pbart {BART} | R Documentation |

## Probit BART for dichotomous outcomes with Normal latents

### Description

BART is a Bayesian “sum-of-trees” model.

For a binary response `y`

, `P(Y=1 | x) = F(f(x))`

, where `F`

denotes the standard Normal CDF (probit link).

In both cases, `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

```
pbart(
x.train, y.train, x.test=matrix(0.0,0,0),
sparse=FALSE, theta=0, omega=1,
a=0.5, b=1, augment=FALSE, rho=NULL,
xinfo=matrix(0.0,0,0), usequants=FALSE,
cont=FALSE, rm.const=TRUE,
k=2.0, power=2.0, base=.95,
binaryOffset=NULL,
ntree=50L, numcut=100L,
ndpost=1000L, nskip=100L, keepevery=1L,
nkeeptrain=ndpost, nkeeptest=ndpost,
nkeeptreedraws=ndpost,
printevery=100L, transposed=FALSE
)
```

### Arguments

`x.train` |
Explanatory variables for training (in sample) data. |

`y.train` |
Binary dependent variable for training (in sample) data. |

`x.test` |
Explanatory variables for test (out of sample) data. |

`sparse` |
Whether to perform variable selection based on a sparse Dirichlet prior rather than simply uniform; see Linero 2016. |

`theta` |
Set |

`omega` |
Set |

`a` |
Sparse parameter for |

`b` |
Sparse parameter for |

`rho` |
Sparse parameter: typically |

`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 |

`usequants` |
If |

`cont` |
Whether or not to assume all variables are continuous. |

`rm.const` |
Whether or not to remove constant variables. |

`k` |
For binary y,
k is the number of prior standard deviations |

`power` |
Power parameter for tree prior. |

`base` |
Base parameter for tree prior. |

`binaryOffset` |
Used for 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 |

`ndpost` |
The number of posterior draws returned. |

`nskip` |
Number of MCMC iterations to be treated as burn in. |

`nkeeptrain` |
Number of MCMC iterations to be returned for train data. |

`nkeeptest` |
Number of MCMC iterations to be returned for test data. |

`nkeeptreedraws` |
Number of MCMC iterations to be returned for tree draws. |

`keepevery` |
Every keepevery draw is kept to be returned to the user. |

`printevery` |
As the MCMC runs, a message is printed every printevery draws. |

`transposed` |
When running |

### Details

BART is an Bayesian MCMC method.
At each MCMC interation, we produce a draw from
`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)`

where * denotes a particular draw.
The `x`

is either a row from the training data (x.train) or the test data (x.test).

### Value

`pbart`

returns an object of type `pbart`

which is
essentially a list.

`yhat.train` |
A matrix with ndpost rows and nrow(x.train) columns.
Each row corresponds to a draw |

`yhat.test` |
Same as yhat.train but now the x's are the rows of the test data. |

`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. |

In addition the list has a binaryOffset component giving the value used.

Note that in the binary `y`

, case yhat.train and yhat.test are
`f(x)`

+ binaryOffset. If you want draws of the probability
`P(Y=1 | x)`

you need to apply the Normal CDF (`pnorm`

)
to these values.

