PRIMsrc (version 0.6.0)

PRIMsrc-package: Bump Hunting by Patient Rule Induction Method in Survival, Regression and Classification settings

Description

Performs a unified treatment of Bump Hunting by Patient Rule Induction Method (PRIM) in Survival, Regression and Classification settings (SRC). The method generates decision rules delineating a region in the predictor space, where the response is larger than its average over the entire space. The region is shaped as a hyperdimensional box or hyperrectangle that is not necessarily contiguous. Assumptions are that the multivariate input variables can be discrete or continuous and the univariate response variable can be discrete (Classification), continuous (Regression) or a time-to event, possibly censored (Survival). It is intended to handle low and high-dimensional multivariate datasets, including the situation where the number of covariates exceeds or dominates that of samples ($p > n$ or $p \gg n$ paradigm).

Details

The current version is a development release that only implements the case of a survival response. At this point, survival bump hunting is also restricted to a directed peeling search of the first box covered by the recursive coverage (outer) loop of our Patient Recursive Survival Peeling (PRSP) algorithm. New features will be added soon. The main function relies on an optional variable pre-selection procedure that is run before the PRSP algorithm. At this point, this is done by a cross-validated penalization of the partial likelihood using the R package glmnet. The following describes the end-user functions that are needed to run a complete procedure. The other internal subroutines are not documented in the manual and are not to be called by the end-user at any time. For computational efficiency, some end-user functions offer a parallelization option that is done by passing a few parameters needed to configure a cluster. This is indicated by an asterisk (* = optionally involving cluster usage). The R functions are categorized as follows:

