Pre- and post-test probability: Difference between revisions

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{{Short description|Probabilities of the presence of a condition}}

{{Use dmy dates|date=AugustApril 20132024}}

'''Pre-test probability''' and '''post-test probability''' (alternatively spelled pretest and posttest probability) are the [[probabilities]] of the presence of a condition (such as a [[disease]]) before and after a [[diagnostic test]], respectively. ''Post-test probability'', in turn, can be ''positive'' or ''negative'', depending on whether the test falls out as a [[positive test|positive test or a negative test]], respectively. In some cases, it is used for the probability of developing the condition of interest in the future.

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==Estimation of post-test probability==

In clinical practice, post-test probabilities are often just roughly estimated or even guessed. This is usually acceptable in the finding of a ''[[pathognomonic]]'' sign or symptom, in which case it is almost certain that the target condition is present; or in the absence of finding a ''[[sine qua non]]'' sign or symptom, in which case it is almost certain that the target condition is absent.

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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| 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_precisionAccuracy and precision#In_binary_classificationIn binary classification|Accuracy]]</span>

|}

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The post-test probability of disease given a negative result is calculated as:

Negative posttest probability = False1 - (True negatives / (False negatives + True negatives))

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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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 = (Pretest probability / (1 - Pretest probability)

*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 |vauthors=Zhang W, Doherty M, Pascual E, etal |title=EULAR evidence based recommendations for gout. Part I: Diagnosis. Report of a task force of the Standing Committee for International Clinical Studies Including Therapeutics (ESCISIT) |journal=Ann. Rheum. Dis. |volume=65 |issue=10 |pages=1301–11 |date=October 2006 |pmid=16707533 |pmc=1798330 |doi=10.1136/ard.2006.055251 |url=http://ard.bmj.com/content/65/10/1301.abstract}}</ref>]]

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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</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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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 the onethat of the population sample, although the individual's post-test probability was less than twice the onethat of the population sample (which is estimated by the positive predictive value of the test of 10%), opposite to what would result by a less accurate method of simply multiplying relative risks.

====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>[https://books.google.com/books?id=CQuBkXDspBkC&pg=PA750 Page 750] (Chapter 10) in: {{cite book |author1=Dunning, Marshall Barnett |author2=Fischbach, Frances Talaska |title=A manual of laboratory and diagnostic tests [electronic resource] |publisher=Wolters Kluwer Health/Lippincott Williams & Wilkins |___location=Philadelphia |year=2009 |isbn=978-0-7817-7194-38 }}</ref> in effect decreasing the sensitivities and specificities of such subsequent tests. On the other hand, the effect of interference can potentially improve the efficacy of subsequent tests as compared to usage in the reference group, such as some abdominal examinations being easier when performed on underweight people.

=====Overlap of tests=====

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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 approximately 280 cases per 100.000 per year,<ref name=cancerresearchuk>[http://info.cancerresearchuk.org/prod_consump/groups/cr_common/@nre/@sta/documents/generalcontent/cases_crude_breast1_xls.xls Excel chart] for ''Figure 1.1: Breast Cancer (C50), Average Number of New Cases per Year and Age-Specific Incidence Rates, UK, 2006-2008'' at [http://info.cancerresearchuk.org/cancerstats/types/breast/incidence/ Breast cancer -– UK incidence statistics] {{webarchive|url=https://web.archive.org/web/20120514135436/http://info.cancerresearchuk.org/cancerstats/types/breast/incidence/ |date=14 May 2012 }} at Cancer Research UK. Section updated 18/07/11 July 2011.</ref> and the risk factor of having been exposed to high-dose [[ionizing radiation]] to the chest (for example, as treatments for other cancers) confers a relative risk of breast cancer between 2.1 and 4.0,<!--

--><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 |format=PDF|access-date=2007-04-26 |archive-url = https://web.archive.org/web/20070613192148/http://www.cancer.org/downloads/STT/CAFF2005BrFacspdf2005.pdf <!-- Bot retrieved archive --> |archive-date = 2007-06-13 |author-link= American Cancer Society}}</ref> compared to unexposed. Because a low fraction of the population is exposed, the prevalence in the unexposed population can be assumed equal to the prevalence in the general population. Subsequently, it can be estimated that a woman in the United Kingdom that is aged between 55 and 59 and that has been exposed to high-dose ionizing radiation should have a risk of developing breast cancer over a period of one year of between 588 and 1.120 in 100.000 (that is, between 0,6% and 1.1%).

