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{{Short description|Probabilities of the presence of a condition}}
{{Use dmy dates|date=
'''Pre-test probability''' and '''post-test probability''' (alternatively spelled pretest and posttest probability) are the
Test, in this sense, can refer to any [[medical test]] (but usually in the sense of diagnostic tests), and in a broad sense also including questions and even assumptions (such as assuming that the target individual is a female or male). The ability to make a difference between pre- and post-test probabilities of various conditions is a major factor in the [[
The subjectivity of the probabilities is based on the fact that, in reality, an individual either has the condition or not (with the probability always being either 0% or 100%), so pre- and post-test probabilities for individuals can rather be regarded as psychological phenomena in the minds of those involved in the [[diagnostics]] at hand.▼
▲Test, in this sense, can refer to any [[medical test]] (but usually in the sense of diagnostic tests), and in a broad sense also including questions and even assumptions (such as assuming that the target individual is a female or male). The ability to make a difference between pre- and post-test probabilities of various conditions is a major factor in the [[Medical_test#Indications|indication of medical tests]].
==Pre-test probability==
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==Estimation of post-test probability==
In clinical practice, post-test probabilities are often just
In reality, however, the subjective probability of the presence of a condition is never exactly 0 or 100%. Yet, there are several systematic methods to estimate that probability. Such methods are usually based on previously having performed the test on a [[reference group]] in which the presence or absence on the condition is known (or at least estimated by another test that is considered highly accurate, such as by "[[Gold standard (test)|Gold standard]]"), in order to establish data of test performance. These data are subsequently used to interpret the test result of any individual tested by the method. An alternative or complement to ''reference group''-based methods is comparing a test result to a previous test on the same individual, which is more common in tests for [[monitoring (medicine)|monitoring]].
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The most important systematic ''reference group''-based methods to estimate post-test probability includes the ones summarized and compared in the following table, and further described in individual sections below.
{|class="wikitable"
! Method !! Establishment of performance data !! Method of individual interpretation !! Ability to accurately interpret subsequent tests !! Additional advantages
|-
! By [[predictive value]]s
| Direct quotients from reference group ||<span style="color:DarkGreen;">Most straightforward: Predictive value equals probability</span> ||<span style="color:DarkRed;"> Usually low: Separate reference group required for every subsequent pre-test state</span> ||<span style="color:DarkGreen;"> Available both for [[binary classification|binary]] and [[Continuity (mathematics)|continuous]] values
|-
! By [[Likelihood
| Derived from [[sensitivity and specificity]] || Post-test odds given by multiplying pretest odds with the ratio ||<span style="color:DarkGreen;"> Theoretically limitless</span> ||<span style="color:DarkGreen;"> Pre-test state (and thus the pre-test probability) does not have to be same as in reference group
|-
! By [[relative risk]]
| Quotient of risk among exposed and risk among unexposed || Pre-test probability multiplied by the relative risk ||<span style="color:DarkRed;"> Low, unless subsequent relative risks are derived from same [[multivariate regression analysis]]</span> ||<span style="color:DarkGreen;"> Relatively intuitive to use
|-
! By [[diagnostic criteria]] and [[clinical prediction rules]]
| Variable, <span style="color:DarkRed;">but usually most tedious</span> || Variable ||<span style="color:DarkGreen;"> Usually excellent for all test included in criteria</span> ||<span style="color:DarkGreen;"> Usually most preferable if available
|}
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| rowspan="2" |
|-
| style="background: #ddffdd;" |'''''Positive'''''
| style="background: #ddffdd;" |'''''Negative'''''
|-
| rowspan="2" style="background: #ffdddd;"| '''Test<br>outcome'''
| style="background: #ffdddd;"|'''''Positive'''''
| style="background: #eeeeff;"| <span style="color:#007700;"> '''True Positive'''</span>
| <span style="color:#770000;"> '''False Positive'''<BR>([[
| <span style="color:#770077;"> → [[Positive predictive value]]</span>
|-
| style="background: #ffdddd;"|'''''Negative'''''
| style="background: #eeeeff;"|<span style="color:#770000;"> '''False Negative'''<BR>([[
| <span style="color:#007700;"> '''True Negative'''</span>
| <span style="color:#770077;"> → [[Negative predictive value]]</span>
|-
| colspan="2" |
| style="background: #eeeeff;" | <span style="color:#770077;"> ↓<br>[[Sensitivity and specificity|Sensitivity]]</span>
| <span style="color:#770077;"> ↓<br>[[Sensitivity and specificity|Specificity]]</span>
| <span style="color:#770077;"> ↘<br>[[Accuracy and precision#In binary classification|Accuracy]]</span>
|}
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The post-test probability of disease given a negative result is calculated as:
Negative posttest probability =
The validity of the equations above also depend on that the sample from the population does not have substantial [[sampling bias]] that make the groups of those who have the condition and those who do not substantially disproportionate from corresponding prevalence and "non-prevalence" in the population. In effect, the equations above are not valid with merely a [[case-control study]] that separately collects one group with the condition and one group without it.
