Diagnostic Tests

Table of Contents

1. Understanding diagnostic tests
   1. What is a 2 x 2 (read two by two) table, and what is it used for?
   2. Implications in clinical practice
   3. Likelihood ratios
   4. Using likelihood ratios
   5. Conclusion
2. Measures of diagnostic tests
3. Diagnosis

Likelihood ratios

When making a diagnosis, it is important that as a practitioner you recognise that you are dealing with uncertainty and probabilities, and that you are recognise and are comfortable with this concept.

Let us consider the cases of Fred, Jean and Kylie.

Fred, a 57-year-old man presents at your reception desk with squeezing retrosternal pain radiating to his left arm that started 1 hour ago. He is perspiring. His blood pressure is 110/70 mm Hg, his heart rate is 74/min, and he has an audible fourth heart sound.

Jean, a 50-year-old woman presents to A&E with retrosternal burning of 1 hour's duration and nausea. Antacids provided no relief. The findings of the clinical examination were unremarkable.

Kylie, a 40-year-old woman comes to the surgery with a 24-hour history of left-sided chest pain. The pain is worsened by exertion and movement. Prior history is unremarkable. Examination reveals normal vital signs and tenderness with palpation of the left lower costal cartilages

What might the potential diagnoses be for each of these patients?

One of the potential diagnosis is myocardial infarction, but there are a number of other possible diagnoses.

You would need to undertake some further examination and diagnostic tests to determine what might be wrong with these patients.

You will want to find out about the type of chest pain, and look for other signs and symptoms. If you found any of the following, how many times more (or less) likely are you to have an MI if you develop chest pain and have these signs / symptoms?

• Chest pain sharp or stabbing
• Chest pain radiates to left arm
• Chest pain most important symptom
• Nausea or vomiting
• Perspiring
• BP < 80mmHg
• Chest pain reproduced by palpation

By systematically adding more information to our clinical picture of the patient we begin to estimate how much more, or less likely it is that the patient has a myocardial infarction.

Effectively you have estimated a likelihood ratio

Therefore the goal of performing any diagnostic investigation is to increase the precision of our estimate of the likelihood that the patient has or doesn't have a particular disease

What is a likelihood ratio (LR)?

The likelihood ratio is a measure, like sensitivity and specificity, that tells us the accuracy with which the test identifies the target disorder. The likelihood ratio tells us, after the test results are known, how much the pretest probability is increased or decreased. A positive likelihood ratio for a specific test of 19, for example, simply means that the likelihood of the disease being present is 19 times higher than the pretest probability (or likelihood) would have us think. Likewise, a negative likelihood ratio of 0.5 simply means that individuals testing negative are half as likely to have the disease as that predicted by their pretest probability.

The best part about likelihood ratios is that, by converting percentages into odds, we can multiply the odds by the likelihood ratio and derive the new odds, and then convert again back to percentages (the last step is unnecessary if you spend a lot of time at the track and can think in terms of odds). This is mathematically difficult for most clinicians and patients to do in their heads, but clinical decision rules found on computers do the math for us. All we have to do is enter the probability (percentage) of patients who have the disease before the test, and the rule calculates the post test probability (percentage) depending on whether the test is negative or positive.

Likelihood ratios give us a greater range of interpretation of a test result - which may be good or may be bad. The table lists examples of different likelihood ratios and their clinical interpretation.

This guide just provides a rough understanding of how to use a likelihood ratio to determine the accuracy of a test. It doesn't get rid of the problem of pretest probability (prevalence). Even a test with a very high or very low likelihood ratio can be misleading if the prevalence is low. For example, in the case of Baby Jeff, using CPK to identify muscular dystrophy has a likelihood ratio of 500, yet, because of the extremely low prevalence, the test is wrong half the time.