The nft2()/nft() function is for fitting
NFT BART (Nonparametric Failure Time
Bayesian Additive Regression Tree) models
with different train/test matrices for
\(f\) and \(sd\) functions.
nft2(
## data
xftrain, xstrain, times, delta=NULL,
xftest=matrix(nrow=0, ncol=0),
xstest=matrix(nrow=0, ncol=0),
rm.const=TRUE, rm.dupe=TRUE,
## multi-threading
tc=getOption("mc.cores", 1),
##MCMC
nskip=1000, ndpost=2000, nadapt=1000, adaptevery=100,
chvf=NULL, chvs=NULL,
method="spearman", use="pairwise.complete.obs",
pbd=c(0.7, 0.7), pb=c(0.5, 0.5),
stepwpert=c(0.1, 0.1), probchv=c(0.1, 0.1),
minnumbot=c(5, 5),
## BART and HBART prior parameters
ntree=c(50, 10), numcut=100,
xifcuts=NULL, xiscuts=NULL,
power=c(2, 2), base=c(0.95, 0.95),
## f function
fmu=NA, k=5, tau=NA, dist='weibull',
## s function
total.lambda=NA, total.nu=10, mask=NULL,
## survival analysis
K=100, events=NULL, TSVS=FALSE,
## DPM LIO
drawDPM=1L,
alpha=1, alpha.a=1, alpha.b=0.1, alpha.draw=1,
neal.m=2, constrain=1,
m0=0, k0.a=1.5, k0.b=7.5, k0=1, k0.draw=1,
a0=3, b0.a=2, b0.b=1, b0=1, b0.draw=1,
## misc
na.rm=FALSE, probs=c(0.025, 0.975), printevery=100,
transposed=FALSE, pred=FALSE
)nft(
## data
x.train, times, delta=NULL, x.test=matrix(nrow=0, ncol=0),
rm.const=TRUE, rm.dupe=TRUE,
## multi-threading
tc=getOption("mc.cores", 1),
##MCMC
nskip=1000, ndpost=2000, nadapt=1000, adaptevery=100,
chv=NULL,
method="spearman", use="pairwise.complete.obs",
pbd=c(0.7, 0.7), pb=c(0.5, 0.5),
stepwpert=c(0.1, 0.1), probchv=c(0.1, 0.1),
minnumbot=c(5, 5),
## BART and HBART prior parameters
ntree=c(50, 10), numcut=100, xicuts=NULL,
power=c(2, 2), base=c(0.95, 0.95),
## f function
fmu=NA, k=5, tau=NA, dist='weibull',
## s function
total.lambda=NA, total.nu=10, mask=NULL,
## survival analysis
K=100, events=NULL, TSVS=FALSE,
## DPM LIO
drawDPM=1L,
alpha=1, alpha.a=1, alpha.b=0.1, alpha.draw=1,
neal.m=2, constrain=1,
m0=0, k0.a=1.5, k0.b=7.5, k0=1, k0.draw=1,
a0=3, b0.a=2, b0.b=1, b0=1, b0.draw=1,
## misc
na.rm=FALSE, probs=c(0.025, 0.975), printevery=100,
transposed=FALSE, pred=FALSE
)
These are XPtrs to the BART
\(f(x)\) objects in RAM that are only available for fits generated
in the current R session.
Similarly, these are XPtrs to the
HBART \(sd(x)\) objects.
The constant \(mu\).
The trained \(f(x)\) and \(sd(x)\)
respectively: matrices with ndpost rows and \(n\) columns.
The posterior mean of the trained \(f(x)\) and \(sd(x)\) respectively: vectors of length \(n\).
Character strings representing the trained fits
of \(f(x)\) and \(sd(x)\) respectively to facilitate usage of the
predict function when XPtrs are unavailable.
The draws of the DPM concentration parameter \(alpha\).
The number of atom clusters per DPM, \(J\), for all draws including burn-in and excluding burn-in respectively.
