abart {BART} R Documentation

## AFT BART for time-to-event outcomes

### Description

BART is a Bayesian “sum-of-trees” model.
For a numeric response y, we have y = f(x) + e, where e ~ N(0,sigma^2).

f is the sum of many tree models. The goal is to have very flexible inference for the uknown function f.

In the spirit of “ensemble models”, each tree is constrained by a prior to be a weak learner so that it contributes a small amount to the overall fit.

### Usage

```abart(
x.train, times, delta,
x.test=matrix(0,0,0), K=100,
type='abart', ntype=1,
sparse=FALSE, theta=0, omega=1,
a=0.5, b=1, augment=FALSE, rho=NULL,
xinfo=matrix(0,0,0), usequants=FALSE,
rm.const=TRUE,
sigest=NA, sigdf=3, sigquant=0.90,
k=2, power=2, base=0.95,

lambda=NA, tau.num=c(NA, 3, 6)[ntype],
offset=NULL, w=rep(1, length(times)),
ntree=c(200L, 50L, 50L)[ntype], numcut=100L,

ndpost=1000L, nskip=100L,
keepevery=c(1L, 10L, 10L)[ntype],
printevery=100L, transposed=FALSE,
mc.cores = 1L, ## mc.abart only
nice = 19L,    ## mc.abart only
seed = 99L     ## mc.abart only
)

mc.abart(
x.train, times, delta,
x.test=matrix(0,0,0), K=100,
type='abart', ntype=1,
sparse=FALSE, theta=0, omega=1,
a=0.5, b=1, augment=FALSE, rho=NULL,
xinfo=matrix(0,0,0), usequants=FALSE,
rm.const=TRUE,
sigest=NA, sigdf=3, sigquant=0.90,
k=2, power=2, base=0.95,

lambda=NA, tau.num=c(NA, 3, 6)[ntype],
offset=NULL, w=rep(1, length(times)),

ntree=c(200L, 50L, 50L)[ntype], numcut=100L,
ndpost=1000L, nskip=100L,
keepevery=c(1L, 10L, 10L)[ntype],
printevery=100L, transposed=FALSE,
mc.cores = 2L, nice = 19L, seed = 99L
)

```

### Arguments

 `x.train` Explanatory variables for training (in sample) data. May be a matrix or a data frame, with (as usual) rows corresponding to observations and columns to variables. If a variable is a factor in a data frame, it is replaced with dummies. Note that q dummies are created if q>2 and one dummy created if q=2 where q is the number of levels of the factor. `abart` will generate draws of f(x) for each x which is a row of `x.train`. `times` The time of event or right-censoring. If `y.train` is `NULL`, then `times` (and `delta`) must be provided. `delta` The event indicator: 1 is an event while 0 is censored. If `y.train` is `NULL`, then `delta` (and `times`) must be provided. `x.test` Explanatory variables for test (out of sample) data. Should have same structure as `x.train`. `abart` will generate draws of f(x) for each x which is a row of `x.test`. `K` If provided, then coarsen `times` per the quantiles 1/K, 2/K, ..., K/K. `type` You can use this argument to specify the type of fit. `'abart'` for AFT BART. `ntype` The integer equivalent of `type` where `'abart'` is 1. `sparse` Whether to perform variable selection based on a sparse Dirichlet prior rather than simply uniform; see Linero 2016. `theta` Set theta parameter; zero means random. `omega` Set omega parameter; zero means random. `a` Sparse parameter for Beta(a, b) prior: 0.5<=a<=1 where lower values inducing more sparsity. `b` Sparse parameter for Beta(a, b) prior; typically, b=1. `rho` Sparse parameter: typically rho=p where p is the number of covariates under consideration. `augment` Whether data augmentation is to be performed in sparse variable selection. `xinfo` You can provide the cutpoints to BART or let BART choose them for you. To provide them, use the `xinfo` argument to specify a list (matrix) where the items (rows) are the covariates and the contents of the items (columns) are the cutpoints. `usequants` If `usequants=FALSE`, then the cutpoints in `xinfo` are generated uniformly; otherwise, if `TRUE`, uniform quantiles are used for the cutpoints. `rm.const` Whether or not to remove constant variables. `sigest` The prior for the error variance (sigma\^2) is inverted chi-squared (the standard conditionally conjugate prior). The prior is specified by choosing the degrees of freedom, a rough estimate of the corresponding standard deviation and a quantile to put this rough estimate at. If `sigest=NA` then the rough estimate will be the usual least squares estimator. Otherwise the supplied value will be used. Not used if y is binary. `sigdf` Degrees of freedom for error variance prior. Not used if y is binary. `sigquant` The quantile of the prior that the rough estimate (see `sigest`) is placed at. The closer the quantile is to 1, the more aggresive the fit will be as you are putting more prior weight on error standard deviations (sigma) less than the rough estimate. Not used if y is binary. `k` For numeric y, `k` is the number of prior standard deviations E(Y|x) = f(x) is away from +/-0.5. The response, codey.train, is internally scaled to range from -0.5 to 0.5. For binary y, `k` is the number of prior standard deviations f(x) is away from +/-3. The bigger `k` is, the more conservative the fitting will be. `power` Power parameter for tree prior. `base` Base parameter for tree prior.
 `lambda` The scale of the prior for the variance. Not used if y is binary. `tau.num` The numerator in the `tau` definition, i.e., `tau=tau.num/(k*sqrt(ntree))`.
 `offset` Continous BART operates on `y.train` centered by `offset` which defaults to `mean(y.train)`. With binary BART, the centering is P(Y=1 | x) = F(f(x) + offset) where `offset` defaults to `F^{-1}(mean(y.train))`. You can use the `offset` parameter to over-ride these defaults. `w` Vector of weights which multiply the standard deviation. Not used if y is binary. `ntree` The number of trees in the sum. `numcut` The number of possible values of c (see `usequants`). If a single number if given, this is used for all variables. Otherwise a vector with length equal to `ncol(x.train)` is required, where the i^th element gives the number of c used for the i^th variable in `x.train`. If usequants is false, numcut equally spaced cutoffs are used covering the range of values in the corresponding column of `x.train`. If `usequants` is true, then min(numcut, the number of unique values in the corresponding columns of x.train - 1) values are used. `ndpost` The number of posterior draws returned. `nskip` Number of MCMC iterations to be treated as burn in. `printevery` As the MCMC runs, a message is printed every printevery draws. `keepevery` Every keepevery draw is kept to be returned to the user. `transposed` When running `abart` in parallel, it is more memory-efficient to transpose `x.train` and `x.test`, if any, prior to calling `mc.abart`. `seed` Setting the seed required for reproducible MCMC. `mc.cores` Number of cores to employ in parallel. `nice` Set the job niceness. The default niceness is 19: niceness goes from 0 (highest) to 19 (lowest).

