# Relationship between specificity and sensitivity table

### Concepts: Sensitivity, Specificity & Likelihood Ratios

Unlike sensitivity and specificity, predictive values vary with the prevalence of a of a case definition or the results of a diagnostic test or algorithm (Table ). The NLR is the ratio between the false negative and true negative rates and. To calculate the sensitivity, specificity, and predictive value of your fall risk Before reading the examples, please review the general notes about 2 x 2 tables on. Unlike sensitivity and specificity, the PPV and However, if a patient has signs of SLE a test are inserted into a 2×2 contingency table, PPV, NPPV, and likelihood ratio.

Predictive values You may have noticed that sensitivity and specificity were calculated beginning from the actual diagnosis "how many of the people who really have the disease does the test identify? But obviously, as the physician using the test, you don't know who really has the disease: Referring back to the 2 x 2 diagram, you will in effect be looking across the rows a positive or negative score on the test.

So sensitivity and specificity do not really apply: Look again at the diagram: Now a crucial fact to grasp is that the positive predictive value varies according to the prevalence of the disease in the population from which your patient comes.

If you are really keen, you can work this out for yourself; the notes from the Critical Appraisal course Module 4, pages 23 and 24 explain how.

## Sensitivity and specificity

Or else, you can take the intuitive route, as follows So, a patient may get a positive test result but if the prevalence in the population is very low, because of the small number of true cases mixed in with all those false positives, the test result may not mean very much.

Imagine you are a general practitioner and the disease is relatively rare among your patients. The pre-test probability of your patient having a disease will be low, and this will bring down the predictive value of a positive test result, even if the test itself is quite good. However, when the same patient attends a specialist clinic at the hospital, where a lot of selection has already taken place and a larger proportion of all the patients have the disease, the predictive value of the same test will be much higher.

This was well illustrated in the BMJ article mentioned earlier. More on sensitivity, prevalence and predictive values Conclusion: This introduces likelihood ratios. So, how do I combine prevalence and sensitivity of the test? Welcome to the world of Likelihood Ratios. These show how much knowing the test result will improve on a diagnostic guess based simply on pre-test probability: This shows how much more likely is a person with the disease to score positive than a person without the disease.

To bring in the prevalence piece there's a neat little nomogram diagram below. You need to know the likelihood ratio for this particular test, and also the pre-test probability or prevalence. Draw a line through the pre-test probability on the left of the diagram, through the likelihood ratio in the central column, and then read off the post-test probability on the right-hand column.

LRs higher than about 5 can be useful in ruling in a disease. There is also a likelihood ratio for a negative test result "LR-". It gives a result below 1; values below about 0.

Calculators from the Knowledge Translation clearinghouse. You have to type in the numbers of cases in each of the four cells of the table.

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• Understanding and using sensitivity, specificity and predictive values
• 10.3 - Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value

Sensitivity, specificity, and other terms The following terms are fundamental to understanding the utility of clinical tests: When evaluating a clinical test, the terms sensitivity and specificity are used. The terms positive predictive value PPV and negative predictive value NPV are used when considering the value of a test to a clinician and are dependent on the prevalence of the disease in the population of interest.

Sensitivity The sensitivity of a clinical test refers to the ability of the test to correctly identify those patients with the disease. A high sensitivity is clearly important where the test is used to identify a serious but treatable disease e. Screening the female population by cervical smear testing is a sensitive test. However, it is not very specific and a high proportion of women with a positive cervical smear who go on to have a colposcopy are ultimately found to have no underlying pathology.

Specificity The specificity of a clinical test refers to the ability of the test to correctly identify those patients without the disease. As discussed above, a test with a high sensitivity but low specificity results in many patients who are disease free being told of the possibility that they have the disease and are then subject to further investigation.

### Understanding and using sensitivity, specificity and predictive values

In this way, nearly all of the false positives may be correctly identified as disease negative. Positive predictive value The PPV of a test is a proportion that is useful to clinicians since it answers the question: This is defined as how much more likely is it that a patient who tests positive has the disease compared with one who tests negative.

Consider the following example: However, if a patient has signs of SLE e. We may also consider a woman who presents with breathlessness post-partum and where one of the differential diagnoses is pulmonary embolism.

A D-dimer test would almost certainly be elevated in this patient population; therefore, the test has a low PPV for pulmonary embolism. However, it has a high NPV for pulmonary embolism since a low D-dimer is unlikely to be associated with pulmonary embolism.

Screening this population would therefore yield true positives and true negatives with 20 patients being tested positive when they in fact are well and 20 patients testing negative when they are ill.

This discussion highlights the fact that the ability to make a diagnosis or screen for a condition depends both on the discriminatory value of the test and on the prevalence of the disease in the population of interest. Receiver operator characteristic curves Consider the following hypothetical example: A sample of SpRs is tested before the examination resulting in a range of endorphin values.