backVarElimination_Bin: IDI/NRI-based backwards variable elimination

Description

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

Usage

backVarElimination_Bin(object,
	                   pvalue = 0.05,
	                   Outcome = "Class",
	                   data,
	                   startOffset = 0,
	                   type = c("LOGIT", "LM", "COX"),
	                   selectionType = c("zIDI", "zNRI")
					   )

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

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 getVar.Bin function

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)

at.opt.model

the model before the BH procedure

beforeFSC.formula

the string formula of the model before the BH procedure

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 improvement is selected. The hypothesis: the term adds classification improvement is tested by checking the pvalue of 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.