### Details

BART is a Bayesian MCMC method. At each MCMC interation, we produce a draw from the joint posterior (f,sigma) \| (x,y) in the numeric y case and just f in the binary y case.

Thus, unlike a lot of other modelling methods in R, we do not produce a single model object from which fits and summaries may be extracted. The output consists of values f*(x) (and sigma* in the numeric case) where * denotes a particular draw. The x is either a row from the training data, `x.train` or the test data, `x.test`.

### Value

`abart` returns an object of type `abart` which is essentially a list. In the numeric y case, the list has components:

 `yhat.train` A matrix with ndpost rows and nrow(x.train) columns. Each row corresponds to a draw f* from the posterior of f and each column corresponds to a row of x.train. The (i,j) value is f*(x) for the i\^th kept draw of f and the j\^th row of x.train. Burn-in is dropped. `yhat.test` Same as yhat.train but now the x's are the rows of the test data. `yhat.train.mean` train data fits = mean of yhat.train columns. `yhat.test.mean` test data fits = mean of yhat.test columns. `sigma` post burn in draws of sigma, length = ndpost. `first.sigma` burn-in draws of sigma. `varcount` a matrix with ndpost rows and nrow(x.train) columns. Each row is for a draw. For each variable (corresponding to the columns), the total count of the number of times that variable is used in a tree decision rule (over all trees) is given. `sigest` The rough error standard deviation (sigma) used in the prior.

`wbart`

### Examples

```
N = 1000
P = 5       #number of covariates
M = 8

set.seed(12)
x.train=matrix(runif(N*P, -2, 2), N, P)
mu = x.train[ , 1]^3
y=rnorm(N, mu)
offset=mean(y)
T=exp(y)
C=rexp(N, 0.05)
delta=(T<C)*1
table(delta)/N
times=(T*delta+C*(1-delta))

##test BART with token run to ensure installation works
set.seed(99)
post1 = abart(x.train, times, delta, nskip=5, ndpost=10)

## Not run:

post1 = mc.abart(x.train, times, delta,
mc.cores=M, seed=99)
post2 = mc.abart(x.train, times, delta, offset=offset,
mc.cores=M, seed=99)

Z=8

plot(mu, post1\$yhat.train.mean, asp=1,
xlim=c(-Z, Z), ylim=c(-Z, Z))
abline(a=0, b=1)

plot(mu, post2\$yhat.train.mean, asp=1,
xlim=c(-Z, Z), ylim=c(-Z, Z))
abline(a=0, b=1)

plot(post1\$yhat.train.mean, post2\$yhat.train.mean, asp=1,
xlim=c(-Z, Z), ylim=c(-Z, Z))
abline(a=0, b=1)

## End(Not run)

```

[Package BART version 2.9 Index]