sbh: Cross-Validated Survival Bump Hunting

In PRIMsrc: PRIM Survival Regression Classification

Description

Main end-user function for fitting a Survival Bump Hunting (SBH) model (or Group Survival Bump Hunting (GSBH)). It returns an object of class sbh, as generated by our Patient Recursive Survival Peeling (PRSP) algorithm (or Patient Recursive Group Survival Peeling (PRGSP)), containing cross-validated estimates of the target region of the input space with end-points statistics of interest.

Usage

  sbh(X, 
      y, 
      delta, 
      B = 30, 
      K = 5, 
      A = 1000, 
      vs = TRUE, 
      vstype = "ppl",
      vsarg = "alpha=1,
               nalpha=1,
               nlambda=100",
      vscons = 0.5,
      cv = TRUE, 
      cvtype = "combined", 
      cvarg = "alpha=0.01,
               beta=0.10,
               peelcriterion=\"lrt\",
               cvcriterion=\"cer\"",
      groups = NULL,
      pv = FALSE,
      decimals = 2, 
      onese = FALSE,
      probval = NULL, 
      timeval = NULL, 
      parallel.vs = FALSE,
      parallel.rep = FALSE,
      parallel.pv = FALSE,
      conf = NULL,
      verbose = TRUE, 
      seed = NULL)

