9.4.7 Diagnostic Accuracy and Nomograms


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For studies Evaluating Diagnostic Accuracy, Applies the Results of a Test to Another Population Using Likelihood Ratios and Nomograms

In studies evaluating diagnostic accuracy, it is important to apply the results of a test to another population to assess its utility in clinical practice. This can be done using likelihood ratios and nomograms.

Likelihood ratios:

Likelihood ratios (LR) are used to estimate the probability of a patient having a disease given a positive or negative test result. They are calculated by dividing the true positive rate (sensitivity) by the false positive rate (1-specificity) for a positive test result and dividing the false negative rate (1-sensitivity) by the true negative rate (specificity) for a negative test result. LR greater than 1 indicates that the test result is more likely to be true positive than false positive, while LR less than 1 indicate that the test result is more likely to be false positive than true positive.

LR indicate how much a given test result changes the odds of having the disease. The LR equations for a positive test result and a negative test result are:

The positive likelihood ratio (LR+ve) is calculated as:

The negative likelihood ratio (LR-ve) is calculated as:

An LR+ve greater than 1 indicates that a positive test result increases the likelihood of having the disease, while an LR+ve less than 1 indicates that a positive test result decreases the likelihood of having the disease.

An LR-ve less than 1 indicates that a negative test result increases the likelihood of not having the disease, while an LR-ve greater than 1 indicates that a negative test result decreases the likelihood of not having the disease.

Sensitivity: the proportion of true positives among all people with the condition

Specificity: the proportion of true negatives among all people without the condition

LR+ve indicates how much more likely a positive test result is to occur in people with the condition compared to those without the condition. An LR+ve greater than 1 indicates that a positive test result increases the likelihood of the condition, while an LR+ve less than 1 indicates that a positive test result decreases the likelihood of the condition.

LR-ve indicates how much more likely a negative test result is to occur in people without the condition compared to those with the condition. An LR-ve less than 1 indicates that a negative test result increases the likelihood of the condition, while an LR-ve greater than 1 indicates that a negative test result decreases the likelihood of the condition.

These equations can be used to calculate post-test probability using the pre-test probability and likelihood ratios in a nomogram, which is a graphical tool that provides a visual representation of the calculations.

Nomograms:

Nomograms are graphical representations of likelihood ratios that can be used to estimate the post-test probability of a disease given the pre-test probability and the likelihood ratio of a test. They consist of a series of lines and curves that intersect at a point representing the post-test probability. Nomograms can be useful in clinical practice to estimate the probability of a disease and to guide decision-making about further testing or treatment.

In the context of diagnostic accuracy, a Fagan nomogram is often used to apply LRs and calculate the post-test probability of disease present in a new population.

To use a Fagan nomogram:

  1. Identify the pre-test probability of the disease in the new population. This can be based on the disease prevalence in the specific population or clinical setting.
  2. Determine the LR+ or LR- of the diagnostic test from the original study population.
  3. Locate the pre-test probability on the left axis of the Fagan nomogram and draw a straight line through the corresponding LR value on the centre axis.
  4. The point where the line intersects the right axis represents the post-test probability of the disease in the new population.

It is important to note that likelihood ratios and nomograms are only useful if the pre-test probability of a disease is known or can be estimated accurately. This can be challenging in some clinical situations, and it is important to consider the context and other clinical factors when interpreting diagnostic test results.

References:

  1. Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios. BMJ. 2004;329(7458):168-9.
  2. Simel DL, Rennie D. The rational clinical examination. Evidence-based clinical diagnosis. JAMA. 1995;273(5):408-12.
  3. Feinstein AR. Clinical biostatistics. XLV. Nomograms for statistical inference. Clin Pharmacol Ther. 1978;23(2):225-7.