By likelihood ratio Pre- and post-test probability

1 likelihood ratio

1.1 example
1.2 specific sources of inaccuracy

1.2.1 interference test
1.2.2 overlap of tests
1.2.3 methods overcome inaccuracy

by likelihood ratio

the above methods inappropriate use if pretest probability differs prevalence in reference group used establish, among others, positive predictive value of test. such difference can occur if test preceded, or person involved in diagnostics considers pretest probability must used because of knowledge of, example, specific complaints, other elements of medical history, signs in physical examination, either calculating on each finding test in own sensitivity , specificity, or @ least making rough estimation of individual pre-test probability.

in these cases, prevalence in reference group not accurate in representing pre-test probability of individual, and, consequently, predictive value (whether positive or negative) not accurate in representing post-test probability of individual of having target condition.

in these cases, posttest probability can estimated more accurately using likelihood ratio test. likelihood ratio calculated sensitivity , specificity of test, , thereby not depend on prevalence in reference group, and, likewise, not change changed pre-test probability, in contrast positive or negative predictive values (which change). also, in effect, validity of post-test probability determined likelihood ratio not vulnerable sampling bias in regard , without condition in population sample, , can done case-control study separately gathers , without condition.

estimation of post-test probability pre-test probability , likelihood ratio goes follows:

pretest odds = (pretest probability / (1 - pretest probability)
posttest odds = pretest odds * likelihood ratio

in equation above, positive post-test probability calculated using likelihood ratio positive, , negative post-test probability calculated using likelihood ratio negative.

posttest probability = posttest odds / (posttest odds + 1)


fagan nomogram

the relation can estimated so-called fagan nomogram (shown @ right) making straight line point of given pre-test probability given likelihood ratio in scales, which, in turn, estimates post-test probability @ point straight line crosses scale.

the post-test probability can, in turn, used pre-test probability additional tests if continues calculated in same manner.

it possible calculation of likelihood ratios tests continuous values or more 2 outcomes similar calculation dichotomous outcomes. purpose, separate likelihood ratio calculated every level of test result , called interval or stratum specific likelihood ratios.

example

an individual screened test of fecal occult blood (fob) estimate probability person having target condition of bowel cancer, , fell out positive (blood detected in stool). before test, individual had pre-test probability of having bowel cancer of, example, 3% (0.03), have been estimated evaluation of, example, medical history, examination , previous tests of individual.

the sensitivity, specificity etc. of fob test established population sample of 203 people (without such heredity), , fell out follows:

from this, likelihood ratios of test can established:

pretest probability (in example) = 0.03
pretest odds = 0.03 / (1 - 0.03) = 0.0309
positive posttest odds = 0.0309 * 7.4 = 0.229
positive posttest probability = 0.229 / (0.229 + 1) = 0.186 or 18.6%

thus, individual has post-test probability (or post-test risk ) of 18.6% of having bowel cancer.

the prevalence in population sample calculated be:

prevalence = (2 + 1) / 203 = 0.0148 or 1.48%

the individual s pre-test probability more twice 1 of population sample, although individual s post-test probability less twice 1 of population sample (which estimated positive predictive value of test of 10%), opposite result less accurate method of multiplying relative risks.

specific sources of inaccuracy

specific sources of inaccuracy when using likelihood ratio determine post-test probability include interference determinants or previous tests or overlap of test targets, explained below:

interference test

post-test probability, estimated pre-test probability likelihood ratio, should handled caution in individuals other determinants (such risk factors) general population, in individuals have undergone previous tests, because such determinants or tests may influence test in unpredictive ways, still causing inaccurate results. example risk factor of obesity additional abdominal fat can make difficult palpate abdominal organs , decrease resolution of abdominal ultrasonography, , similarly, remnant barium contrast previous radiography can interfere subsequent abdominal examinations, in effect decreasing sensitivities , specificities of such subsequent tests. on other hand, effect of interference can potentially improve efficacy of subsequent tests compared usage in reference group, such abdominal examinations being easier when performed on underweight people.

overlap of tests

furthermore, validity of calculations upon pre-test probability derived previous test depend on 2 tests not overlap in regard target parameter being tested, such blood tests of substances belonging 1 , same deranged metabolic pathway. example of extreme of such overlap sensitivity , specificity has been established blood test detecting substance x , , likewise 1 detecting substance y . if, in fact, substance x , substance y 1 , same substance, then, making 2 consecutive tests of 1 , same substance may not have diagnostic value @ all, although calculation appears show difference. in contrast interference described above, increasing overlap of tests decreases efficacy. in medical setting, diagnostic validity increased combining tests of different modalities avoid substantial overlap, example in making combination of blood test, biopsy , radiograph.

methods overcome inaccuracy

to avoid such sources of inaccuracy using likelihood ratios, optimal method gather large reference group of equivalent individuals, in order establish separate predictive values use of test in such individuals. however, more knowledge of individual s medical history, physical examination , previous test etc. individual becomes more differentiated, increasing difficulty find reference group establish tailored predictive values, making estimation of post-test probability predictive values invalid.

another method overcome such inaccuracies evaluating test result in context of diagnostic criteria, described in next section.