 10) ## print results for diet and genotype y values print(mv.obj, outcome.target = "diet") print(mv.obj, outcome.target = "genotype") ## extract standardized VIMP svimp < get.mv.vimp(mv.obj, standardize = TRUE) ## plot standardized VIMP for diet, genotype and lipid for each gene boxplot(t(svimp), col = "bisque", cex.axis = .7, las = 2, outline = FALSE, ylab = "standardized VIMP", main = "diet/genotype/lipid VIMP for each gene") ##  ## custom splitting using the precoded examples ##  ## motor trend cars mtcars.obj < rfsrc(mpg ~ ., data = mtcars, splitrule = "custom") ## iris analysis iris.obj < rfsrc(Species ~., data = iris, splitrule = "custom1") ## WIHS analysis wihs.obj < rfsrc(Surv(time, status) ~ ., wihs, nsplit = 3, ntree = 100, splitrule = "custom1") # }