Diagnostic Test Calculations

Diagnostic Standard

• Diagnostic Standard: The method used to confirm the presence or absence of the target disorder, often referred to as the “gold” or “reference” standard.

Definitions and Formulas

1. True Positive (a): Individuals who have the target disorder and a positive test result.
2. False Positive (b): Individuals who do not have the target disorder but have a positive test result.
3. True Negative (d): Individuals who do not have the target disorder and have a negative test result.
4. False Negative (c): Individuals who have the target disorder but have a negative test result

Sensitivity

• Sensitivity tells us how good a test is at correctly identifying people who actually have the condition.
• Sensitivity is how well a test finds people who really have the condition.
• If the sensitivity is high, it means the test is good at catching almost everyone who is sick, so very few people with the disease will be missed
• Example:
  • If a test for flu has 90% sensitivity, it means that out of 100 people who have the flu, the test will correctly identify 90 of them as positive. However, it will miss 10 people who actually have the flu, giving them a false negative result.
• High Sensitivity:
  • Best for catching people with the condition, so it’s useful for screening tests, where missing someone with the disease could have serious consequences. For example, high sensitivity is important in tests for serious conditions like HIV, where you want to make sure almost no one with the disease is missed.

Specificity

• Specificity is the ability of a test to correctly identify people who do not have the condition. In other words, it tells us how well a test avoids false positives.
• If a test has high specificity, it means it correctly identifies most people without the disease, resulting in very few false positive results.
• High specificity is important when it is critical to minimize false positives, so most people without the disease are correctly identified as disease-free.
• This is important when the diagnostic confirmation of a disease is associated with serious consequences, like invasive testing or heavy social stigma.
• Example of Specificity:
  • If a flu test has 90% specificity, it means that out of 100 people who do not have the flu, the test will correctly identify 90 as negative. However, it may falsely identify 10 people as having the flu when they actually do not (false positives).

High Sensitivity and High Specificity:

• When to prioritize: In situations where both false positives and false negatives can have significant consequences, a balance of high sensitivity and high specificity is ideal. This often applies to confirmatory diagnostic tests or tests guiding major medical interventions.
• Example: Diagnostic Test for Tuberculosis (TB) Before Initiating Treatment
  When diagnosing TB, both high sensitivity and high specificity are desirable. Missing TB (false negative) could lead to untreated disease and public health risks, while false positives might expose the patient to unnecessary and potentially toxic medications. Therefore, a balance is necessary to accurately diagnose the disease while minimizing the chance of over- or under-treatment.

Summary Table:

Situation	Priority	Example
High Sensitivity	When it’s crucial to catch almost all cases, even if some false positives occur	HIV screening tests
High Specificity	When avoiding false positives is critical to prevent unnecessary treatments or interventions	Confirmatory cancer tests
High Sensitivity and High Specificity	When both accurate detection and minimizing false results are necessary	Tuberculosis diagnostic testing

Pre-Test Probability (Prevalence)

the proportion of individuals who have the target disorder before the test is carried out.

• What it means: This is how likely it is that a person has a condition before any test results are known.
• How to explain:
  “Before we do any tests, we already have an idea of how likely it is that you have a condition. This likelihood is based on things like your symptoms and medical history. That’s the pre-test probability.”
• High Pre-test Probability:
  • What it means: This indicates a strong likelihood that the patient already has the condition, even before testing.
  • Example: If a patient has multiple risk factors for heart disease (like chest pain, high cholesterol, and a family history of heart disease), the pre-test probability of them having heart disease would be high.
  • Why it matters: If the pre-test probability is high, a positive test result is more likely to confirm the diagnosis, and even a negative test might not fully rule it out because the initial suspicion was strong.
• Low Pre-test Probability:
  • What it means: This suggests a low likelihood that the patient has the condition before any testing is done.
  • Example: If a healthy young patient with no symptoms or risk factors comes in worried about heart disease, their pre-test probability of having it is low.
  • Why it matters: If the pre-test probability is low, a positive test result might not be as convincing, as it could be a false positive. Similarly, a negative test might be more reassuring in ruling out the condition.
• Summary:
  • High Pre-test Probability: There’s a strong chance the patient has the condition, so tests are used to confirm or further clarify the diagnosis.
  • Low Pre-test Probability: There’s a low chance the patient has the condition, so tests are more likely to rule it out or catch an unexpected diagnosis.
  • In short, high pre-test probability means you already think the condition is likely, while low pre-test probability means the condition is unlikely, and the test is more of a precaution.

example: DVT and PE

pre-test probability to the example of a D-dimer test, which is commonly used to help rule out blood clots like deep vein thrombosis (DVT) or pulmonary embolism (PE).

High Pre-test Probability for Blood Clots:

• What it means: The patient has a lot of signs or risk factors that suggest they may have a blood clot before the D-dimer test is done.
• Example: If a patient has swelling in one leg, pain, recent surgery, and a history of blood clots, their pre-test probability of having a blood clot is high.
  • How the D-dimer test works in this case:
    • If the D-dimer test is positive, it supports the idea that the patient likely has a blood clot, and further imaging (like an ultrasound or CT scan) is usually needed to confirm the diagnosis.
    • If the D-dimer test is negative, it might not be enough to rule out a clot completely, because the patient’s risk is already high, so further testing might still be necessary.

Low Pre-test Probability for Blood Clots:

• What it means: The patient doesn’t have many signs, symptoms, or risk factors for a blood clot.
• Example: A young, healthy person with mild calf pain but no swelling, no recent surgery, and no history of blood clots would have a low pre-test probability of having a clot.
  • How the D-dimer test works in this case:
    • If the D-dimer test is negative, it’s very reassuring, and it’s likely that the patient does not have a blood clot, so no further testing is usually needed.
    • If the D-dimer test is positive, it might be a false positive because the pre-test probability was low to begin with. In this case, more tests may still be required to confirm or rule out the diagnosis.

Summary:

• High pre-test probability (lots of risk factors or symptoms): A positive D-dimer result is more meaningful, but a negative result might not be enough to rule out a clot.
• Low pre-test probability (few risk factors or symptoms): A negative D-dimer result is very reliable in ruling out a clot, but a positive result might not be as convincing, and further testing is needed to confirm.

Post-test Probability

• What it means: This is how likely it is that a person has a condition after getting the test results.
• How to explain:
  “Once we have the test results, we can be more certain about whether you have the condition or not. The post-test probability tells us how likely it is that you actually have the condition after the test.

Pre-Test Odds

• Pre-Test Odds: The odds that an individual has the target disorder before the test is carried out