Arguments

X	(n x p) data.frame or numeric matrix of n observations and p input covariates. If a data.frame is provided, it will be coerced to a numeric matrix. Discrete nominal covariates will be treated as ordinal variables. NA missing values are not allowed.
y	n-numeric vector of observed times to event. NA missing values are not allowed.
delta	n-numeric vector of observed status (censoring) indicator variable.
B	Postitive integer of the number of replications of the cross-validation procedure. Defaults to 30.
K	Postitive integer of the number of cross-validation folds (partitions) into which the total number of observations (n) should be randomly split. K must be bigger than 2 for a regular K-fold cross-validation procedure to work and should be greater than 3 for a regular procedure to make sense; K \in {5,...,10} is recommended; defaults to K=5. Setting K also specifies the type of cross-validation to be done: K = 1 carries no cross-validation out, or set-value when cv = FALSE (see below). K \in {2,...,n-1} carries out K-fold cross-validation. K = n carries out leave-one-out cross-validation.
A	Positive integer of the number of permutations for the computation of log-rank permutation p-values. Defaults to 1000. Ignored if pv=FALSE or cv=FALSE.
vs	logical scalar. Flag for optional variable (covariate) screening (pre-selection). Defaults to TRUE.
vstype	character vector in {"prsp", "pcqr", "ppl", "spca"} of one of the four possible variable screening (pre-selection) procedure. See details below. Defaults to "ppl". Ignored if vs is FALSE.
vsarg	Character vector of parameters of the cross-validated variable screening (pre-selection) procedure. Defaults to parameters values of default variable screening (pre-selection) procedure "ppl": vsarg="alpha=1,nalpha=1,nlambda=100". Note that vsarg comes as a character string between double quotes, with comas separated values, and without white spaces. All the following parameters are ignored if vs is FALSE. PRSP: alpha = numeric data quantile in (0,1) to peel off at each step of the peeling sequence of the PRSP algorithm. Suggests 0.01. beta = numeric scalar of minimum box support at the end of the peeling sequence. Suggests 0.10. msize = positive integer or NULL to control the model size, i.e the number of screened variables used for fitting the Survival Bump Hunting model. Use a single non-NULL value as the maximum model size (cardinal of subset of top-screened variables) within the allowable range [1,floor(p)]. Alternatively, use msize=NULL to allow the optimal model size to be determined by cross-validation. See below for details. Suggests NULL. peelcriterion in {"lhr", "lrt", "chs", "grp"} stands for the peeling criterion Log-Hazard Ratio (LHR), Log-Rank Test (LRT), Cumulative Hazard Summary (CHS), or Group (GRP), respectively, that is used in the PRSP algorithm (LHR, LRT, CHS) or the PRGSP algorithm (GRP). Suggests "lrt". cvcriterion in {"lhr", "lrt", "cer"} stands for the cross-validation criterion Log-Hazard Ratio (LHR), Log-Rank Test (LRT), or Concordance Error Rate (CER), respectively, that is used for optimizing the model size (cardinal of subset of top-screened variables) and the optimal number of peeling steps (optimal peeling sequence length) in the PRSP variable screening procedure. Suggests "cer". PCQR: tau = numeric quantile in [0, 0.5] used in the censored quantile regression model. It is the tuning parameter of the censored quantile loss. It represents the conditional censored quantile of the survival response to be estimated. It includes the absolute loss when tau=0.5. Suggests 0.5. alpha = numeric elasticnet mixing parameter in [0, 1] that controls the relative contribution from the lasso and the ridge penalty. The penalty is defined as (1-alpha)/2||beta||_2^2+alpha||beta||_1. alpha = 1 is the lasso penalty, and alpha = 0 the ridge penalty. If alpha is set to NULL, a vector of values of length nalpha is used, else alpha value is used and nalpha is set to 1. Suggests alpha=1 (lasso). nalpha = positive integer of number of alpha values to consider in the grid search. Suggests 1 (see above: lasso). nlambda = positive integer of number of elasticnet penalization lambda values to consider in the grid search. Suggests 100. PPL: alpha = numeric elasticnet mixing parameter in [0, 1] that controls the relative contribution from the lasso and the ridge penalty. See R package glmnet. The penalty is defined as (1-alpha)/2||beta||_2^2+alpha||beta||_1. alpha = 1 is the lasso penalty, and alpha = 0 the ridge penalty. If alpha is set to NULL, a vector of values of length nalpha is used, else alpha value is used and nalpha is set to 1. Suggests alpha=1 (lasso). nalpha = positive integer of number of alpha values to consider in the grid search. Suggests 1 (see above: lasso). nlambda = positive integer of number of elasticnet penalization lambda values to consider in the grid search. Suggests 100. SPCA: n.thres = number of thresholds to consider in the grid search. It cannot be less than n (sample size). Suggests 20. n.pcs = number of cross-validation principal components to use in {1,2,3}. It cannot be less than n (sample size) and more than p (dimensionality), and will be reset to n.pcs = p - 1 otherwise. Suggests 3. n.var = minimum number of variables to include in determining range for threshold. If cannot be more than p (dimensionality), and will be reset to n.var = p - 1 otherwise. Suggests 5.
vscons	numeric scalar in [1/K, 1], specifying the conservativeness of the variable screening (pre-selection) procedure, where 1/K is the least conservative and 1 is the most. Suggests 0.5
cv	logical scalar. Flag for optional cross-validation (CV) of variable screening (pre-selection) parameters and Survival Bump Hunting fitting by PRSP algorithm. See below for details. Defaults to TRUE.
cvtype	character vector in {"combined", "averaged"} specifying the cross-validation technique. Defaults to "combined". Ignored if cv is FALSE.
cvarg	character vector describing the parameters used in the PRSP algorithm for fitting the Survival Bump Hunting model. Defaults to: cvarg="alpha=0.01,beta=0.10,peelcriterion=\"lrt\",cvcriterion=\"cer\"". Note that cvarg comes as a character string between double quotes, with comas separated values, and without white spaces. alpha = numeric data quantile in (0,1) to peel off at each step of the peeling sequence of the PRSP algorithm. Defaults to 0.01. beta = numeric scalar of minimum box support at the end of the peeling sequence. Defaults to 0.10. peelcriterion in {"lhr", "lrt", "chs", "grp"} stands for the peeling criterion Log-Hazard Ratio (LHR), Log-Rank Test (LRT), Cumulative Hazard Summary (CHS), or Group (GRP), respectively, that is used in the PRSP or PRGSP algorithm. Defaults to "lrt". cvcriterion in {"lhr", "lrt", "cer"} stands for the cross-validation criterion Log-Hazard Ratio (LHR), Log-Rank Test (LRT), or Concordance Error Rate (CER), respectively, that is used for tuning/optimizing the optimal number of peeling steps (i.e. optimal peeling sequence length) in the PRSP algorithm. Defaults to "cer". Ignored if cv is FALSE. if peelcriterion is in {"lhr", "lrt", "chs"}, groups is automatically set to NULL.
groups	character or numeric vector, or factor of group membership indicator variable of length the data sample size with as many different values or levels as the number of data sample groups. To be specified if algorithm Patient Recursive Group Survival Peeling (PRGSP) is to be used, i.e. with option peelcriterion = "grp". Only two groups are allowed at this point. Defaults to NULL, i.e. when regular PRSP is to be used.
pv	logical scalar. Flag for computation of log-rank p-values. Defaults to FALSE.
decimals	Positive integer of the number of user-specified significant decimals to output results. Defaults to 2.
onese	logical scalar. Flag for using the 1-standard error rule instead of extremum value of the cross-validation criterion when tuning/optimizing model parameters. Defaults to FALSE.
probval	numeric scalar of the survival probability at which we want to get the endpoint box survival time. Defaults to NULL (i.e. maximal survival probability value).
timeval	numeric scalar of the survival time at which we want to get the endpoint box survival probability. Defaults to NULL (i.e. maximal survival time value).
parallel.vs	logical. Is parallelization to be performed for variable screening? Defaults to FALSE, because it is not implemented yet.
parallel.rep	logical. Is parallelization to be performed for replications? Defaults to FALSE.
parallel.pv	logical. Is parallelization to be performed for computation of log-rank p-values? Defaults to FALSE.
conf	list of 5 fields containing the parameters values needed for creating the parallel backend (cluster configuration). See details below for usage. Optional, defaults to NULL, but all fields are required if used: type : character vector specifying the cluster type ("SOCKET", "MPI"). spec : A specification (character vector or integer scalar) appropriate to the type of cluster. homogeneous : logical scalar to be set to FALSE for inhomogeneous clusters. verbose : logical scalar to be set to FALSE for quiet mode. outfile : character vector of an output log file name to direct the stdout and stderr connection output from the workernodes. "" indicates no redirection.
verbose	logical scalar. Is the output to be verbose? Optional, defaults to TRUE.
seed	Positive integer scalar of the user seed to reproduce all the results. Defaults to NULL.

