Greg Snow wrote:
Actually, somewhat counterintuitively, ppv tends to me more affected by
specificity and npv by sensitivity. You can see this from the function
SensSpec.demo in the TeachingDemos package (also see the corresponding example
on the help page for tkexamp (same package)).
I don't think that Frank is saying that Sensitivity and Specificity are not
related to ppv and npv and that they don't measure what is claimed. I think
his argument is more based on the fact that sens, spec, ppv, and npv are all
based on grouping the predicted values from the logistic regression into 2
groups and any time you categorize something that is not categorical, you lose
information.
Imagine 2 models (model 1 and model 2) from which we use 50% as the cutt-off.
Model 1 produces predicted probabilities in the range of 0.47 - 0.54 and model
2 produces most of its predicted probabilities in either 0.9-0.98 or 0.01-0.09
with only a few between those 2 ranges, but both agree on which side of 0.5 the
predicted probabilities are. Based on Sensitivity and Specificity, these 2
models are equivalent, but I certainly want my doctor using model 2.
Or imagine that you go to the doctor and are given a set of tests, the test
results are put into the logistic model and the doctor sees that you have a 51%
chance of having disease A, would you want the doctor to treat you the same
(without further testing) as the patient who had a predicted value of 97%? and
what if you had taken a couple more deep breaths just before having your blood
pressure measured and insted had a predicted probability of 49%, would you want
to be treated the same as the patient with a predicted probability of 1%?
I would hope that a doctor seeing a predicted probability of 51% or 49% would
do additional testing. But if we focus on only sens and spec, then 51% is the
same as 100% and 49% is the same as 0%. I think Frank's issue is with throwing
out the information contained in the actual predicted probabilities. Judge the
model based on how the predicted probabilities match what is observed rather
than on a dicotimization of them.
One more analogy, if you have a coin that comes up heads 60% of the time, the
probability that best predicts future tosses is to predict heads 100% of the
time, but that does not describe the true state of nature of 60%. Some of the
common measures used are not optimal for describing the true state of nature,
if you are more interested in the true state of nature than in a different
question, don't use these measures.
Well put Greg. That was a large part of where I was coming from. The
other point is that when you compute probabilities that are in backwards
causal order you have to work hard to undo the damage using Bayes' rule.
Starting with forwards probabilities things are much simpler and the
result is probabilities of actual interest to patients and physicians.
Frank
________________________________________
From: [EMAIL PROTECTED] [EMAIL PROTECTED] On Behalf Of John Sorkin [EMAIL
PROTECTED]
Sent: Monday, October 13, 2008 4:14 PM
To: Ph.D. Robert W. Baer; Frank E Harrell Jr
Cc: r-help@r-project.org; [EMAIL PROTECTED]; [EMAIL PROTECTED]
Subject: Re: [R] Fw: Logistic regresion - Interpreting (SENS) and (SPEC)
Of course Prof Baer is correct the positive predictive value (PPV) and the
negative predictive values (NPV) serve the function of providing conditional
post-test probabilities
PPV: Post-test probability of disease given a positive test
NPV: Post-test probability of no disease given a negative test.
Further, PPV is a function of sensitivity (for a given specificity in a
population with a given disease prevalence), the higher the sensitivity almost
always the greater the PPV (it can by unchanged, but I don't believe it can be
lower) and as
NPV is a function of specificity (for a given sensitivity in a
population with a given disease prevelance), the higher the specificity almost
always the greater the NPV (it can by unchanged, but I don't believe it can be
lower) .
Thus using Prof Harrell's suggestion to use the test that move a pre-test
probability a great deal in one or both directions, the test to choose is the
one with largest sensitivity and or specificity, and thus
sensitivity and specificity are, I believe is a good summary measures of the
"quality" of a clinical test.
Finally I think Prof Harrell's observation that sensitivity and specificity
change quite a bit, and mathematically must change if the disease is not
all-or-nothing while true is a degenerate case of little practical importance.
