nullThe Receiver Operating Characteristic (ROC) CurveThe Receiver Operating Characteristic (ROC) CurveEPP 245
Statistical Analysis of
Laboratory DataBinary ClassificationBinary ClassificationSuppose we have two groups for which each case is a member of one or the other, and that we know the correct classification (“truth”).
Suppose we have a prediction method that produces a single numerical value, and that small values of that number suggest membership in group 1 and large values suggest membership in group 2nullIf we pick a cutpoint t, we can assign any case with a predicted value ≤ t to group 1 and the others to group 2.
For that value of t, we can compute the number correctly assigned to group 2 and the number incorrectly assigned to group 2 (true positives and false positives).
For t small enough, all will be assigned to group 2 and for t large enough all will be assigned to group 1.
The ROC curve is a plot of true positives vs. false positivesnullJuul's IGF data
Description:
The 'juul' data frame has 1339 rows and 6 columns. It contains a
reference sample of the distribution of insulin-like growth factor
(IGF-I), one observation per subject in various ages with the bulk
of the data collected in connection with school physical
examinations.
Variables:
age a numeric vector (years).
menarche a numeric vector. Has menarche occurred (code 1: no, 2:
yes)?
sex a numeric vector (1: boy, 2: girl).
igf1 a numeric vector. Insulin-like growth factor ($mu$g/l).
tanner a numeric vector. Codes 1-5: Stages of puberty a.m. Tanner.
testvol a numeric vector. Testicular volume (ml).
Predicting MenarchePredicting MenarcheSubset Juul data to only females between 8 and 20 years old
Predict menarch from age as a quantitative variable and Tanner score as a qualitative variable using dummy variables
Menarch re-coded to be 0/1null. logistic men1 age tan2 tan3 tan4 tan5
Logistic regression Number of obs = 519
LR chi2(5) = 568.74
Prob > chi2 = 0.0000
Log likelihood = -75.327218 Pseudo R2 = 0.7906
------------------------------------------------------------------------------
men1 | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | 3.944062 .7162327 7.56 0.000 2.762915 5.630151
tan2 | .0444044 .0486937 -2.84 0.005 .0051761 .3809341
tan3 | .1369598 .095596 -2.85 0.004 .0348712 .5379227
tan4 | .6969611 .3898228 -0.65 0.519 .2328715 2.085935
tan5 | 9.169558 7.638664 2.66 0.008 1.791671 46.9287
------------------------------------------------------------------------------
. predict pmen
(option p assumed; Pr(men1))
. predict pmen1, xb
null. histogram pmen
. graph export pmenhist.wmf
. histogram pmen if men1==0, title("Pre-Menarch")
. graph export pmenhist0.wmf
. histogram pmen if men1==1, title("Post-Menarch")
. graph export pmenhist1.wmf
. histogram pmen1
. graph export pmen1hist.wmf
. hist pmen1 if men1==0, title("Pre-Menarche")
. graph export pmen1hist0.wmf
. hist pmen1 if men1==1, title("Post-Menarche")
. graph export pmen1hist1.wmf
. lroc
Logistic model for men1
number of observations = 519
area under ROC curve = 0.9867
. graph export pmenroc.wmf
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