FRESA.CAD (version 2.0.2)

bootstrapVarElimination: IDI/NRI-based backwards variable elimination with bootstrapping

Description

This function removes model terms that do not improve the bootstrapped integrated discrimination improvement (IDI) or net reclassification improvement (NRI) significantly.

Usage

bootstrapVarElimination(object,
	                        pvalue = 0.05,
	                        Outcome = "Class",
	                        data,
	                        startOffset = 0, 
	                        type = c("LOGIT", "LM", "COX"),
	                        selectionType = c("zIDI", "zNRI"),
	                        loops = 250,
	                        fraction = 1.0,
	                        print=TRUE,
	                        plots=TRUE)

Arguments

object

An object of class lm, glm, or coxph containing the model to be analyzed

pvalue

The maximum p-value, associated to either IDI or NRI, allowed for a term in the model

Outcome

The name of the column in data that stores the variable to be predicted by the model

data

A data frame where all variables are stored in different columns

startOffset

Only terms whose position in the model is larger than the startOffset are candidates to be removed

type

Fit type: Logistic ("LOGIT"), linear ("LM"), or Cox proportional hazards ("COX")

selectionType

The type of index to be evaluated by the improveProb function (Hmisc package): z-score of IDI or of NRI

loops

The number of bootstrap loops

fraction

The fraction of data (sampled with replacement) to be used as train

print

Logical. If TRUE, information will be displayed

plots

Logical. If TRUE, plots are displayed

Value

• back.model
  An object of the same class as object containing the reduced model
• loops
  The number of loops it took for the model to stabilize
• reclas.info
  A list with the NRI and IDI statistics of the reduced model, as given by the getVarReclassification function
• bootCV
  An object of class bootstrapValidation containing the results of the bootstrap validation in the reduced model
• back.formula
  An object of class formula with the formula used to fit the reduced model
• lastRemoved
  The name of the last term that was removed (-1 if all terms were removed)

Details

For each model term $x_i$, the IDI or NRI is computed for the full model and the reduced model( where the term $x_i$ removed). The term whose removal results in the smallest drop in bootstrapped improvement is selected. The hypothesis: the term adds classification improvement is tested by checking the pvalue of average improvement. If $p(IDI or NRI)>pvalue$, then the term is removed. In other words, only model terms that significantly aid in subject classification are kept. The procedure is repeated until no term fulfils the removal criterion.

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.

See Also

bootstrapVarNeRIElimination, backVarElimination, backVarNeRIElimination

Examples

# 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:
	# - A lax p-value
	# - 10 bootstrap loops
	# - Age as a covariate
	# - zIDI as the feature inclusion criterion
	# - First order interactions
	cancerModel <- ReclassificationFRESA.Model(pvalue = 0.1,
	                                           loops = 10,
	                                           covariates = "1 + age",
	                                           Outcome = "pgstat",
	                                           variableList = cancerVarNames,
	                                           data = dataCancer,
	                                           type = "COX",
	                                           timeOutcome = "pgtime",
	                                           selectionType = "zIDI",
	                                           interaction = 2)
	# Remove not significant variables from the previous model:
	# - Using a strict p-value
	# - Excluding the covariate as a candidate for feature removal
	# - Using zIDI as the feature removal criterion
	# - Using 50 bootstrap loops
	reducedCancerModel <- bootstrapVarElimination(object = cancerModel$final.model,
	                                              pvalue = 0.005,
	                                              Outcome = "pgstat",
	                                              data = dataCancer,
	                                              startOffset = 1,
	                                              type = "COX",
	                                              selectionType = "zIDI",
	                                              loops = 50)
	# Shut down the graphics device driver
	dev.off()