FRESA.CAD (version 2.2.0)

improvedResiduals: Estimate the significance of the reduction of predicted residuals

Description

This function will test the hypothesis that, given a set of two residuals (new vs. old), the new ones are better than the old ones as measured with non-parametric tests. Four p-values are provided: one for the binomial sign test, one for the paired Wilcoxon rank-sum test, one for the paired t-test, and one for the F-test. The proportion of subjects that improved their residuals, the proportion that worsen their residuals, and the net residual improvement (NeRI) will be returned.

Usage

improvedResiduals(oldResiduals,
	                  newResiduals,
	                  testType = c("Binomial", "Wilcox", "tStudent", "Ftest"))

Arguments

oldResiduals

A vector with the residuals of the original model

newResiduals

A vector with the residuals of the new model

testType

Type of non-parametric test to be evaluated: Binomial test ("Binomial"), Wilcoxon rank-sum test ("Wilcox"), Student's t-test ("tStudent"), or F-test ("Ftest")

Value

p1

Proportion of subjects that improved their residuals to the total number of subjects

p2

Proportion of subjects that worsen their residuals to the total number of subjects

NeRI

The net residual improvement (p1-p2)

p.value

The one tail p-value of the test specified in testType

BinP.value

The p-value associated with a significant improvement in residuals

WilcoxP.value

The single sided p-value of the Wilcoxon rank-sum test comparing the absolute values of the new and old residuals

tP.value

The single sided p-value of the paired t-test comparing the absolute values of the new and old residuals

FP.value

The single sided p-value of the F-test comparing the residual variances of the new and old residuals

Details

This function will test the hypothesis that the new residuals are "better" than the old residuals. To test this hypothesis, four types of tests are performed:

1. The paired t-test, which compares the absolute value of the residuals
2. The paired Wilcoxon rank-sum test, which compares the absolute value of residuals
3. The binomial sign test, which evaluates whether the number of subjects with improved residuals is greater than the number of subjects with worsened residuals
4. The F-test, which is the standard test for evaluating whether the residual variance is "better" in the new residuals.

The proportions of subjects that improved and worsen their residuals are returned, and so is the NeRI.

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:
# 	# - 10 bootstrap loops
# 	# - All variables except for age
# 	# - The Wilcoxon rank-sum test as the feature inclusion criterion
# 	cancerModel <- ForwardSelection.Model.Res(loops = 10,
# 	                                    Outcome = "pgstat",
# 	                                    variableList = cancerVarNames[-1,],
# 	                                    data = dataCancer,
# 	                                    type = "COX",
# 	                                    testType= "Wilcox",
# 	                                    timeOutcome = "pgtime")
# 	# Add age to the formula of the obtained model
# 	frm <- format(cancerModel$formula)
# 	frm[length(frm)] <- paste(frm[length(frm)], "+ age")
# 	# Fit the new formula to the same data
# 	cancerModelAge <- modelFitting(formula(frm), dataCancer, "COX")
# 	# Get the residuals of the original model
# 	cancerModelRes <- residualForFRESA(object = cancerModel$final.model,
# 	                                   testData = dataCancer,
# 	                                   Outcome = "pgstat")
# 	# Get the residuals of the model with the added term
# 	cancerModelAgeRes <- residualForFRESA(object = cancerModelAge,
# 	                                      testData = dataCancer,
# 	                                      Outcome = "pgstat")
# 	# Estimate the significance of the NeRI when adding age to the model
# 	NeRI <- improvedResiduals(oldResiduals = cancerModelRes,
# 	                          newResiduals = cancerModelAgeRes,
# 	                          testType = "Wilcox")
# 	# Shut down the graphics device driver
# 	dev.off()## End(Not run)