Details

The main function sbh relies on an optional variable screening (pre-selection) procedure that is run before the actual variable usage (selection) is done at the time of fitting the Survival Bump Hunting (SBH) or Group Survival Bump Hunting (GSBH) model using our PRSP or PRGSP algorithm, respectively. At this point, the user can choose between four possible variable screening (pre-selection) procedures:

• Patient Recursive Survival Peeling (PRSP) (by univariate screening of our algorithm)

• Penalized Censored Quantile Regression (PCQR) (by Semismooth Newton Coordinate Descent fiting algorithm adapted from package hqreg)

• Penalized Partial Likelihood (PPL) (by Elasticnet Regularization adapted from package glmnet)

• Supervised Principal Component Analysis (SPCA) (by Supervised Principal Component adapted from package superpc)

NA missing values are not allowed in PRIMsrc, because it depends on R package glmnet, which doesn't handle missing values. In case of high-dimensional data (p >> n), the recommendation is to use PPL or SPCA because of computational efficiency. Variable screening (pre-selection) is done by computing occurrence frequencies of top-ranking variables over the cross-validation folds and replicates. The conservativeness of the procedure is controled by the argument vscons.

Example of vscons values for pre-selection are as follows:

• '1.0' represents a presence in all the folds (unanimity vote)

• '0.5' represents a presence in at least half of the folds (majority vote)

• '1/K' represents a presence in at least one of the folds (minority vote)

Although any value in the interval [1/K,1] is accepted, we recommand using the interval [1/K, 1/2] to avoid excessive conservativeness. Final variable usage (selection) is done at the time of fitting the Survival Bump Hunting (SBH) model itself using our PRSP algorithm on previously screened variables by collecting those variables that have the maximum occurrence frequency in each peeling step over cross-validation folds and replicates.

If cross-validation is done (cv = TRUE, the optimal number of peeling steps (optimal peeling sequence length), and the optimal model size (cardinal of subset of top-screened variables) will be determined by cross-validation. If cv = FALSE, no cross-validation at all will be performed, and the values of K and vscons will both be reset to 1, and traditional log-rank Mantel-Haenszel p-values will be computed (using the Chi-Squared distribution with 1 df for the null distribution) instead of log-rank permutation p-values (using the permutation distribution for the null distribution).

The argument groups is to be specified if the Patient Recursive Group Survival Peeling (PRGSP) algorithm is used. The PRGSP algorithm is a derivation of our original Patient Recursive Survival Peeling (PRSP) algorithm (Dazard et al. 2016) to search for (or find an extreme of) outcome difference within existing (fixed) groups of observations. See Rao et al. (2018) for details and an application in Disparity Subtyping.

