Talk:Pre- and post-test probability: Difference between revisions

Revision as of 14:27, 23 February 2011

Latest revision as of 08:53, 8 February 2024

(17 intermediate revisions by 9 users not shown)

Line 1:

{{WikiProject banner shell|class=B|

{{WikiProject Statistics|importance=mid}}

}}

{{Broken anchors|links=

* <nowiki>[[Type I and type II errors#False positive rate|Type I error]]</nowiki> The anchor (#False positive rate) has been [[Special:Diff/539977887|deleted by other users]] before. <!-- {"title":"False positive rate","appear":{"revid":60629361,"parentid":60596745,"timestamp":"2006-06-26T09:29:49Z","removed_section_titles":["False negative","False positive"],"added_section_titles":["False negative vs. false positive","Bayes' theorem","Computers","Computer security","Spam filtering","Malware","Computer database searching","Optical character recognition (OCR)","Security screening","Biometrics","Medical screening","Medical testing","Paranormal investigation","False negative rate","False positive rate","Notes","See also","External links"]},"disappear":{"revid":539977887,"parentid":539386967,"timestamp":"2013-02-24T00:22:56Z","removed_section_titles":["False positive rate","False negative rate"],"added_section_titles":["False positive and false negative rates"]}} -->

* <nowiki>[[Type I and type II errors#False negative rate|Type II error]]</nowiki> The anchor (#False negative rate) has been [[Special:Diff/539977887|deleted by other users]] before. <!-- {"title":"False negative rate","appear":{"revid":60629361,"parentid":60596745,"timestamp":"2006-06-26T09:29:49Z","removed_section_titles":["False negative","False positive"],"added_section_titles":["False negative vs. false positive","Bayes' theorem","Computers","Computer security","Spam filtering","Malware","Computer database searching","Optical character recognition (OCR)","Security screening","Biometrics","Medical screening","Medical testing","Paranormal investigation","False negative rate","False positive rate","Notes","See also","External links"]},"disappear":{"revid":539977887,"parentid":539386967,"timestamp":"2013-02-24T00:22:56Z","removed_section_titles":["False positive rate","False negative rate"],"added_section_titles":["False positive and false negative rates"]}} -->

}}

==Motivation for having own article==

I forked this section from [[Likelihood ratios in diagnostic testing]], partly to provide a common fork som that one and [[positive predictive value]], and partly because so many incoming links (such as positive pre-test probability, negative post-test probability, negative post-test odds etc) cannot feasibly be redirected to a section. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|talk]]) 08:30, 30 January 2011 (UTC)

Line 10 ⟶ 18:

But that can be read directly off of the chart given in the article, in one calculation, by the definition of conditional probability:

:<math> P( Cancer = True | Test = True) = \frac{ P(Cancer = True \andland Test = True)}{P(Test=True)} = \frac{2}{2+8} = 0.10</math>

That seems '''way''' easier than the complicated multi-step process described in the example. So why would you ever do it that way?

In fact, it's easy to prove mathematically. Let's let the following table be true:

{| class="wikitable"

|-

! !! Disease = True !! Disease = False

|-

| Test = Positive || ''a'' || ''b''

|-

| Test = Negative || ''c'' || ''d''

|}

Where ''a,b,c,d'' are probabilities. I.e. ''a+b+c+d=1''. (This is without loss of generality.)

Then, the definitions as given in the article are:

* Sensitivity = <math>\frac{a}{a+c}</math>

* Specificity = <math>\frac{d}{b+d}</math>

And now we can just follow the algorithm of the article:

# Likelihood ratio positive = sensitivity / (1 − specificity) = <math>\frac{a(b+d)}{b(a+c)}</math>

# Pretest probability = <math>a+c</math>

# Pretest odds = pretest prob / (1 - pretest prob) = <math>\frac{a+c}{1-(a+c)} = \frac{a+c}{b+d}</math>

# Positive posttest odds = pretest odds * likelihood ratio positive = <math>\frac{a+c}{b+d}\cdot\frac{a(b+d)}{b(a+c)} = \frac{a}{b}</math>

# Positive posttest probability = positive posttest odds / (1+positive posttest odds) = <math>\frac{a/b}{1+a/b} = \frac{a}{a+b}</math>

Thus we see that it would be '''way''' easier just to calculate the positive predictive value.

