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help for ^nproc^                                          
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Nonparametric Receiver Operating Curves  
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^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
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        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

See Also
--------

 Manual: [R] lroc
On-line: @lroc@, @rocgraph@ if installed
