.- help for ^nproc^ .-

Nonparametric Receiver Operating Curves ---------------------------------------

^nproc^ varlist, ^by^(grouping variable) [^file^(file name) ^nog^raph ^pause^]

Description -----------

^nproc^ calculates nonparametric AUCs and standard errors for ROC curves for the varlist. If more than 2 curves are requested, a chi-square test for the difference between the first and subsequent curves is calculated. The default graph option displays the graph of each variable as the statistics are being calculated. In addition, the default graph option saves sensitivity and specificity data, AUCs, standard errors, and Chi-square and p-value data to an output file for subsequent analysis by the companion graph program, ^rocgraph^. While graphs are being displayed by ^nproc^ and statistics calculated, graphs may be selected and printed. ^rocgraph^ also displays summary statistics. ROC analysis is a method of measuring and comparing the accuracy of one or more variables at predicting whether each observation is a member of one of two groups/categories. The ROC curve plots the Sensitivity (True Positive rate) against 1-Specificity (False Positive rate). The larger the Area Under the ROC Curve(AUC) , the better the variable is at predicting group membership. This command uses the methodology of DeLong (1988) and Bamber (1975). The AUC of the empirical ROC curve is equivalent to the Mann-Whitney two-sample U-statistic. Therefore the Standard Error of an AUC and the covariance between two correlated AUCs can be calculated using the SE and covariances of the Mann-Whitney U-statistics for the variable being analysed. A Chi-square test is then used to test if two AUCs are significantly different. If the p-value of the Chi-square statistic is small then conclude that the AUCs are significantly different. These methods do not require any distributional assumptions or numerical constraints on any of the variables.

Options -------

^by^(varname) is required. It is the grouping variable, It can be coded either as 0/1 or 1/2. ^file^(filename) is the file to which the sensitivity/specificity data and summary statistics will be saved. The file is saved as filename.dta. You will usually want to enable this option because it allows manipulation of the data and graphs. If ^nograph^ is selected ^file^(filename) will be ignored. ^nog^raph stops the displaying of graphs and saving of data. ^pause^ turns on Stata's -more- command.

Examples --------

-nproc mpg weight hd turn price,by(foreign) file(autoroc) pause- Nonparametric Receiver Operating Curves (ROC) Grouping variable: foreign Positives 22 negatives 52 The AUC of the empirical ROC curve for mpg =.73 The Standard Error of the AUC=.065 Grouping variable: foreign Positives 22 negatives 52 The AUC of the empirical ROC curve for weight =.88 The Standard Error of the AUC=.04 Chisq statistic for the difference in AUCs = 6.13, p=.013 Grouping variable: foreign Positives 22 negatives 52 The AUC of the empirical ROC curve for hdroom =.69 The Standard Error of the AUC=.057 Chisq statistic for the difference in AUCs = .34, p=.558 Grouping variable: foreign Positives 22 negatives 52 The AUC of the empirical ROC curve for turn =.89 The Standard Error of the AUC=.037 Chisq statistic for the difference in AUCs = 4.58, p=.032 Grouping variable: foreign Positives 22 negatives 52 The AUC of the empirical ROC curve for price =.58 The Standard Error of the AUC=.072 Chisq statistic for the difference in AUCs = 1.32, p=.25 -nproc mpg weight hd turn price,by(foreign) nog pause-

Author ------ Statistical section: Phillip Price, Phillip.Price@@nrma.com.au Graphics and interface: Fred Wolfe, fwolfe@@southwind.net

References ----------

DeLong ER et al, (1988) "Comparing the Areas Under Two or more Correlated Receiver Operating Characteristic Curves: A Nonparametric approach" Biometrics. 44,837-845

Bamber, D (1975) "The Area Above the Ordinal Dominance Graph and the area below the receiver operating characteristic graph" Journal of Mathematical Psychology, 12,387-415