Now, all of this is assuming that the pretest probability for the patient in question is the same as the population probability. However, if that is not the case, then the entire chart is invalid. By using the chart you are assuming that the properties of the diagnostic test (i.e. the predictive values, sensitivity, specificity, etc.) are the '''same''' for the population (or the sample group) as they are for the patient in question. There's no reason to think that has to be the case. If we're willing to assume that the ''a+c'' for our patient is different than the sample group, why are we willing to assume that ''a/(a+c)'' is the same?

I just think that perhaps the article should point out some of this.

:I agree your example is more simple. The calculation from likelihood ratio is better only if the pre-test probability is different from the prevalence in the population, but, as you pointed out, that was not the case in the example, and therefore the example is a bit overkill (the reason I took it was that it was easy to copy-paste from [[Positive predictive value]]. I'm now doing a reorganization of the article to hopefully make it more simple. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|talk]]) 19:19, 24 February 2011 (UTC)

==Footnotes added==

I added more footnotes from a reference, as requested by the tag [http://en.wikipedia.org/w/index.php?title=Pre-_and_post-test_probability&action=historysubmit&diff=446947036&oldid=446946032]. The article surely needs more referenced entries, but I don't think it lacks specifically in in-line citations of existing references. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|talk]]) 09:09, 27 August 2011 (UTC)

== Disadvantage of Likelihood ratios ==

I deleted the disadvantage of LR in the table because it is possible to do a calculation of likelihood ratios for tests with continuous values or more than two outcomes which is similar to the calculation for dichotomous outcomes; a separate likelihood ratio is simply calculated for every level of test result and is called interval or stratum specific likelihood ratios.<span style="font-size:x-small;">{{cite journal | doi = 10.1067/mem.2003.274 | author = Brown MD, Reeves MJ. | year = 2003 | title = Evidence-based emergency medicine/skills for evidence-based emergency care. Interval likelihood ratios: another advantage for the evidence-based diagnostician | url = | journal =Ann Emerg Med | volume = 42 | issue = 2| pages = 292-297 | pmid = 12883521 }}</span> [[User:Gcastellanos|Gcastellanos]] ([[User talk:Gcastellanos|talk]]) 10:56, 16 February 2015 (UTC)

:I didn't know that was possible. Thanks for pointing this out {{=)}} I mentioned it in the article too. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|talk]]) 08:16, 18 February 2015 (UTC)

== Subjectivity discussion is confusing and irrelevant ==

The use of the term "subjective" ignores that pre-test probability is derived from studies that are actually pretty straight forward. For example, HIV testing, you have some defined indication for testing and you simply count how many positive results you get, and how many negative. What is subjective about that? The editor using "subjective" misinterprets the subject matter of pretest probability away from the formal term to what "pre-test probability" would mean in colloquial language - what is the probability that my patient has HIV? Or is that all in my mind? [[Special:Contributions/205.203.58.1|205.203.58.1]] ([[User talk:205.203.58.1|talk]]) 20:18, 28 October 2016 (UTC)

That seems '''way''' easier than the complicated 4 step process described in the example. So why would you ever do it that way? <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Quadari|Quadari]] ([[User talk:Quadari|talk]] • [[Special:Contributions/Quadari|contribs]]) 14:26, 23 February 2011 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

:I moved the subjectivity section to the bottom, because, as you say, it is not that relevant. The same can be argued for any kind of [[probability]], but that's rather a discussion about [[Determinism]]. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|talk]]) 05:53, 1 November 2016 (UTC)