Pre- and post-test probability: Difference between revisions

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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>{{citeCite journal pmid| 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>{{citeCite journal pmid| 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 : a publication of the American Association for Cancer Research, cosponsored by the American Society of Preventive Oncology | 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.