Pre- and post-test probability: Difference between revisions

Revision as of 01:28, 5 August 2013

Revision as of 04:27, 4 December 2013

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==Pre-test probability==

The pre-test probability of an individual can be chosen to beas one of the following:

*The [[prevalence]] of the disease, which may have to be chosen if no other characteristic is known for the individual, or it can be chosen for ease of calculation even if other characteristics are known although such omission may cause inaccurate results

*The post-test probability of the condition resulting from one or more preceding tests

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===By predictive values===

[[Predictive value]]s can be used to estimate the post-test probability of an individual if the pre-test probability of the individual can be assumed to be roughly equal to the prevalence in a [[reference group]] on which both test results and knowledge on the presence or absence of the condition (for example a disease, such as may determined by "[[Gold standard (test)|Gold standard]]") are available.

If the test result is of a [[binary classification]] into either [[positive or negative test]]s, then the following table can be made:

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Negative posttest probability = False 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 could causemake the groups of those who have the condition and those who do not to be 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.

===By likelihood ratio===

The above methods are inappropriate to use if the pretest probability differs from the prevalence in the reference group used to establish, among others, the positive predictive value of the test. Such difference can occur if another test preceded, or the person involved in the diagnostics considers that another pretest probability has tomust be used because of knowledge of, for example, specific complaints, other elements of a [[medical history]], signs in a [[physical examination]], either by calculating on each finding as a test in itself with its own sensitivity and specificity, or at least making a rough estimation of the individual pre-test probability.

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.

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To establish a relative risk, the risk in an exposed group is divided by the risk in an unexposed group.

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 to be 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 to beat 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] 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 to 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|accessdate=2007-04-26 |archiveurl = http://web.archive.org/web/20070613192148/http://www.cancer.org/downloads/STT/CAFF2005BrFacspdf2005.pdf <!-- Bot retrieved archive --> |archivedate = 2007-06-13 |authorlink= 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 to be 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====

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*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 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 to beat 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 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.

A method to compensate for both sources of inaccuracy above is to establish the relative risks by [[multivariate regression analysis]]. However, to retain its validity, relative risks established as such need tomust be multiplied with all the other risk factors in the same regression analysis, and without any addition of other factors beyond the regression analysis.

In addition, multiplying multiple relative risks has the same risk of missing important overlaps of the included risk factors, similarly to when using likelihood ratios. Also, different risk factors can act in [[synergy]], with the result that, for example, two factors that both individually have a relative risk of 2 have a total relative risk of 6 when both are present, or can inhibit each other, somewhat similarly to the interference described for using likelihood ratios.

===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 regarded to beconsidered 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 [[Systemic_lupus_erythematosus#Diagnostic_criteria|ACR criteria for systemic lupus erythematosis]] 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.