### See Also

### Examples

```
data(ACTG175)
## exclude those who do not have CD4 count at 96 weeks
ex <- is.na(ACTG175$cd496)
table(ex)
## inclusion criteria are CD4 counts between 200 and 500
ACTG175$cd40 <- min(500, max(250, ACTG175$cd40))
## calculate relative CD4 decline
y <- ((ACTG175$cd496-ACTG175$cd40)/ACTG175$cd40)[!ex]
summary(y)
## 0=failure, 1=success
y <- 1*(y > -0.5)
## summarize CD4 outcomes
table(y, ACTG175$arms[!ex])
table(y, ACTG175$arms[!ex])/
matrix(table(ACTG175$arms[!ex]), nrow=2, ncol=4, byrow=TRUE)
## drop unneeded and unwanted variables
## 1: 'pidnum' patient ID number
##14: 'str2' which will be handled by strat1 below
##15: 'strat' which will be handled by strat1-strat3 below
##17: 'treat' handled by arm0-arm3 below
##18: 'offtrt' indicator of off-treatment before 96 weeks
##20: 'cd420' CD4 T cell count at 20 weeks
##21: 'cd496' CD4 T cell count at 96 weeks
##22: 'r' missing CD4 T cell count at 96 weeks
##24: 'cd820' CD8 T cell count at 20 weeks
##25: 'cens' indicator of observing the event in days
##26: 'days' number of days until the primary endpoint
##27: 'arms' handled by arm0-arm3 below
train <- as.matrix(ACTG175)[!ex, -c(1, 14:15, 17, 18, 20:22, 24:27)]
train <- cbind(1*(ACTG175$strat[!ex]==1), 1*(ACTG175$strat[!ex]==2),
1*(ACTG175$strat[!ex]==3), train)
dimnames(train)[[2]][1:3] <- paste0('strat', 1:3)
train <- cbind(1*(ACTG175$arms[!ex]==0), 1*(ACTG175$arms[!ex]==1),
1*(ACTG175$arms[!ex]==2), 1*(ACTG175$arms[!ex]==3), train)
dimnames(train)[[2]][1:4] <- paste0('arm', 0:3)
N <- nrow(train)
test0 <- train; test0[ , 1:4] <- 0; test0[ , 1] <- 1
test1 <- train; test1[ , 1:4] <- 0; test1[ , 2] <- 1
test2 <- train; test2[ , 1:4] <- 0; test2[ , 3] <- 1
test3 <- train; test3[ , 1:4] <- 0; test3[ , 4] <- 1
test <- rbind(test0, test1, test2, test3)
##test BART with token run to ensure installation works
set.seed(21)
post <- pbart(train, y, test, nskip=5, ndpost=5)
## Not run:
set.seed(21)
post <- pbart(train, y, test)
## turn z-scores into probabilities
post$prob.test <- pnorm(post$yhat.test)
## average over the posterior samples
post$prob.test.mean <- apply(post$prob.test, 2, mean)
## place estimates for arms 0-3 next to each other for convenience
itr <- cbind(post$prob.test.mean[(1:N)], post$prob.test.mean[N+(1:N)],
post$prob.test.mean[2*N+(1:N)], post$prob.test.mean[3*N+(1:N)])
## find the BART ITR for each patient
itr.pick <- integer(N)
for(i in 1:N) itr.pick[i] <- which(itr[i, ]==max(itr[i, ]))-1
## arms 0 and 3 (monotherapy) are never chosen
table(itr.pick)
## do arms 1 and 2 show treatment heterogeneity?
diff. <- apply(post$prob.test[ , 2*N+(1:N)]-post$prob.test[ , N+(1:N)], 2, mean)
plot(sort(diff.), type='h', main='ACTG175 trial: 50% CD4 decline from baseline at 96 weeks',
xlab='Arm 2 (1) Preferable to the Right (Left)', ylab='Prob.Diff.: Arms 2 - 1')
library(rpart)
library(rpart.plot)
## make data frame for nicer names in the plot
var <- as.data.frame(train[ , -(1:4)])
dss <- rpart(diff. ~ var$age+var$gender+var$race+var$wtkg+var$cd40+var$cd80+
var$karnof+var$symptom+var$hemo+var$homo+var$drugs+var$z30+
var$zprior+var$oprior+var$strat1+var$strat2+var$strat3,
method='anova', control=rpart.control(cp=0.1))
rpart.plot(dss, type=3, extra=101)
## if strat1==1 (antiretroviral naive), then arm 2 is better
## otherwise, arm 1
print(dss)
all0 <- apply(post$prob.test[ , (1:N)], 1, mean)
all1 <- apply(post$prob.test[ , N+(1:N)], 1, mean)
all2 <- apply(post$prob.test[ , 2*N+(1:N)], 1, mean)
all3 <- apply(post$prob.test[ , 3*N+(1:N)], 1, mean)
## BART ITR
BART.itr <- apply(post$prob.test[ , c(N+which(itr.pick==1), 2*N+which(itr.pick==2))], 1, mean)
test <- train
test[ , 1:4] <- 0
test[test[ , 5]==0, 2] <- 1
test[test[ , 5]==1, 3] <- 1
## BART ITR simple
BART.itr.simp <- pwbart(test, post$treedraws)
BART.itr.simp <- apply(pnorm(BART.itr.simp), 1, mean)
plot(density(BART.itr), xlab='Value', xlim=c(0.475, 0.775), lwd=2,
main='ACTG175 trial: 50% CD4 decline from baseline at 96 weeks')
lines(density(BART.itr.simp), col='brown', lwd=2)
lines(density(all0), col='green', lwd=2)
lines(density(all1), col='red', lwd=2)
lines(density(all2), col='blue', lwd=2)
lines(density(all3), col='yellow', lwd=2)
legend('topleft', legend=c('All Arm 0 (ZDV only)', 'All Arm 1 (ZDV+DDI)',
'All Arm 2 (ZDV+DDC)', 'All Arm 3 (DDI only)',
'BART ITR simple', 'BART ITR'),
col=c('green', 'red', 'blue', 'yellow', 'brown', 'black'), lty=1, lwd=2)
## End(Not run)
```

*BART*version 2.9.9 Index]