A home drug screening test kit is currently being developed. The cut-off level is initially set at 4 mg/uL, which is associated with a sensitivity of 92% and a specificity of 97%. How might the sensitivity and specificity of the test change if the cut-off level is changed to 2 mg/uL?

Sensitivity = 97%, specificity = 96%

Sensitivity = 92%, specificity = 97%

Sensitivity = 95%, specificity = 98%

Sensitivity = 100%, specificity = 97%

Sensitivity = 90%, specificity = 99%

A 27-year-old man interested in pre-exposure therapy for HIV (PrEP) is being evaluated to qualify for a PrEP study. In order to qualify, patients must be HIV- and hepatitis B- and C-negative. Any other sexually transmitted infections require treatment prior to initiation of PrEP. The medical history is positive for a prior syphilis infection and bipolar affective disorder, for which he takes lithium. On his next visit, the liver and renal enzymes are within normal ranges. HIV and hepatitis B and C tests are negative. Which of the following about the HIV test is true?

It is a qualitative test used for screening purposes.

It is a quantitative test used for screening purposes.

A secondary reagent is needed to interpret the results.

A known antigen binds directly to the patient's serum.

An unknown antigen binds to the known serum.

A pharmaceutical company develops a sequential testing protocol for a rare genetic disorder (prevalence 0.01%). Initial screening test has sensitivity 95% and specificity 90%. Positive results undergo confirmatory testing with sensitivity 99% and specificity 99.5%. The company claims this approach achieves PPV >80% for the final positive result. Evaluate this claim and the rationale for sequential testing in this context.

The claim is true; sequential testing increases PPV by enriching the population tested in the second step

The claim is false; sensitivity decreases with sequential testing, reducing PPV

Sequential testing is unnecessary; the first test alone achieves adequate PPV

The claim is false; sequential testing cannot achieve PPV >80% with such low prevalence

The claim is true; the high specificity of the confirmatory test ensures high PPV regardless of prevalence

A hospital system is implementing a sepsis screening algorithm using clinical criteria with sensitivity of 92% and specificity of 75%. False positives result in unnecessary antibiotics, cultures, and ICU evaluations costing $3,000 per case. Missing true sepsis cases (false negatives) results in average increased mortality and morbidity costs of $50,000 per case. Hospital sepsis prevalence is 8%. Evaluate the optimal threshold adjustment strategy.

Decrease threshold to improve sensitivity despite more false positives

Maintain current threshold as it balances sensitivity and specificity equally

Implement risk stratification with different thresholds for different populations

Abandon screening due to unacceptable false positive rate

Increase threshold to improve specificity and reduce costs from false positives

A 58-year-old man with chronic cough undergoes evaluation for tuberculosis. A tuberculin skin test (TST) is positive (15mm induration). TST has sensitivity of 80% and specificity of 95% in immunocompetent adults. However, he received BCG vaccination as a child in Asia. Local TB prevalence is 0.5%, but his occupational exposure increases his pre-test probability to 10%. Evaluate the most appropriate interpretation and management approach.

Calculate post-test probability and obtain interferon-gamma release assay (IGRA)

Repeat TST in 2 weeks to confirm

Treat empirically regardless of test characteristics

Positive test confirms TB; start treatment immediately

False positive due to BCG; no further testing needed

Test characteristics fundamentals | Sensitivity/Specificity

The 2x2 Table - The Truth Grid

The 2x2 table is the foundation for evaluating diagnostic tests against a gold standard. It classifies individuals based on test results versus their true disease status.

	Disease Present	Disease Absent	Row Total
Test Positive	True Positive (TP)	False Positive (FP)	TP + FP
Test Negative	False Negative (FN)	True Negative (TN)	FN + TN
Column Total	TP + FN	FP + TN

Rows represent the test results.

⭐ The vertical columns represent the true disease status, which is the basis for calculating sensitivity $TP/(TP+FN)$ and specificity $TN/(TN+FP)$.

2x2 table for diagnostic test accuracy & related metrics

Sensitivity & Specificity - SnNOut & SpPIn Show

Sensitivity: True Positive Rate. Proportion of people with a disease who test positive. Rules OUT disease if negative.
- Formula: $TP / (TP + FN)$
- 📌 Sn-N-Out: A highly Sensitive test, when Negative, rules Out the disease.
Specificity: True Negative Rate. Proportion of people without a disease who test negative. Rules IN disease if positive.
- Formula: $TN / (TN + FP)$
- 📌 Sp-P-In: A highly Specific test, when Positive, rules In the disease.

⭐ High-sensitivity tests are used for screening (e.g., initial HIV screen). High-specificity tests are used for confirmation (e.g., Western blot for HIV).

Sensitivity & Specificity Venn Diagram

Predictive Values - Crystal Ball Values

Positive Predictive Value (PPV): Probability of having the disease with a positive test.
- Formula: $PPV = \frac{TP}{TP + FP}$
- Directly varies with prevalence. Higher prevalence → Higher PPV.
Negative Predictive Value (NPV): Probability of being disease-free with a negative test.
- Formula: $NPV = \frac{TN}{TN + FN}$
- Inversely varies with prevalence. Higher prevalence → Lower NPV.

📌 Mnemonic: Prevalence Positively affects PPV.

⭐ As disease prevalence decreases, PPV decreases. In a population with very low prevalence, most positive results are actually false positives.

ROC Curves - Curve Appeal

Receiver Operating Characteristic (ROC) Curve curve showing True Positive Rate vs False Positive Rate)

Plots True Positive Rate ($TPR$, Sensitivity) vs. False Positive Rate ($FPR$, 1-Specificity) across various cut-off thresholds.
The Area Under the Curve (AUC) is a measure of overall test accuracy.
- AUC = 1.0: Perfect test.
- AUC = 0.5: Useless test (represented by the diagonal line).
The ideal cut-off point is often the "knee" of the curve, maximizing the distance from the diagonal.

⭐ The optimal threshold balances sensitivity and specificity, often found by maximizing the Youden Index.

High‑Yield Points - ⚡ Biggest Takeaways

Sensitivity is the True Positive Rate (TPR), ideal for screening; a negative result in a high-sensitivity test helps rule OUT disease (SNOUT).

Specificity is the True Negative Rate (TNR), used for confirmation; a positive result in a high-specificity test helps rule IN disease (SPIN).

Positive Predictive Value (PPV) is directly related to prevalence; as prevalence increases, PPV increases.

Negative Predictive Value (NPV) is inversely related to prevalence; as prevalence increases, NPV decreases.

Sensitivity and specificity are intrinsic test characteristics, independent of disease prevalence.