In the PRSP variable screening procedure (vsarg of "prsp"), setting option msize to a single non-NULL value within the allowable range [1,floor(p)] will override the cross-validation setting within the variable screening procedure. This could be recommended for high-dimensional data (p >> n) to reduce the computational burden. In this situation, we suggest an arbitrary value of msize within [1, floor(p/5)]. Conversely, setting msize=NULL will force the cross-validation within the variable screening procedure by automaticaly generating a vector of model sizes (cardinals of subset of top-screened variables) within the restricted range [1, floor(p/5)], which will be used to determine the optimal value of model size.

In fitting the Survival Bump Hunting (SBH) model itself, note that the result contains initial step #0, which corresponds to the entire set of the (training) data. Also, the number of peeling steps that is within the allowable range [1,ceiling(log(1/n) / log(1 - (1/n)))] is further restricted when either of the metaparameter alpha or beta takes on values other than the smallest possible fraction of the (training) data, i.e. \frac{1}{n^t}, where n^t is the training sample size:

• ceiling(log(beta) / log(1 - alpha)) : alpha and beta fixed by user

• ceiling(log(1/n^t) / log(1 - alpha)) : alpha fixed by user and beta fixed by data

• ceiling(log(beta) / log(1 - (1/n^t))) : alpha fixed by data and beta fixed by user

• ceiling(log(1/n^t) / log(1 - (1/n^t))) : alpha and beta fixed by data

When cross-validation is requested (cv=TRUE), the function performs a supervised (stratified) random splitting of the observations accounting for the classes/strata provided by delta (censoring). This is because it is desireable that the data splitting balances the class distributions of the outcome within the cross-validation splits. For each screening method and for building the final Survival Bump Hunting (SBH) model, all model tuning parameters are simultaneously estimated by cross-validation. The function offers a number of options for the cross-validation to be perfomed: the number of replications B; the type of technique; the peeling criterion; and the optimization criterion.

The returned S3-class sbh object contains cross-validated estimates of all the decision-rules of used (selected) covariates and all other statistical quantities of interest at each iteration of the peeling sequence (inner loop of the PRSP algorithm). This enables the graphical display of results of profiling curves for model tuning, peeling trajectories, covariate traces and survival distributions (see plotting functions for more details).

In case replicated cross-validations are performed, a "summary report" of the outputs is done over the B replicates as follows:

• Even thought the PRSP algorithm uses only one covariate at a time at each peeling step, the reported matrix of "Replicated CV" box decision rules may show more than one covariate being used in a given step depending on the replication. In the end, the reported "Replicated CV" trace values are computed (at each peeling step) as a single modal trace value of covariate usage over the B replicates. This is also reflected in the "Replicated CV" importance and usage plots of covariate traces.

• Similarly, the reported "Replicated CV" box membership indicators are computed (at each peeling step) as the point-wise modal membership value, that is majority vote, over the B replicates (right-hand side of equation #22 in Dazard et al. 2016). The reported "Replicated CV" box support and corresponding box sample size are computed (at each peeling step) based on the above "Replicated CV" box membership indicators (i.e. not as equation #23 in Dazard et al. 2016).

• All other reported "Replicated CV" box estimates are computed (at each peeling step) as average statistics over the B replicates (i.e. as equation #21 in Dazard et al. 2016), that is, not as a single box estimate computed from the "Replicated CV" box membership indicators. This includes the decision rules, the p-values, and all other box statistics. This may result in some apparent discordance if these estimates are re-computed directly from the reported "Replicated CV" box membership indicators.

If the computation of log-rank p-values is desired, then running with the parallelization option is strongly advised. In case of large (p > n) or very large (p >> n) datasets, it is also highly recommended to use the parallelization option.

The function sbh relies on the R package parallel to create a parallel backend within an R session. This enables access to a cluster of compute cores and/or nodes on a local and/or remote machine(s) and scaling-up with the number of CPU cores available and efficient parallel execution. To run a procedure in parallel (with parallel RNG), argument parallel is to be set to TRUE and argument conf is to be specified (i.e. non NULL). Argument conf uses the options described in function makeCluster of the R packages parallel and snow. PRIMsrc supports two types of communication mechanisms between master and worker processes: 'Socket' or 'Message-Passing Interface' ('MPI'). In PRIMsrc, parallel 'Socket' clusters use sockets communication mechanisms only (no forking) and are therefore available on all platforms, including Windows, while parallel 'MPI' clusters use high-speed interconnects mechanism in networks of computers (with distributed memory) and are therefore available only in these architectures. A parallel 'MPI' cluster also requires R package Rmpi to be installed. Value type is used to setup a cluster of type 'Socket' ("SOCKET") or 'MPI' ("MPI"), respectively. Depending on this type, values of spec are to be used alternatively:

