univariateRankVariables: Univariate analysis of features

In FRESA.CAD: Feature Selection Algorithms for Computer Aided Diagnosis

Univariate analysis of features

Description

This function reports the mean and standard deviation for each feature in a model, and ranks them according to a user-specified score. Additionally, it does a Kolmogorov-Smirnov (KS) test on the raw and z-standardized data. It also reports the raw and z-standardized t-test score, the p-value of the Wilcoxon rank-sum test, the integrated discrimination improvement (IDI), the net reclassification improvement (NRI), the net residual improvement (NeRI), and the area under the ROC curve (AUC). Furthermore, it reports the z-value of the variable significance on the fitted model.

Usage

	univariateRankVariables(variableList,
	                        formula,
	                        Outcome,
	                        data, 
	                        categorizationType = c("Raw",
	                                               "Categorical",
	                                               "ZCategorical",
	                                               "RawZCategorical",
	                                               "RawTail",
	                                               "RawZTail",
	                                               "Tail",
	                                               "RawRaw"), 
	                        type = c("LOGIT", "LM", "COX"), 
	                        rankingTest = c("zIDI",
	                                        "zNRI",
	                                        "IDI",
	                                        "NRI",
	                                        "NeRI",
	                                        "Ztest",
	                                        "AUC",
	                                        "CStat",
	                                        "Kendall"), 
	                        cateGroups = c(0.1, 0.9),
	                        raw.dataFrame = NULL,
	                        description = ".",
	                        uniType = c("Binary","Regression"),
	                        FullAnalysis=TRUE,
	                        acovariates = NULL,
	                        timeOutcome = NULL
)

Arguments

variableList	A data frame with the candidate variables to be ranked
formula	An object of class formula with the formula to be fitted
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
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, weighted by the z-score, plus the tails ("RawZTail")
type	Fit type: Logistic ("LOGIT"), linear ("LM"), or Cox proportional hazards ("COX")
rankingTest	Variables will be ranked based on: The z-score of the IDI ("zIDI"), the z-score of the NRI ("zNRI"), the IDI ("IDI"), the NRI ("NRI"), the NeRI ("NeRI"), the z-score of the model fit ("Ztest"), the AUC ("AUC"), the Somers' rank correlation ("Cstat"), or the Kendall rank correlation ("Kendall")
cateGroups	A vector of percentiles to be used for the categorization procedure
raw.dataFrame	A data frame similar to data, but with unadjusted data, used to get the means and variances of the unadjusted data
description	The name of the column in variableList that stores the variable description
uniType	Type of univariate analysis: Binary classification ("Binary") or regression ("Regression")
FullAnalysis	If FALSE it will only order the features according to its z-statistics of the linear model
acovariates	the list of covariates
timeOutcome	the name of the Time to event feature

Details

This function will create valid dummy categorical variables if, and only if, data has been z-standardized. The p-values provided in cateGroups will be converted to its corresponding z-score, which will then be used to create the categories. If non z-standardized data were to be used, the categorization analysis would return wrong results.

Value

A sorted data frame. In the case of a binary classification analysis, the data frame will have the following columns:

Name	Name of the raw variable or of the dummy variable if the data has been categorized
parent	Name of the raw variable from which the dummy variable was created
descrip	Description of the parent variable, as defined in description
cohortMean	Mean value of the variable
cohortStd	Standard deviation of the variable
cohortKSD	D statistic of the KS test when comparing a normal distribution and the distribution of the variable
cohortKSP	Associated p-value to the cohortKSD
caseMean	Mean value of cases (subjects with Outcome equal to 1)
caseStd	Standard deviation of cases
caseKSD	D statistic of the KS test when comparing a normal distribution and the distribution of the variable only for cases
caseKSP	Associated p-value to the caseKSD
caseZKSD	D statistic of the KS test when comparing a normal distribution and the distribution of the z-standardized variable only for cases
caseZKSP	Associated p-value to the caseZKSD
controlMean	Mean value of controls (subjects with Outcome equal to 0)
controlStd	Standard deviation of controls
controlKSD	D statistic of the KS test when comparing a normal distribution and the distribution of the variable only for controls
controlKSP	Associated p-value to the controlsKSD
controlZKSD	D statistic of the KS test when comparing a normal distribution and the distribution of the z-standardized variable only for controls
controlZKSP	Associated p-value to the controlsZKSD
t.Rawvalue	Normal inverse p-value (z-value) of the t-test performed on raw.dataFrame
t.Zvalue	z-value of the t-test performed on data
wilcox.Zvalue	z-value of the Wilcoxon rank-sum test performed on data
ZGLM	z-value returned by the lm, glm, or coxph functions for the z-standardized variable
zNRI	z-value returned by the improveProb function (Hmisc package) when evaluating the NRI
zIDI	z-value returned by the improveProb function (Hmisc package) when evaluating the IDI
zNeRI	z-value returned by the improvedResiduals function when evaluating the NeRI
ROCAUC	Area under the ROC curve returned by the roc function (pROC package)
cStatCorr	c index of Somers' rank correlation returned by the rcorr.cens function (Hmisc package)
NRI	NRI returned by the improveProb function (Hmisc package)
IDI	IDI returned by the improveProb function (Hmisc package)
NeRI	NeRI returned by the improvedResiduals function
kendall.r	Kendall \tau rank correlation coefficient between the variable and the binary outcome
kendall.p	Associated p-value to the kendall.r
TstudentRes.p	p-value of the improvement in residuals, as evaluated by the paired t-test
WilcoxRes.p	p-value of the improvement in residuals, as evaluated by the paired Wilcoxon rank-sum test
FRes.p	p-value of the improvement in residual variance, as evaluated by the F-test
caseN_Z_Low_Tail	Number of cases in the low tail
caseN_Z_Hi_Tail	Number of cases in the top tail
controlN_Z_Low_Tail	Number of controls in the low tail
controlN_Z_Hi_Tail	Number of controls in the top tail

In the case of regression analysis, the data frame will have the following columns:

Name	Name of the raw variable or of the dummy variable if the data has been categorized
parent	Name of the raw variable from which the dummy variable was created
descrip	Description of the parent variable, as defined in description
cohortMean	Mean value of the variable
cohortStd	Standard deviation of the variable
cohortKSD	D statistic of the KS test when comparing a normal distribution and the distribution of the variable
cohortKSP	Associated p-value to the cohortKSP
cohortZKSD	D statistic of the KS test when comparing a normal distribution and the distribution of the z-standardized variable
cohortZKSP	Associated p-value to the cohortZKSD
ZGLM	z-value returned by the glm or Cox procedure for the z-standardized variable
zNRI	z-value returned by the improveProb function (Hmisc package) when evaluating the NRI
NeRI	NeRI returned by the improvedResiduals function
cStatCorr	c index of Somers' rank correlation returned by the rcorr.cens function (Hmisc package)
spearman.r	Spearman \rho rank correlation coefficient between the variable and the outcome
pearson.r	Pearson r product-moment correlation coefficient between the variable and the outcome
kendall.r	Kendall \tau rank correlation coefficient between the variable and the outcome
kendall.p	Associated p-value to the kendall.r
TstudentRes.p	p-value of the improvement in residuals, as evaluated by the paired t-test
WilcoxRes.p	p-value of the improvement in residuals, as evaluated by the paired Wilcoxon rank-sum test
FRes.p	p-value of the improvement in residual variance, as evaluated by the F-test

Author(s)

Jose G. Tamez-Pena

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.

FRESA.CAD documentation built on Nov. 25, 2023, 1:07 a.m.