| 词条 | Pre- and post-test probability | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 释义 |
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 or a negative test, respectively. In some cases, it is used for the probability of developing the condition of interest in the future. Test, in this sense, can refer to any medical test (but usually in the sense of diagnostic tests), and in a broad sense also including questions and even assumptions (such as assuming that the target individual is a female or male). The ability to make a difference between pre- and post-test probabilities of various conditions is a major factor in the indication of medical tests. Pre-test probabilityThe pre-test probability of an individual can be chosen as one of the following:
Estimation of post-test probabilityIn 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"), 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. The most important systematic reference group-based methods to estimate post-test probability includes the ones summarized and compared in the following table, and further described in individual sections below.
By predictive valuesPredictive values can be used to estimate the post-test probability of an individual if the pre-test probability of the individual can be assumed 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") are available. If the test result is of a binary classification into either positive or negative tests, then the following table can be made:
Pre-test probability can be calculated from the diagram as follows: Pretest probability = (True positive + False negative) / Total sample Also, in this case, the positive post-test probability (the probability of having the target condition if the test falls out positive), is numerically equal to the positive predictive value, and the negative post-test probability (the probability of not having the target condition if the test falls out negative) is numerically complementary to the negative predictive value ([negative post-test probability] = 1 - [negative predictive value]),[1] again assuming that the individual being tested does not have any other risk factors that result in that individual having a different pre-test probability than the reference group used to establish the positive and negative predictive values of the test. In the diagram above, this positive post-test probability, that is, the posttest probability of a target condition given a positive test result, is calculated as: Positive posttest probability = True positives / (True positives + False positives) Similarly: The post-test probability of disease given a negative result is calculated as: 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 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. By likelihood ratioThe 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 must 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. In these cases, a posttest probability can be estimated more accurately by using a likelihood ratio for the test. Likelihood ratio is calculated from sensitivity and specificity of the test, and thereby it does not depend on prevalence in the reference group,[2] and, likewise, it does not change with changed pre-test probability, in contrast to positive or negative predictive values (which would change). Also, in effect, the validity of post-test probability determined from likelihood ratio is not vulnerable to sampling bias in regard to those with and without the condition in the population sample, and can be done as a case-control study that separately gathers those with and without the condition. Estimation of post-test probability from pre-test probability and likelihood ratio goes as follows:[2]
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.
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. The post-test probability can, in turn, be used as pre-test probability for additional tests if it continues to be calculated in the same manner.[2] 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.[4] ExampleAn individual was screened with the test of fecal occult blood (FOB) to estimate the probability for that person having the target condition of bowel cancer, and it fell out positive (blood were detected in stool). Before the test, that individual had a pre-test probability of having bowel cancer of, for example, 3% (0.03), as could have been estimated by evaluation of, for example, the medical history, examination and previous tests of that individual. The sensitivity, specificity etc. of the FOB test were established with a population sample of 203 people (without such heredity), and fell out as follows:
From this, the likelihood ratios of the test can be established:[2]
Thus, that individual has a post-test probability (or "post-test risk") of 18.6% of having bowel cancer. The prevalence in the population sample is calculated to be:
The individual's pre-test probability was more than twice the one of the population sample, although the individual's post-test probability was less than twice the one 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 inaccuracySpecific sources of inaccuracy when using likelihood ratio to determine a post-test probability include interference with determinants or previous tests or overlap of test targets, as explained below: Interference with testPost-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,[5] 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 testsFurthermore, the validity of calculations upon any pre-test probability that itself is derived from a previous test depend on that the two tests do not significantly overlap in regard to the target parameter being tested, such as blood tests of substances belonging to one and the same deranged metabolic pathway. An example of the extreme of such an overlap is where the sensitivity and specificity has been established for a blood test detecting "substance X", and likewise for one detecting "substance Y". If, in fact, "substance X" and "substance Y" are one and the same substance, then, making a two consecutive tests of one and the same substance may not have any diagnostic value at all, although the calculation appears to show a difference. In contrast to interference as described above, increasing overlap of tests only decreases their efficacy. In the medical setting, diagnostic validity is increased by combining tests of different modalities to avoid substantial overlap, for example in making a combination of a blood test, a biopsy and radiograph. Methods to overcome inaccuracyTo avoid such sources of inaccuracy by using likelihood ratios, the optimal method would be to gather a large reference group of equivalent individuals, in order to establish separate predictive values for use of the test in such individuals. However, with more knowledge of an individual's medical history, physical examination and previous test etc. that individual becomes more differentiated, with increasing difficulty to find a reference group to establish tailored predictive values, making an estimation of post-test probability by predictive values invalid. Another method to overcome such inaccuracies is by evaluating the test result in the context of diagnostic criteria, as described in the next section. By relative riskPost-test probability can sometimes be estimated by multiplying the pre-test probability with a relative risk given by the test. In clinical practice, this is usually applied in evaluation of a medical history of an individual, where the "test" usually is a question (or even assumption) regarding various risk factors, for example, sex, tobacco smoking or weight, but it can potentially be a substantial test such as putting the individual on a weighing scale. When using relative risks, the resultant probability is usually rather related to the individual developing the condition over a period of time (similarly to the incidence in a population), instead of being the probability of an individual of having the condition in the present, but can indirectly be an estimation of the latter. Usage of hazard ratio can be used somewhat similarly to relative risk. One risk factorTo 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 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 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,[6] 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, |archivedate = 2007-06-13 |authorlink= American Cancer Society}} 3 : Medical statistics|Evidence-based medicine|Summary statistics for contingency tables |
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