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In these cases, the ''prevalence'' in the reference group is not completely accurate in representing the ''pre-test probability'' of the individual, and, consequently, the ''predictive value'' (whether ''positive'' or ''negative'') is not completely accurate in representing the ''post-test probability'' of the individual of having the target condition.
In these cases, a posttest probability can be estimated more accurately by using a [[Likelihood
Estimation of post-test probability from pre-test probability and likelihood ratio goes as follows:<ref name=cebm>[http://www.cebm.net/index.aspx?o=1043 Likelihood Ratios] {{webarchive|url=https://web.archive.org/web/20101222032115/http://www.cebm.net/index.aspx?o=1043 |date=22 December 2010 }}, from CEBM (Centre for Evidence-Based Medicine). Page last edited: 1 February 2009. When used in examples, the general formulas are taken from reference, while example numbers are different</ref>
*Pretest odds =
*Posttest odds = Pretest odds * Likelihood ratio
In equation above, ''positive post-test probability'' is calculated using the ''likelihood ratio positive'', and the ''negative post-test probability'' is calculated using the ''likelihood ratio negative''.
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*Posttest probability = Posttest odds / (Posttest odds + 1)
[[File:Fagan nomogram.svg|thumb|''Fagan nomogram''<ref>Parameters taken from [http://ard.bmj.com/content/65/10/1301/F4.large.jpg image] in: {{cite journal |
The relation can also be estimated by a so-called ''Fagan nomogram'' (shown at right) by making a straight line from the point of the given ''pre-test probability'' to the given ''likelihood ratio'' in their scales, which, in turn, estimates the ''post-test probability'' at the point where that straight line crosses its scale.
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File:Pre- and post-test probabilities for various likelihood ratios.png|Relation between pre-and post-test probabilities for various likelihood ratio positives (upper left half) and various likelihood ratio negatives (lower right half).
</gallery>
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. For this purpose, a separate likelihood ratio is calculated for every level of test result and is called interval or stratum specific likelihood ratios.<ref>{{cite journal | doi = 10.1067/mem.2003.274 |vauthors=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 | journal =Ann Emerg Med | volume = 42 | issue = 2| pages = 292–297 | pmid = 12883521 | doi-access = free }}</ref>
====Example====
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| style="background: #ddffdd;" |'''''Negative'''''
|-
| rowspan="2" style="background: #ffdddd;"| '''Fecal<br>occult<br>blood<br>screen<br>test<br>outcome'''
| style="background: #ffdddd;"|'''''Positive'''''
| style="background: #eeeeff;"| <span style="color:#007700;"> '''TP = 2'''</span>
| <span style="color:#770000;"> '''FP = 18'''</span>
| → Positive predictive value<BR>= TP / (TP + FP)<BR>= 2 / (2 + 18)<BR>= 2 / 20<BR>'''= 10%'''
|-
| style="background: #ffdddd;"|'''''Negative'''''
| style="background: #eeeeff;"|<span style="color:#770000;"> '''FN = 1'''</span>
| <span style="color:#007700;"> '''TN = 182'''</span>
| → Negative predictive value<BR>= TN / (FN + TN)<BR>= 182 / (1 + 182)<BR>= 182 / 183<BR>'''≈ 99.5%'''
|-
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| style="background: #eeeeff;" | ↓<BR>Sensitivity<BR>= TP / (TP + FN)<BR>= 2 / (2 + 1)<BR>= 2 / 3<BR>'''≈ 66.67%'''
| ↓<BR>Specificity<BR>= TN / (FP + TN)<BR>= 182 / (18 + 182)<BR>= 182 / 200<BR>'''= 91%'''
| ↘<BR>Accuracy<BR>= (TP + TN) / Total<BR>= (2 + 182) / 203<BR>= 184 / 203<BR>'''= 90.64%'''
|}
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*Positive posttest probability = 0.229 / (0.229 + 1) = 0.186 or 18.6%
Thus, that individual has a post-test probability (or "post-test risk") of 18.6% of having bowel cancer.
The [[prevalence]] in the population sample is calculated to be:
*Prevalence = (2 + 1) / 203 = 0.0148 or 1.48%
The individual's pre-test probability was more than twice
====Specific sources of inaccuracy====
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=====Interference with test=====
''Post-test probability'', as estimated from the ''pre-test probability'' with ''likelihood ratio'', should be handled with caution in individuals with other determinants (such as risk factors) than the general population, as well as in individuals that have undergone previous tests, because such determinants or tests may also influence the test itself in unpredictive ways, still causing inaccurate results. An example with the risk factor of [[obesity]] is that additional abdominal fat can make it difficult to palpate abdominal organs and decrease the resolution of [[abdominal ultrasonography]], and similarly, remnant [[barium contrast]] from a previous radiography can interfere with subsequent abdominal examinations,<ref>[
=====Overlap of tests=====
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=====Methods to overcome inaccuracy=====
To avoid such sources of inaccuracy by using likelihood ratios, the optimal method would be to gather a large reference group of equivalent individuals, in order to establish separate ''predictive values'' for use of the test in such individuals. However, with more knowledge of an individual's medical history, physical examination and previous test etc. that individual becomes more
Another method to overcome such inaccuracies is by evaluating the test result in the context of diagnostic
===By relative risk===
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If only one risk factor of an individual is taken into account, the post-test probability can be estimated by multiplying the relative risk with the risk in the control group. The control group usually represents the unexposed population, but if a very low fraction of the population is exposed, then the prevalence in the general population can often be assumed equal to the prevalence in the control group. In such cases, the post-test probability can be estimated by multiplying the relative risk with the risk in the general population.