• For 'Socket' clusters (conf$type="SOCKET"), spec should be a character vector naming the hosts on which to run the job; it can default to a unique local machine, in which case, one may use the unique host name "localhost". Each host name can potentially be repeated to the number of CPU cores available on the local machine. It can also be an integer scalar specifying the number of processes to spawn on the local machine; or a list of machine specifications if you have ssh installed (a character value named host specifying the name or address of the host to use).

• For 'MPI' clusters (conf$type="MPI"), spec should be an integer scalar specifying the total number of processes to be spawned across the network of available nodes, counting the workernodes and masternode.

The actual creation of the cluster, its initialization, and closing are all done internally. For more details, see the reference manual of R package snow and examples below.

When random number generation is needed, the creation of separate streams of parallel RNG per node is done internally by distributing the stream states to the nodes. For more details, see the vignette of R package parallel. The use of a seed allows to reproduce the results within the same type of session: the same seed will reproduce the same results within a non-parallel session or within a parallel session, but it will not necessarily give the exact same results (up to sampling variability) between a non-parallelized and parallelized session due to the difference of management of the seed between the two (see parallel RNG and value of returned seed below).

Value

Object of class sbh (Patient Recursive Survival Peeling) list containing the following 23 fields:

X	numeric matrix of original dataset.
y	numeric vector of observed failure / survival times.
delta	numeric vector of observed event indicator in {1,0}.
B	positive integer of the number of replications used in the cross-validation procedure.
K	positive integer of the number of folds used in the cross-validation procedure.
A	positive integer of the number of permutations used for the computation of log-rank p-values.
vs	logical scalar of returned flag of optional variable pre-selection.
vstype	character vector of the optional variable pre-selection procdure used.
vsarg	list of parameters used in the pre-selection procedure.
vscons	numeric scalar of conservativeness of the variable screening (pre-selection) procedure.
cv	logical scalar of returned flag of optional cross-validation.
cvtype	character vector of the cross-validation technique used.
cvarg	list of parameters used in the Survival Bump Hunting procedure.
groups	vector of group membership if algorithm Patient Recursive Group Survival Peeling (PRGSP) is used.
pv	logical scalar of returned flag of optional computation of log-rank p-values.
onese	logical scalar of returned flag of 1-standard error rule.
decimals	integer of the number of user-specified significant decimals.
probval	Numeric scalar of survival probability used.
timeval	Numeric scalar of survival time used.
cvprofiles	list of 10 fields of cross-validated tuning profiles and estimates, each of length B (one for each replicate): cv.varprofiles: numeric matrix of cross-validation criterion used for tuning/optimizing the variable screening size in the PRSP variable screening (pre-selection) procedure (NULL otherwise). Values are by columns (peeling steps) and replicates (rows). cv.varprofiles.mean: numeric vector of means (across replicates) of the above cross-validation criterion by peeling steps. cv.varprofiles.se: numeric vector of standard errors (across replicates) of the above cross-validation criterion by peeling steps. cv.varset.opt: numeric scalar of optimal variable screening size according to the extremum. cv.varset.1se: numeric scalar of optimal variable screening size according to 1SE rule. cv.stepprofiles: numeric matrix of cross-validation criterion used for tuning/optimizing the peeling sequence length (i.e. number of peeling steps) in the PRSP algorithm. Values are by columns (peeling steps) and replicates (rows). cv.stepprofiles.mean: numeric vector of means (across replicates) of the above cross-validation criterion by peeling steps. cv.stepprofiles.se: numeric vector of standard errors (across replicates) of the above cross-validation criterion by peeling steps. cv.nsteps.opt: numeric scalar of optimal number of peeling steps according to the extremum. cv.nsteps.1se: numeric scalar of optimal number of peeling steps according to 1SE rule.
cvfit	list with 12 fields of cross-validated SBH output estimates, each of length B (one for each replicate): cv.maxsteps: numeric scalar of maximal number of peeling steps (counting step #0 - see Details section). cv.nsteps: numeric scalar of optimal number of peeling steps (counting step #0 - see Details section). cv.boxind: logical matrix in TRUE, FALSE of individual observation box membership indicator (columns) for all peeling steps (rows). cv.boxind.size: numeric vector of box sample size for all peeling steps. cv.boxind.support: numeric vector of box support for all peeling steps. cv.rules: data.frame of decision rules on the covariates (columns) for all peeling steps (rows). cv.screened: numeric vector of screened (pre-selected) covariates, indexed in reference to original index. cv.trace: numeric vector of the modal trace values of covariate usage for all peeling steps. cv.sign: numeric vector in {-1,+1} of directions of peeling for all used (selected) covariates. cv.used: numeric vector of covariates used (selected) for peeling, indexed in reference to original index. cv.stats: numeric matrix of box endpoint quantities of interest (columns) for all peeling steps (rows). cv.pval: list with 2 fields of two vectors. The first cvfit$pval is a numeric vector for log-rank p-values of separation of survival distributions, The second cvfit$seed is is an integer scalar if parallelization is used, or an integer vector of A values, one for each permutation, if parallelization is not used.
success	logical scalar of the returned flag of success at fitting the SBH model.
seed	User seed. An integer scalar if parallelization is used, or an integer vector of B values, one for each replication, if parallelization is not used.