1. END-USER FUNCTION FOR PACKAGE NEWS

PRIMsrc.news Display the PRIMsrc Package News Function to display the log file NEWS of updates of the PRIMsrc package. END-USER S3-GENERIC FUNCTIONS FOR SUMMARY, DISPLAY, PLOT AND PREDICTION summary Summary Function S3-generic summary function to summerize the main parameters used to generate the PRSP object. print Print Function S3-generic print function to display the cross-validated fitted values of the PRSP object. plot 2D Visualization of Data Scatter and Box Vertices S3-generic function to plot a scatterplot of the data and the cross-validated box vertices of a PRSP object in a plane defined by the user. The plot is for a given peeling step of the peeling sequence (inner loop of our PRSP algorithm) defined by the user. predict Predict Function S3-generic predict function to predict the box membership and box vertices on an independent set from a PRSP object trained by a SBH model. END-USER SURVIVAL BUMP HUNTING FUNCTION sbh (*) Cross-Validated Survival Bump Hunting Main end-user function for fitting a cross-validated Survival Bump Hunting (SBH) model. It returns a cross-validated PRSP object, as generated by our Patient Recursive Survival Peeling or PRSP algorithm. The function relies on an internal variable pre-selection procedure before the PRSP algorithm is run. At this point, this is done by regular Cox-regression (from the R package survival) or a cross-validated Elasticnet Regularized Cox-Regression (from the R package glmnet), depending on whether the number of covariates is less ($p \le n$) or greater ($p > n$) than the number of samples, respectively. At this point, the main function sbh performs the search of the first box of the recursive coverage (outer) loop of our Patient Recursive Survival Peeling (PRSP) algorithm. The PRSP object contains cross-validated estimates of all the decision-rules of pre-selected covariates and all other statistical quantities of interest at each iteration of the peeling sequence (inner loop of the PRSP algorithm). It enables the display of results graphically of/for model tuning/selection, all peeling trajectories, covariate traces, and survival distributions (see plotting functions below for more details). The function offers a few options such as the type of $K$-fold cross-validation desired ((replicated)-averaged or-combined), the peeling criterion for peeling the next box, the optimization criterion for model tuning and selection and a few more parameters for the PRSP algorithm. The function takes advantage of the R package parallel for efficient parallel execution. It allows users to create a cluster of workstations on a local and/or remote machine(s), enabling scaling-up to the number of specified CPU cores. END-USER PLOTTING FUNCTIONS FOR MODEL VALIDATION AND VISUALIZATION OF RESULTS plot_profile Visualization for Model Selection/Validation Function for plotting the cross-validated profiles of a PRSP object. It uses the user's choice of statistics among the Log Hazard Ratio (LHR), Log-Rank Test (LRT) or Concordance Error Rate (CER) as a function of the model tuning parameter, that is, the optimal number of peeling steps of the peeling sequence (inner loop of our PRSP algorithm). plot_boxtraj Visualization of Peeling Trajectories/Profiles Function for plotting the cross-validated peeling trajectories/profiles of a PRSP object. Applies to the user-specified covariates among the pre-selected ones and all other statistical quantities of interest at each iteration of the peeling sequence (inner loop of our PRSP algorithm). plot_boxtrace Visualization of Covariates Traces Function for plotting the cross-validated covariates traces of a PRSP object. Plot the cross-validated modal trace curves of covariate importance and covariate usage of the user-specified covariates among the pre-selected ones at each iteration of the peeling sequence (inner loop of our PRSP algorithm). plot_boxkm Visualization of Survival Distributions Function for plotting the cross-validated survival distributions of a PRSP object. Plot the cross-validated Kaplan-Meir estimates of survival distributions for the highest risk (inbox) versus lower-risk (outbox) groups of samples at each iteration of the peeling sequence (inner loop of our PRSP algorithm). END-USER DATASETS Synthetic.1, Synthetic.2, Synthetic.3, Synthetic.4, Synthetic.5 Five Simulated Survival Models Datasets Modeling survival models #1-5 with censoring as a regression function of some informative predictors, depending on the model used. In models where non-informative noisy covariates were used, these covariates were not part of the design matrix (models #2-3 and #5). In one example, the signal is limited to a box-shaped region $R$ of the predictor space (model #4). In the last example, the signal is limited to 10% of the predictors in a $p > n$ situation (model #5). Survival time was generated from an exponential model with with rate parameter $\lambda$ (and mean $\frac{1}{\lambda}$) according to a Cox-PH model with hazard exp(eta), where eta(.) is the regression function. Censoring indicator were generated from a uniform distribution on [0,3] (models #1-4) or [0,2] (model #5). In these synthetic examples, all covariates are continuous, i.i.d. from a multivariate uniform distribution on [0,1] (models #1-4) or from a multivariate standard normal distribution (model #5). Real.1 Clinical Dataset Publicly available dataset from the Women's Interagency HIV cohort Study (WIHS). Inclusion criteria of the study were that women at enrolment were (i) alive, (ii) HIV-1 infected, and (iii) free of clinical AIDS symptoms. Women were followed until the first of the following occurred: (i) treatment initiation (HAART), (ii) AIDS diagnosis, (iii) death, or administrative censoring. The studied outcomes were the competing risks "AIDS/Death (before HAART)" and "Treatment Initiation (HAART)". However, here, for simplification purposes, only the first of the two competing events (i.e. the time to AIDS/Death), was used in this dataset example. Likewise, the entire study enrolled 1164 women, but only the complete cases were used in this dataset example for simplification. Variables included history of Injection Drug Use ("IDU") at enrollment, African American ethnicity ("Race"), age ("Age"), and baseline CD4 count ("CD4"). The question in this dataset example was whether it is possible to achieve a prognostication of patients for AIDS and HAART. Real.2 Genomic Dataset Publicly available lung cancer data from the Chemores Cohort Study. This was an integrated study of mRNA, miRNA and clinical variables to characterize the molecular distinctions between squamous cell carcinoma (SCC) and adenocarcinoma (AC) in Non Small Cell Lung Cancer (NSCLC). Tissue samples were analysed from a cohort of 123 patients who underwent complete surgical resection at the Institut Mutualiste Montsouris (Paris, France) between 30 January 2002 and 26 June 2006. In this genomic dataset, only the expression levels of Agilent miRNA probes ($p=939$) were included from the $n=123$ samples of the Chemores cohort. It represents a situation where the number of covariates dominates the number of complete observations, or $p >> n$ case.

References

• Dazard J-E., Choe M., LeBlanc M. and Rao J.S. (2015). "Cross-validation and Peeling Strategies for Survival Bump Hunting using Recursive Peeling Methods." (Submitted).
• 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 packageparallel)
• plot.survfit(R packagesurvival)
• glmnet(R packageglmnet)