Appraising diagnostic study (Part 2)

Once we establish the validity of a diagnostic study, the next step is to assess whether the test accurately distinguishes between people who do and do not have the condition.

1. Understanding Test Performance Metrics

To illustrate, consider a study of 1,000 elderly individuals suspected of having dementia.

• The prevalence of dementia in this group is 25% (250 people).

• Participants undergo both the new diagnostic test and the gold standard reference test.

We can calculate important diagnostic measures based on the table summarises the test results below:

2. Key Measures of Test Accuracy

a. Pretest Probability (Prevalence)

• The likelihood of having the condition before testing.

In this study:

[ frac{250}{1000} = 0.25 text{ (25%)} ]

b. Sensitivity (True Positive Rate)

• Measures how well the test detects people with the condition.

Formula:

[ text{Sensitivity} = frac{text{True Positives (TP)}}{text{Total with Disease}} = frac{240}{250} = 0.96 ]

Interpretation: The test correctly identifies 96% of dementia cases, meaning only 4% are missed (false negatives).

c. Specificity (True Negative Rate)

• Measures how well the test detects people without the condition.

Formula:

[ text{Specificity} = frac{text{True Negatives (TN)}}{text{Total without Disease}} = frac{600}{750} = 0.8 ]

• Interpretation: The test correctly identifies 80% of people without dementia, but 20% are falsely classified as having the disease (false positives).

d. Positive Predictive Value (PPV)

• Tells us the probability that a positive test result means the patient actually has the disease.

Formula:

[ text{PPV} = frac{text{TP}}{text{Total Positive Tests}} = frac{240}{390} = 0.62 ]

• Interpretation: If a patient tests positive, there is a 62% chance they truly have dementia.

e. Negative Predictive Value (NPV)

• Tells us the probability that a negative test result means the patient truly does not have the disease.

Formula:

[ text{NPV} = frac{text{TN}}{text{Total Negative Tests}} = frac{600}{610} = 0.98 ]

• Interpretation: If a patient tests negative, there is a 98% chance they do not have dementia.

3. Likelihood Ratios: A Better Tool for Clinical Decision-Making

While sensitivity and specificity describe test performance, likelihood ratios (LRs) are more useful in practice because they adjust post-test probability.

a. Positive Likelihood Ratio (LR⁺)

• Indicates how much more likely a person with the disease is to test positive.

Formula:

[ text{LR}^+ = frac{text{Sensitivity}}{1 – text{Specificity}} = frac{0.96}{1 – 0.8} = 4.8 ]

• Interpretation: A positive test result makes the odds of dementia 4.8 times more likely.

b. Negative Likelihood Ratio (LR⁻)

• Indicates how much less likely a person without the disease is to test negative.

Formula:

[ text{LR}^- = frac{1 – text{Sensitivity}}{text{Specificity}} = frac{1 – 0.96}{0.8} = 0.05 ]

• Interpretation: A negative test result makes the odds of dementia 24 times less likely.

Key Takeaways

• Sensitivity & Specificity measure test performance.

• Predictive Values (PPV & NPV) show real-world application in a population.

• Likelihood Ratios (LRs) are more useful for clinical decision-making.

By understanding these measures, we can determine whether a diagnostic test is accurate and useful in practice.