For example, the [[Incidence (epidemiology)|incidence]] of [[breast cancer]] in a woman in the United Kingdom at age 55 to 59 is estimated at
--><ref name="acs bc facts 2005-6">{{cite web |author=ACS |year=2005 |title=Breast Cancer Facts & Figures 2005–2006 |url=http://www.cancer.org/downloads/STT/CAFF2005BrFacspdf2005.pdf |
====Multiple risk factors====
Theoretically, the total risk in the presence of multiple risk factors can be
*Relative risks are affected by the prevalence of the condition in the reference group (in contrast to likelihood ratios, which are not), and this issue results in that the validity of post-test probabilities become less valid with increasing difference between the prevalence in the reference group and the pre-test probability for any individual. Any known risk factor or previous test of an individual almost always confers such a difference, decreasing the validity of using relative risks in estimating the total effect of multiple risk factors or tests. Most physicians do not appropriately take such differences in prevalence into account when interpreting test results, which may cause unnecessary testing and diagnostic errors.<ref>{{
*A separate source of inaccuracy of multiplying several relative risks, considering only positive tests, is that it tends to overestimate the total risk as compared to using likelihood ratios. This overestimation can be explained by the inability of the method to compensate for the fact that the total risk cannot be more than 100%. This overestimation is rather small for small risks, but becomes higher for higher values. For example, the risk of developing breast cancer at an age younger than 40 years in women in the United Kingdom can be estimated at
The (latter mentioned) effect of overestimation can be compensated for by converting risks to odds, and relative risks to [[odds ratio]]s. However, this does not compensate for (former mentioned) effect of any difference between pre-test probability of an individual and the prevalence in the reference group.
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===By diagnostic criteria and clinical prediction rules===
Most major diseases have established [[diagnostic criteria]] and/or [[clinical prediction rule]]s. The establishment of diagnostic criteria or clinical prediction rules consists of a comprehensive evaluation of many tests that are considered important in estimating the probability of a condition of interest, sometimes also including how to divide it into subgroups, and when and how to treat the condition. Such establishment can include usage of predictive values, likelihood ratios as well as relative risks.
For example, the [[
Also, there are risk assessment tools for estimating the combined risk of several risk factors, such as the
Still, an experienced physician may estimate the post-test probability (and the actions it motivates) by a broad consideration including criteria and rules in addition to other methods described previously, including both individual risk factors and the performances of tests that have been carried out.
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A major factor for such an absolute difference is the power of the test itself, such as can be described in terms of, for example, sensitivity and specificity or likelihood ratio. Another factor is the pre-test probability, with a lower pre-test probability resulting in a lower absolute difference, with the consequence that even very powerful tests achieve a low absolute difference for very unlikely conditions in an individual (such as [[rare disease]]s in the absence of any other indicating sign), but on the other hand, that even tests with low power can make a great difference for highly suspected conditions.
The probabilities in this sense may also need to be considered in context of conditions that are not primary targets of the test, such as [[
The absolute difference can be put in relation to the benefit for an individual that a [[medical test]] achieves, such as can roughly be estimated as:
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*''b<sub>n</sub>'' is the net benefit of performing a medical test
*''Λp'' is the absolute difference between pre- and posttest probability of conditions (such as diseases) that the test is expected to achieve.
*''r<sub>i</sub>'' is the rate of how much ''probability differences'' are expected to result in ''changes in interventions'' (such as a change from "no treatment" to "administration of low-dose medical treatment").
*''b<sub>i</sub>'' is the benefit of ''changes in interventions'' for the individual
*''h<sub>i</sub>'' is the harm of ''changes in interventions'' for the individual, such as [[side
*''h<sub>t</sub>'' is the harm caused by the test itself
In this formula, what constitutes benefit or harm largely varies by [[Value (personal and cultural)|personal and cultural values]], but general conclusions can still be drawn. For example, if the only expected effect of a medical test is to make one disease more likely than another, but the two diseases have the same treatment (or neither can be treated), then ''r<sub>i</sub>'' = 0 and the test is essentially without any benefit for the individual.
Additional factors that influence a decision whether a medical test should be performed or not include: cost of the test, availability of additional tests, potential interference with subsequent test (such as an [[abdominal palpation]] potentially inducing intestinal activity whose sounds interfere with a subsequent [[abdominal auscultation]]), time taken for the test or other practical or administrative aspects. Also, even if not beneficial for the individual being tested, the results may be useful for the establishment of statistics in order to improve health care for other individuals.
==Subjectivity==
▲
==See also==
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