Pre- and post-test probability: Difference between revisions

Revision as of 19:03, 8 May 2021

Revision as of 21:05, 14 March 2022

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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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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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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.</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.