FRESA.CAD (version 2.2.0)

FRESA.Model: Automated model selection

Description

This function uses a wrapper procedure to select the best features of a non-penalized linear model that best predict the outcome, given the formula of an initial model template (linear, logistic, or Cox proportional hazards), an optimization procedure, and a data frame. A filter scheme may be enabled to reduce the search space of the wrapper procedure. The false selection rate may be empirically controlled by enabling bootstrapping, and model shrinkage can be evaluated by cross-validation.

Usage

FRESA.Model(formula,
	            data,
	            OptType = c("Binary", "Residual"),
	            pvalue = 0.05,
	            filter.p.value = 0.10,
	            loops = 1,
	            maxTrainModelSize = 10,
	            loop.threshold = 20,
	            elimination.bootstrap.steps = 100,
	            bootstrap.steps = 100,
	            interaction = c(1,1),
	            print = TRUE,
	            plots = TRUE,
	            CVfolds = 10,
	            repeats = 1,
	            nk = 0,
	            categorizationType = c("Raw",
	                                   "Categorical",
	                                   "ZCategorical",
	                                   "RawZCategorical",
	                                   "RawTail",
	                                   "RawZTail"),
	            cateGroups = c(0.1, 0.9),
	            raw.dataFrame = NULL,
	            var.description = NULL,
	            testType = c("zIDI",
	                         "zNRI",
	                         "Binomial",
	                         "Wilcox",
	                         "tStudent",
	                         "Ftest",
	                         "Both"),
	                         zbaggRemoveOutliers=4.0)

Arguments

formula

An object of class formula with the formula to be fitted

data

A data frame where all variables are stored in different columns

OptType

Optimization type: Based on the integrated discrimination improvement (Binary) index for binary classification ("Binary"), or based on the net residual improvement (NeRI) index for linear regression ("Residual")

pvalue

The maximum p-value, associated to the testType, allowed for a term in the model (controls the false selection rate)

filter.p.value

The maximum p-value, associated to the Kendall rank correlation test, allowed for a variable to be included to the feature selection procedure

loops

The number of bootstrap loops for the forward selection procedure

maxTrainModelSize

Maximum number of terms that can be included in the model

loop.threshold

After loop.threshold cycles, only variables that have already been selected in previous cycles will be candidates to be selected in posterior cycles

elimination.bootstrap.steps

The number of bootstrap loops for the backwards elimination procedure

bootstrap.steps

The number of bootstrap loops for the bootstrap validation procedure

interaction

A vector of size two. The terms are used by the search and update procedures, respectively. Set to either 1 for first order models, or to 2 for second order models

print

Logical. If TRUE, information will be displayed

plots

Logical. If TRUE, plots are displayed

CVfolds

The number of folds for the final cross-validation

repeats

The number of times that the cross-validation procedure will be repeated

nk

The number of neighbors used to generate a k-nearest neighbors (KNN) classification. If zero, k is set to the square root of the number of cases. If less than zero, it will not perform the KNN classification

categorizationType

How variables will be analyzed: As given in data ("Raw"); broken into the p-value categories given by cateGroups ("Categorical"); broken into the p-value categories given by cateGroups, and weighted by the z-score ("ZCategorical"); broken into the p-value categories given by cateGroups, weighted by the z-score, plus the raw values ("RawZCategorical"); raw values, plus the tails ("RawTail"); or raw values, wighted by the z-score, plus the tails ("RawZTail")

cateGroups

A vector of percentiles to be used for the categorization procedure

raw.dataFrame

A data frame similar to data, but with unajusted data, used to get the means and variances of the unadjusted data

var.description

A vector of the same length as the number of columns of data, containing a description of the variables

testType

For an Binary-based optimization, the type of index to be evaluated by the improveProb function (Hmisc package): z-value of Binary or of NRI. For a NeRI-based optimization, the type of non-parametric test to be evaluated by the improvedResiduals function: Binomial test ("Binomial"), Wilcoxon rank-sum test ("Wilcox"), Student's t-test ("tStudent"), or F-test ("Ftest")

zbaggRemoveOutliers

For linear regresion, zbaggRemoveOutliers is used to set the z-treshold to be used in the outlier detection.

