Re: st: Combining ROC curves in one graph

[Charles Lindsey <clindsey@stata.com>]

Kim Peters wrote:
> I have plotted three ROC curves using
>
> roctab x1 y1, graph name(rocgraph1) nodraw
> roctab x2 y2, graph name(rocgraph2) nodraw
> roctab x3 y3, graph name(rocgraph3) nodraw
>
> How can I combine these three roclines into one graph.
>  || or (...) do not seem to work.

All the receiver operating characteristic (ROC) commands in Stata use a
single status variable, with one or more classification variables. You 
can automatically draw ROC curves for different classifiers using the 
same status variable.  A new command, -rocreg- can be used to draw ROC 
curves for different status variables in the same graph.
Kim can use the new command -rocreg- to draw the graph she desires.

Here is a short answer to Kim's question.

You can use -rocreg- to fit several models, create the new variables
containing the false-positive rate and ROC values, and then plot the ROC
curves using -twoway-.

Here is a more detailed answer to Kim's question.

Let's consider an example using the Hanley data, where an individual's
neurological disease status is classified on a single 5-scale rating.

In the code below, we load the data and create a fictional 
disease-status variable, -ndisease-, which zeroes the true status 
variable, -disease-, with probability 2/10.
. set seed 12345671
. webuse hanley, clear
. generate ndisease = disease
. replace ndisease = 0 if runiform() > .8

Now we use -rocreg- to estimate a nonparametric ROC curve of -disease- 
and classification variable -rating-.  We use the -quietly- prefix to 
suppress output, and the -nobootstrap- option to prevent the bootstrap 
calculation of standard errors because we are only interested in the 
estimates of the false-positive rate and ROC value.
. quietly rocreg disease rating, nobootstrap

The ROC and false-positive rate values are saved as variables 
-_roc_rating- and -_fpr_rating-.  We rename the -_roc_rating- and 
-_fpr_rating- variables before fitting the next ROC model, because we 
will need them for the graph.
. rename _roc_rating roc_disease
. rename _fpr_rating fpr_disease

Now we run -rocreg- on the -ndisease- status variable.

. quietly rocreg ndisease rating, nobootstrap

We rename the generated ROC and false-positive rate variables that this
execution of rocreg creates.

. rename _roc_rating roc_ndisease
. rename _fpr_rating fpr_ndisease

Now we will draw the ROC curves with -rating- as a classifier for 
-disease-, and with -rating- as a classifier for -ndisease-.  -twoway 
scatter- is used with the || overlay operator.  Since we are using the 
empirical estimate of the ROC curve, We use the -connect(J)- option 
rather than a simple line connector.
. twoway scatter roc_disease fpr_disease, connect(J) sort || ///
  scatter roc_ndisease fpr_ndisease, connect(J) sort         ///
  legend(label(1 disease) label(2 ndisease))

Kim Peters also wrote:
> Moreover, I would like to do the same thing after rocfit and rocplot:
>
> rocfit x1 y1
> rocplot, confband name(rocfit1) nodraw
> rocfit x2 y2
> rocplot, confband name(rocfit2) nodraw
> rocfit x3 y3
> rocplot, confband name(rocfit3) nodraw
>
> P.S. I don't want to array the separately drawn graphs into one using
> graph combine. I just need one graph that contains all three ROC
> lines.

Kim can use a similar method with -rocreg- and the -probit ml- options 
to get combined ROC curves for the parametric case.
Charles Lindsey,
StataCorp

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