John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
"Robert W. Baer, Ph.D." <[EMAIL PROTECTED]> 10/13/2008 4:41 PM >>>
----- Original Message -----
From: "Frank E Harrell Jr" <[EMAIL PROTECTED]>
To: "John Sorkin" <[EMAIL PROTECTED]>
Cc: <r-help@r-project.org>; <[EMAIL PROTECTED]>;
<[EMAIL PROTECTED]>
Sent: Monday, October 13, 2008 2:09 PM
Subject: Re: [R] Fw: Logistic regresion - Interpreting (SENS) and (SPEC)
John Sorkin wrote:
Frank,
Perhaps I was not clear in my previous Email message. Sensitivity and
specificity do tell us about the quality of a test in that given two
tests the one with higher sensitivity will be better at identifying
subjects who have a disease in a pool who have a disease, and the more
sensitive test will be better at identifying subjects who do not have a
disease in a pool of people who do not have a disease. It is true that
positive predictive and negative predictive values are of greater utility
to a clinician, but as you know these two measures are functions of
sensitivity, specificity and disease prevalence. All other things being
equal, given two tests one would select the one with greater sensitivity
and specificity so in a sense they do measure the "quality" of a clinical
test - but not, as I tried to explain the quality of a statistical model.
That is not very relevant John. It is a function of all those things
because those quantities are all deficient.
I would select the test that can move the pre-test probability a great
deal in one or both directions.
Of course, this quantity is known as a likelihood ratio and is a function of
sensitivity and specificity. For 2 x 2 data one often speaks of postive
likelihood ratio and negative likelihood ratio, but for multi-row
contingency table one can define likelihood ratios for a series of cut-off
points. This has become a popular approach in evidence-based medicine when
diagnostic tests have continuous rather than binary outputs.
You are of course correct that sensitivity and specificity are not truly
"inherent" characteristics of a test as their values may change from
population-to-population, but paretically speaking, they don't change all
that much, certainly not as much as positive and negative predictive
values.
They change quite a bit, and mathematically must change if the disease is
not all-or-nothing.
I guess we will disagree about the utility of sensitivity and specificity
as simplifying concepts.
Thank you as always for your clear thoughts and stimulating comments.
And thanks for yours John.
Frank
John
among those subjects with a disease and the one with greater specificity
will be better at indentifying John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
Frank E Harrell Jr <[EMAIL PROTECTED]> 10/13/2008 2:35 PM >>>
John Sorkin wrote:
Jumping into a thread can be like jumping into a den of lions but here
goes . . .
Sensitivity and specificity are not designed to determine the quality of
a fit (i.e. if your model is good), but rather are characteristics of a
test. A test that has high sensitivity will properly identify a large
portion of people with a disease (or a characteristic) of interest. A
test with high specificity will properly identify large proportion of
people without a disease (or characteristic) of interest. Sensitivity
and specificity inform the end user about the "quality" of a test. Other
metrics have been designed to determine the quality of the fit, none
that I know of are completely satisfactory. The pseudo R squared is one
such measure.
For a given diagnostic test (or classification scheme), different
cut-off points for identifying subject who have disease can be examined
to see how they influence sensitivity and 1-specificity using ROC
curves.
I await the flames that will surely come my way
John
John this has been much debated but I fail to see how backwards
probabilities are that helpful in judging the usefulness of a test. Why
not condition on what we know (the test result and other baseline
variables) and quit conditioning on what we are trying to find out
(disease status)? The data collected in most studies (other than
case-control) allow one to use logistic modeling with the correct time
order.
Furthermore, sensitivity and specificity are not constants but vary with
subjects' characteristics. So they are not even useful as simplifying
concepts.
Frank
John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
Frank E Harrell Jr <[EMAIL PROTECTED]> 10/13/2008 12:27 PM >>>
Maithili Shiva wrote:
Dear Mr Peter Dalgaard and Mr Dieter Menne,
I sincerely thank you for helping me out with my problem. The thing is
taht I already have calculated SENS = Gg / (Gg + Bg) = 89.97%
and SPEC = Bb / (Bb + Gb) = 74.38%.
Now I have values of SENS and SPEC, which are absolute in nature. My
question was how do I interpret these absolue values. How does these
values help me to find out wheher my model is good.
With regards
Ms Maithili Shiva
I can't understand why you are interested in probabilities that are in
backwards time order.
Frank
________________________________________________________________________
Subject: [R] Logistic regresion - Interpreting (SENS) and (SPEC)
To: r-help@r-project.org Date: Friday, October 10, 2008, 5:54 AM
Hi
Hi I am working on credit scoring model using logistic
regression. I havd main sample of 42500 clentes and based on
their status as regards to defaulted / non - defaulted, I
have genereted the probability of default.
I have a hold out sample of 5000 clients. I have calculated
(1) No of correctly classified goods Gg, (2) No of correcly
classified Bads Bg and also (3) number of wrongly classified
bads (Gb) and (4) number of wrongly classified goods (Bg).
My prolem is how to interpret these results? What I have
arrived at are the absolute figures.
--
Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University
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