Value

BSWiMS.model

An object of class lm, fastglm, or coxph containing the final model

reducedModel

The resulting object of the backward elimination procedure

univariateAnalysis

A data frame with the results from the univariate analysis

forwardModel

The resulting object of the feature selection function.

updatedforwardModel

The resulting object of the the update procedure

bootstrappedModel

The resulting object of the bootstrap procedure on final.model

cvObject

The resulting object of the cross-validation procedure

used.variables

The number of terms that passed the filter procedure

call

the function call

Details

This is the main function of FRESA.CAD given an outcome formula, and a data.frame this function will do an univariate analysis of the data (univariateRankVariables), then it will select the top ranked variables; after that it will select the model that best describes the outcome. At output it will return the bootstrapped performance of the model (bootstrapValidation_Bin or bootstrapValidation_Res). It can be set to report the cross-validation performance of the selection process which will return either a crossValidationFeatureSelection_Bin or a crossValidationFeatureSelection_Res object.

References

Pencina, M. J., D'Agostino, R. B., & Vasan, R. S. (2008). Evaluating the added predictive ability of a new marker: from area under the ROC curve to reclassification and beyond. Statistics in medicine 27(2), 157-172.

Examples

	## Not run: 
# 	# Start the graphics device driver to save all plots in a pdf format
# 	pdf(file = "Example.pdf")
# 	# Get the stage C prostate cancer data from the rpart package
# 	library(rpart)
# 	data(stagec)
# 	# Split the stages into several columns
# 	dataCancer <- cbind(stagec[,c(1:3,5:6)],
# 	                    gleason4 = 1*(stagec[,7] == 4),
# 	                    gleason5 = 1*(stagec[,7] == 5),
# 	                    gleason6 = 1*(stagec[,7] == 6),
# 	                    gleason7 = 1*(stagec[,7] == 7),
# 	                    gleason8 = 1*(stagec[,7] == 8),
# 	                    gleason910 = 1*(stagec[,7] >= 9),
# 	                    eet = 1*(stagec[,4] == 2),
# 	                    diploid = 1*(stagec[,8] == "diploid"),
# 	                    tetraploid = 1*(stagec[,8] == "tetraploid"),
# 	                    notAneuploid = 1-1*(stagec[,8] == "aneuploid"))
# 	# Remove the incomplete cases
# 	dataCancer <- dataCancer[complete.cases(dataCancer),]
# 	# Load a pre-stablished data frame with the names and descriptions of all variables
# 	data(cancerVarNames)
# 	# Get a Cox proportional hazards model using:
# 	# - The default parameters
# 	md <- FRESA.Model(formula = Surv(pgtime, pgstat) ~ 1,
# 	                  data = dataCancer,
# 					  var.description = cancerVarNames[,2])
# 	# Get a logistic regression model using
# 	# - The default parameters
# 	md <- FRESA.Model(formula = pgstat ~ 1,
# 	                  data = dataCancer,
# 					  var.description = cancerVarNames[,2])
# 	# Get a logistic regression model using:
# 	# - redidual-based optimization
# 	md <- FRESA.Model(formula = pgstat ~ 1,
# 	                  data = dataCancer,
# 	                  OptType = "Residual",
# 					  var.description = cancerVarNames[,2])
# 	# Get a Cox proportional hazards model using:
# 	# - 250 bootstrap loops
# 	md <- FRESA.Model(formula = Surv(pgtime, pgstat) ~ 1,
# 	                  data = dataCancer,
# 	                  loops = 250,
# 					  var.description = cancerVarNames[,2])
# 	# Get a Cox proportional hazards model using:
# 	# - 250 bootstrap loops
# 	# - First order interactions in the update procedure
# 	md <- FRESA.Model(formula = Surv(pgtime, pgstat) ~ 1,
# 	                  data = dataCancer,
# 	                  loops = 250,
# 	                  interaction = c(1,2),
# 					  var.description = cancerVarNames[,2])
# 	# Get a Cox proportional hazards model using:
# 	# - No bootstrapping
# 	# - No cross-validation
# 	md <- FRESA.Model(formula = Surv(pgtime, pgstat) ~ 1,
# 	                  data = dataCancer,
# 	                  CVfolds = 0,
# 	                  elimination.bootstrap.steps = 1,
# 					  var.description = cancerVarNames[,2])
# 	# Get a Cox proportional hazards model using:
# 	# - NeRI-based optimization
# 	# - 250 bootstrap loops
# 	# - First order interactions in the update procedure
# 	md <- FRESA.Model(formula = Surv(pgtime, pgstat) ~ 1,
# 	                  data = dataCancer,
# 	                  OptType = "Residual",
# 	                  loops = 250,
# 	                  interaction = c(1,2),
# 					  var.description = cancerVarNames[,2])
# 	# Shut down the graphics device driver
# 	dev.off()## End(Not run)