Acknowledgments

This work made use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University. This project was partially funded by the National Institutes of Health NIH - National Cancer Institute (R01-CA160593) to J-E. Dazard and J.S. Rao.

Note

Unique end-user function for fitting the Survival Bump Hunting model.

Author(s)

• "Jean-Eudes Dazard, Ph.D." [e-mail]

• "Michael Choe, M.D." [e-mail]

• "Michael LeBlanc, Ph.D." [e-mail]

• "Alberto Santana, MBA." [e-mail]

• "J. Sunil Rao, Ph.D." [e-mail]

Maintainer: "Jean-Eudes Dazard, Ph.D." [e-mail]

References

• Dazard J-E. and Rao J.S. (2018). "Variable Selection Strategies for High-Dimensional Survival Bump Hunting using Recursive Peeling Methods." (in prep).

• Rao J.S., Huilin Y. and Dazard J-E. (2018). "Disparity Subtyping: Bringing Precision Medicine Closer to Disparity Science." (in prep).

• Diaz-Pachon D.A., Saenz J.P., Dazard J-E. and Rao J.S. (2018). "Mode Hunting through Active Information." (in press).

• Diaz-Pachon D.A., Dazard J-E. and Rao J.S. (2017). "Unsupervised Bump Hunting Using Principal Components." In: Ahmed SE, editor. Big and Complex Data Analysis: Methodologies and Applications. Contributions to Statistics, vol. Edited Refereed Volume. Springer International Publishing, Cham Switzerland, p. 325-345.

• Yi C. and Huang J. (2017). "Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression." J. Comp Graph. Statistics, 26(3):547-557.

• Dazard J-E., Choe M., LeBlanc M. and Rao J.S. (2016). "Cross-validation and Peeling Strategies for Survival Bump Hunting using Recursive Peeling Methods." Statistical Analysis and Data Mining, 9(1):12-42.

• Dazard J-E., Choe M., LeBlanc M. and Rao J.S. (2015). "R package PRIMsrc: Bump Hunting by Patient Rule Induction Method for Survival, Regression and Classification." In JSM Proceedings, Statistical Programmers and Analysts Section. Seattle, WA, USA. American Statistical Association IMS - JSM, p. 650-664.

• Dazard J-E., Choe M., LeBlanc M. and Rao J.S. (2014). "Cross-Validation of Survival Bump Hunting by Recursive Peeling Methods." In JSM Proceedings, Survival Methods for Risk Estimation/Prediction Section. Boston, MA, USA. American Statistical Association IMS - JSM, p. 3366-3380.

• Dazard J-E. and J.S. Rao (2010). "Local Sparse Bump Hunting." J. Comp Graph. Statistics, 19(4):900-92.