The draws of the DPM parameter \(mu[i]\) where
\(i=1,...,n\) indexes subjects: a matrix with ndpost rows and
\(n\) columns.
The draws of the DPM parameter \(mu[j]\) where
\(j=1,...,J\) indexes atom clusters: a matrix with ndpost
rows and \(J\) columns.
The weights for efficient DPM calculations by atom clusters
(as opposed to subjects) for use with \(dpmu.\) (and \(dpsd.\);
see below): a matrix with ndpost rows and \(J\) columns.
Similarly, the draws of the DPM parameter \(tau[i]\) transformed into the standard deviation \(sigma[i]\) for convenience.
The indices \(j\) for each subject \(i\) corresponding to their shared atom cluster.
The data values/augmentation draws of \(log t\).
The min/average/max tier degree of trees in the \(f\) ensemble.
The min/average/max tier degree of trees in the \(s\) ensemble.
Variable importance counts of branch
decision rules for each \(x\) of \(f\) and \(s\) respectively:
matrices with ndpost rows and \(p\) columns.
Similarly, the posterior mean of the variable importance counts for each \(x\) of \(f\) and \(s\) respectively: vectors of length \(p\).
Similarly, re-weighting the posterior mean of the variable importance counts as sum-to-one probabilities for each \(x\) of \(f\) and \(s\) respectively: vectors of length \(p\).
The log Pseudo-Marginal Likelihood as typically calculated for right-/left-censoring.
The object returned from the predict function where
x.test=x.train in order to calculate the soffset
item that is needed to use predict when XPtrs are not
available.
See pred above.
The AFT model fit used to initialize NFT BART.
The elapsed time of the run in seconds.
n x pf matrix of predictor variables for the training data.
n x ps matrix of predictor variables for the training data.
n x p matrix of predictor variables for the training data.
n x 1 vector of the observed times for the training data.
n x 1 vector of the time type for the training data: 0, for right-censoring; 1, for an event; and, 2, for left-censoring.
m x pf matrix of predictor variables for the test set.
m x ps matrix of predictor variables for the test set.
m x p matrix of predictor variables for the test set.
To remove constant variables or not.
To remove duplicate variables or not.
Number of OpenMP threads to use.
Number of MCMC iterations to burn-in and discard.
Number of MCMC iterations kept after burn-in.
Number of MCMC iterations for adaptation prior to burn-in.
Adapt MCMC proposal distributions every adaptevery iteration.
Predictor correlation matrix used as a pre-conditioner for MCMC change-of-variable proposals.
Correlation options for change-of-variable proposal pre-conditioner.
Probability of performing a birth/death proposal, otherwise perform a rotate proposal.
Probability of performing a birth proposal given that we choose to perform a birth/death proposal.
Initial width of proposal distribution for peturbing cut-points.
Probability of performing a change-of-variable proposal. Otherwise, only do a perturb proposal.
Minimum number of observations required in leaf (terminal) nodes.
Vector of length two for the number of trees used for the mean model and the number of trees used for the variance model.
Number of cutpoints to use for each predictor variable.
More detailed construction of cut-points can be specified
by the xicuts function and provided here.
Power parameter in the tree depth penalizing prior.
Base parameter in the tree depth penalizing prior.
Prior parameter for the center of the mean model.
Prior parameter for the mean model.
Desired SD/ntree for f function leaf prior if known.
Distribution to be passed to intercept-only AFT model to center y.train.
A rudimentary estimate of the process standard deviation. Used in calibrating the variance prior.
Shape parameter for the variance prior.
If a proportion is provided, then said quantile
of max.i sd(x.i) is used to mask non-stationary
departures (with respect to convergence) above this threshold.
Number of grid points for which to estimate survival probability.
Grid points for which to estimate survival probability.
Setting to TRUE will avoid unnecessary processing for
Thompson sampling variable selection, i.e., all that is needed is
the variable counts from the tree branch decision rules.
Whether to utilize DPM or not.
