FRESA.CAD (version 2.0.2)

univariateRankVariables: 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"), 
	                        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)

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

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

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

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

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.

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

# 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)
	# Rank the variables:
	# - Analyzing the raw data
	# - According to the zIDI
	rankedDataCancer <- univariateRankVariables(variableList = cancerVarNames,
	                                            formula = "Surv(pgtime, pgstat) ~ 1",
	                                            Outcome = "pgstat",
	                                            data = dataCancer, 
	                                            categorizationType = "Raw", 
	                                            type = "COX", 
	                                            rankingTest = "zIDI",
	                                            description = "Description")
	# Shut down the graphics device driver
	dev.off()