See Also

• makeCluster (R package parallel)

• glmnet, cv.glmnet (R package glmnet)

• hqreg, cv.hqreg (R package hqreg)

• superpc.cv (R package superpc)

Examples

#===================================================
# Loading the library and its dependencies
#===================================================
library("PRIMsrc")

## Not run: 
    #===================================================
    # PRIMsrc Package news
    #===================================================
    PRIMsrc.news()
    
    #===================================================
    # PRIMsrc Package citation
    #===================================================
    citation("PRIMsrc")
    
    #===================================================
    # Demo with a synthetic dataset
    # Use help for descriptions
    #===================================================
    data("Synthetic.1", package="PRIMsrc")
    ?Synthetic.1

## End(Not run)

#===================================================
# Simulated dataset #1 (n=250, p=3)
# Peeling criterion = LRT
# Cross-Validation criterion = LRT
# With Combined Cross-Validation (RCCV)
# Without Replications (B = 1)
# Without variable screening (pre-selection)
# Without computation of log-rank \eqn{p}-values
# Without parallelization
#===================================================
synt1 <- sbh(X = Synthetic.1[ , -c(1,2), drop=FALSE],
             y = Synthetic.1[ ,1, drop=TRUE],
             delta = Synthetic.1[ ,2, drop=TRUE],
             B = 1,
             K = 3,
             vs = FALSE,
             cv = TRUE,
             cvtype = "combined",
             cvarg = "alpha=0.10,
                      beta=0.10,
                      peelcriterion=\"lrt\",
                      cvcriterion=\"lrt\"",
             groups = NULL,
             pv = FALSE,
             decimals = 2,
             onese = FALSE,
             probval = 0.5,
             timeval = NULL,
             parallel.vs = FALSE,
             parallel.rep = FALSE,
             parallel.pv = FALSE,
             conf = NULL,
             verbose = FALSE,
             seed = 123)

summary(object = synt1)
print(x = synt1)

n <- 100
p <- length(synt1$cvfit$cv.used)
x <- matrix(data = runif(n = n*p, min = 0, max = 1),
            nrow = n, ncol = p, byrow = FALSE,
            dimnames = list(1:n, paste("X", 1:p, sep="")))
synt1.pred <- predict(object = synt1,
                      newdata = x,
                      steps = synt1$cvfit$cv.nsteps)

plot(x = synt1,
     main = paste("Scatter plot for model #1", sep=""),
     proj = c(1,2),
     steps = synt1$cvfit$cv.nsteps,
     pch = 16, cex = 0.5, col = c(1,2),
     boxes = TRUE,
     col.box = 2, lty.box = 2, lwd.box = 1,
     add.caption.box = TRUE, 
     text.caption.box = paste("Step: ", synt1$cvfit$cv.nsteps, sep=""),
     device = NULL)

plot_profile(object = synt1,
             main = "Cross-validated tuning profiles for model #1",
             pch = 20, col = 1, lty = 1, lwd = 0.5, cex = 0.5,
             add.sd = TRUE, 
             add.profiles = TRUE,
             add.caption = TRUE, 
             text.caption = c("Mean","Std. Error"),
             device = NULL)

plot_traj(object = synt1,
          main = paste("Cross-validated peeling trajectories for model #1", sep=""),
          col = 1, lty = 1, lwd = 0.5, cex = 0.5,
          toplot = synt1$cvfit$cv.used,
          device = NULL)

plot_trace(object = synt1,
           main = paste("Cross-validated trace plots for model #1", sep=""),
           xlab = "Box Mass", ylab = "Covariate Range (centered)",
           col = 1, lty = 1, lwd = 0.5, cex = 0.5,
           toplot = synt1$cvfit$cv.used,
           center = TRUE, scale = FALSE,
           device = NULL)

plot_km(object = synt1,
        main = paste("Cross-validated probability curves for model #1", sep=""),
        xlab = "Time", ylab = "Probability",
        ci = TRUE,
        steps = 1:synt1$cvfit$cv.nsteps,
        col = c(1,2), lty = 1, lwd = 0.5, cex = 0.5,
        add.caption = TRUE,
        text.caption = c("outbox","inbox"), 
        device = NULL)
                                