Initial value of DPM concentration parameter.
Gamma prior parameter setting for DPM concentration parameter
where E[alpha]=alpha.a/alpha.b.
See alpha.a above.
Whether to draw alpha or it is fixed at the initial value.
The number of additional atoms for Neal 2000 DPM algorithm 8.
Whether to perform constained DPM or unconstrained.
Center of the error distribution: defaults to zero.
First Gamma prior argument for k0.
Second Gamma prior argument for k0.
Initial value of k0.
Whether to fix k0 or draw it if from the DPM LIO prior
hierarchy: k0~Gamma(k0.a, k0.b), i.e., E[k0]=k0.a/k0.b.
First Gamma prior argument for \(tau\).
First Gamma prior argument for b0.
Second Gamma prior argument for b0.
Initial value of b0.
Whether to fix b0 or draw it from the DPM LIO prior
hierarchy: b0~Gamma(b0.a, b0.b), i.e.,
E[b0]=b0.a/b0.b.
Value to be passed to the predict function.
Value to be passed to the predict function.
Outputs MCMC algorithm status every printevery iterations.
Specify TRUE if all of the pre-processing for
xftrain/xstrain/xftest/xstest has been conducted prior to the call (including
tranposing).
Specify TRUE if you want to return the pred
item that is used to calculate soffset.
Rodney Sparapani: rsparapa@mcw.edu
nft2()/nft() is the function to fit time-to-event data. The most general form of the model allowed is
\(Y({\bf x})=mu+f({\bf x})+sd({\bf x})Z\)
where \(E\) follows a nonparametric error distribution
by default.
The nft2()/nft() function returns a fit object of S3 class type
nft2/nft that is essentially a list containing the following items.
Sparapani R., Logan B., Maiers M., Laud P., McCulloch R. (2023) Nonparametric Failure Time: Time-to-event Machine Learning with Heteroskedastic Bayesian Additive Regression Trees and Low Information Omnibus Dirichlet Process Mixtures Biometrics (ahead of print) <doi:10.1111/biom.13857>.
predict.nft2, predict.nft
##library(nftbart)
data(lung)
N=length(lung$status)
##lung$status: 1=censored, 2=dead
##delta: 0=censored, 1=dead
delta=lung$status-1
## this study reports time in days rather than weeks or months
times=lung$time
times=times/7 ## weeks
## matrix of covariates
x.train=cbind(lung[ , -(1:3)])
## lung$sex: Male=1 Female=2
## token run just to test installation
post=nft2(x.train, x.train, times, delta, K=0,
nskip=0, ndpost=10, nadapt=4, adaptevery=1)
# \donttest{
set.seed(99)
post=nft2(x.train, x.train, times, delta, K=0)
XPtr=TRUE
x.test = rbind(x.train, x.train)
x.test[ , 2]=rep(1:2, each=N)
K=75
events=seq(0, 150, length.out=K+1)
pred = predict(post, x.test, x.test, K=K, events=events[-1],
XPtr=XPtr, FPD=TRUE)
plot(events, c(1, pred$surv.fpd.mean[1:K]), type='l', col=4,
ylim=0:1,
xlab=expression(italic(t)), sub='weeks',
ylab=expression(italic(S)(italic(t), italic(x))))
lines(events, c(1, pred$surv.fpd.upper[1:K]), lty=2, lwd=2, col=4)
lines(events, c(1, pred$surv.fpd.lower[1:K]), lty=2, lwd=2, col=4)
lines(events, c(1, pred$surv.fpd.mean[K+1:K]), lwd=2, col=2)
lines(events, c(1, pred$surv.fpd.upper[K+1:K]), lty=2, lwd=2, col=2)
lines(events, c(1, pred$surv.fpd.lower[K+1:K]), lty=2, lwd=2, col=2)
legend('topright', c('Adv. lung cancer\nmortality example',
'M', 'F'), lwd=2, col=c(0, 4, 2), lty=1)
# }
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