====Multiple risk factors====

Theoretically, the total risk in the presence of multiple risk factors can be roughly estimated by multiplying with each relative risk, but is generally much less accurate than using likelihood ratios, and is usually done only because it is much easier to perform when only relative risks are given, compared to, for example, converting the source data to sensitivities and specificities and calculate by likelihood ratios. Likewise, relative risks are often given instead of likelihood ratios in the literature because the former is more intuitive. Sources of inaccuracy of multiplying relative risks include:

*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>{{Cite journal | last1 = Agoritsas | first1 = T. | last2 = Courvoisier | first2 = D. S. | last3 = Combescure | first3 = C. | last4 = Deom | first4 = M. | last5 = Perneger | first5 = T. V. | title = Does Prevalence Matter to Physicians in Estimating Post-test Probability of Disease? A Randomized Trial | doi = 10.1007/s11606-010-1540-5 | journal = Journal of General Internal Medicine | volume = 26 | issue = 4 | pages = 373–378 | year = 2010 | pmc = 3055966 | pmid = 21053091}}</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 approximately 2%.<ref>2% given from a cumulative incidence 2.075 cases per 100.000 in females younger up to age 39, from the Cancer Research UK reference above.</ref> Also, studies on [[Ashkenazi Jews]] has indicated that a mutation in [[BRCA1]] confers a relative risk of 21.6 of developing breast cancer in women under 40 years of age, and a mutation in [[BRCA2]] confers a relative risk of 3.3 of developing breast cancer in women under 40 years of age.<ref>{{Cite journal | last1 = Satagopan | first1 = J. M. | last2 = Offit | first2 = K. | last3 = Foulkes | first3 = W. | last4 = Robson | first4 = M. E. | last5 = Wacholder | first5 = S. | last6 = Eng | first6 = C. M. | last7 = Karp | first7 = S. E. | last8 = Begg | first8 = C. B. | title = The lifetime risks of breast cancer in Ashkenazi Jewish carriers of BRCA1 and BRCA2 mutations | journal = Cancer Epidemiology, Biomarkers & Prevention | volume = 10 | issue = 5 | pages = 467–473 | year = 2001 | pmid = 11352856}}</ref> From these data, it may be estimated that a woman with a BRCA1 mutation would have a risk of approximately 40% of developing breast cancer at an age younger than 40 years, and woman with a BRCA2 mutation would have a risk of approximately 6%. However, in the rather improbable situation of having ''both'' a BRCA1 and a BRCA2 mutation, simply multiplying with both relative risks would result in a risk of over 140% of developing breast cancer before 40 years of age, which can not possibly be accurate in reality.

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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For example, the [[Systemic lupus erythematosus#Diagnostic criteria|ACR criteria for systemic lupus erythematosus]] defines the diagnosis as presence of at least 4 out of 11 findings, each of which can be regarded as a target value of a test with its own sensitivity and specificity. In this case, there has been evaluation of the tests for these target parameters when used in combination in regard to, for example, interference between them and overlap of target parameters, thereby striving to avoid inaccuracies that could otherwise arise if attempting to calculate the probability of the disease using likelihood ratios of the individual tests. Therefore, if diagnostic criteria have been established for a condition, it is generally most appropriate to interpret any post-test probability for that condition in the context of these criteria.

Also, there are risk assessment tools for estimating the combined risk of several risk factors, such as the online tool [https://web.archive.org/web/20060511202743/http://hp2010.nhlbihin.net/atpiii/calculator.asp?usertype=prof] from the [[Framingham Heart Study]] for estimating the risk for coronary heart disease outcomes using multiple risk factors, including age, gender, blood lipids, blood pressure and smoking, being much more accurate than multiplying the individual relative risks of each risk factor.

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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*''r_i'' 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_i'' is the benefit of ''changes in interventions'' for the individual

*''h_i'' is the harm of ''changes in interventions'' for the individual, such as [[side effectseffect]]s of medical treatment

*''h_t'' 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_i'' = 0 and the test is essentially without any benefit for the individual.

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==References==

{{reflist|30em}}

{{Medical research studies}}