## Not run: 
    #===================================================
    # Examples of parallel backend parametrization 
    #===================================================
    if (require("parallel")) {
       cat("'parallel' is attached correctly \n")
    } else {
       stop("'parallel' must be attached first \n")
    }
    #===================================================
    # Ex. #1 - Multicore PC
    # Running WINDOWS
    # SOCKET communication cluster
    # Shared memory parallelization
    #===================================================
    cpus <- parallel::detectCores(logical = TRUE)
    conf <- list("spec" = rep("localhost", cpus),
                 "type" = "SOCKET",
                 "homo" = TRUE,
                 "verbose" = TRUE,
                 "outfile" = "")
    #===================================================
    # Ex. #2 - Master node + 3 Worker nodes cluster
    # All nodes equipped with identical setups of multicores 
    # (8 core CPUs per machine for a total of 32)
    # SOCKET communication cluster
    # Distributed memory parallelization
    #===================================================
    masterhost <- Sys.getenv("HOSTNAME")
    slavehosts <- c("compute-0-0", "compute-0-1", "compute-0-2")
    nodes <- length(slavehosts) + 1
    cpus <- 8
    conf <- list("spec" = c(rep(masterhost, cpus),
                            rep(slavehosts, cpus)),
                 "type" = "SOCKET",
                 "homo" = TRUE,
                 "verbose" = TRUE,
                 "outfile" = "")
    #===================================================
    # Ex. #3 - Enterprise Multinode Cluster w/ multicore/node  
    # Running LINUX with SLURM scheduler
    # MPI communication cluster
    # Distributed memory parallelization
    #==================================================
    if (require("Rmpi")) {
        cat("'Rmpi' is attached correctly \n")
    } else {
        stop("'Rmpi' must be attached first \n")
    }
    # Below, variable 'cpus' is the total number of requested 
    # taks (threads/CPUs), which is specified from within a 
    # SLURM script.
    cpus <- as.numeric(Sys.getenv("SLURM_NTASKS"))
    conf <- list("spec" = cpus,
                 "type" = "MPI",
                 "homo" = TRUE,
                 "verbose" = TRUE,
                 "outfile" = "")
    #===================================================
    # Simulated dataset #1 (n=250, p=3)
    # Peeling criterion = LRT
    # Cross-Validation criterion = LRT
    # With Combined Cross-Validation (RCCV)
    # With Replications (B = 30)
    # With PPL variable screening (pre-selection)
    # With computation of log-rank \eqn{p}-values
    # With parallelization
    #===================================================                         
    synt1 <- sbh(X = Synthetic.1[ , -c(1,2), drop=FALSE],
                 y = Synthetic.1[ ,1, drop=TRUE],
                 delta = Synthetic.1[ ,2, drop=TRUE],
                 B = 30,
                 K = 5,
                 A = 1000,
                 vs = TRUE,
                 vstype = "ppl",
                 vsarg = "alpha=1,
                          nalpha=1,
                          nlambda=100",
                 vscons = 0.5,
                 cv = TRUE,
                 cvtype = "combined",
                 cvarg = "alpha=0.01,
                          beta=0.10,
                          peelcriterion=\"lrt\",
                          cvcriterion=\"lrt\"",
                 groups = NULL,
                 pv = TRUE,
                 decimals = 2,
                 onese = FALSE,
                 probval = 0.5,
                 timeval = NULL,
                 parallel.vs = FALSE,
                 parallel.rep = TRUE,
                 parallel.pv = TRUE,
                 conf = conf,
                 verbose = TRUE,
                 seed = 123)      
    #===================================================
    # Simulated dataset #4 (n=100, p=1000)
    # Peeling criterion = LRT
    # Cross-Validation criterion = CER
    # With Combined Cross-Validation (RCCV)
    # With Replications (B = 30)
    # With PRSP variable screening (pre-selection)
    # With computation of log-rank \eqn{p}-values
    # With parallelization
    #===================================================                         
    synt4 <- sbh(X = Synthetic.4[ , -c(1,2), drop=FALSE],
                 y = Synthetic.4[ ,1, drop=TRUE],
                 delta = Synthetic.4[ ,2, drop=TRUE],
                 B = 30,
                 K = 5,
                 A = 1000,
                 vs = TRUE,
                 vstype = "prsp",
                 vsarg = "alpha=0.01,
                          beta=0.10,
                          msize=NULL,
                          peelcriterion=\"lrt\",
                          cvcriterion=\"cer\"",
                 vscons = 0.5,
                 cv = TRUE,
                 cvtype = "combined",
                 cvarg = "alpha=0.01,
                          beta=0.10,
                          peelcriterion=\"lrt\",
                          cvcriterion=\"cer\"",
                 groups = NULL,
                 pv = TRUE,
                 decimals = 2,
                 onese = FALSE,
                 probval = 0.5,
                 timeval = NULL,
                 parallel.vs = FALSE,
                 parallel.rep = TRUE,
                 parallel.pv = TRUE,
                 conf = conf,
                 verbose = TRUE,
                 seed = 123)

## End(Not run)

PRIMsrc documentation built on May 2, 2019, 11:45 a.m.