Question 1

What is a 2×2 contingency table?

Accepted Answer

A 2×2 contingency table cross-classifies subjects by true disease status (disease-positive vs disease-negative) and test result (test-positive vs test-negative). The four cells are: true positives (TP), false positives (FP), false negatives (FN), and true negatives (TN). All diagnostic accuracy measures derive from these four counts.

Question 2

What is the difference between sensitivity and specificity?

Accepted Answer

Sensitivity (true positive rate) is the proportion of truly diseased subjects correctly identified by the test: TP / (TP + FN). Specificity (true negative rate) is the proportion of truly non-diseased subjects correctly excluded: TN / (FP + TN). Sensitivity answers "how good is the test at detecting disease?" while specificity answers "how good is the test at excluding disease?"

Question 3

What are positive and negative predictive values?

Accepted Answer

Positive predictive value (PPV) is the probability that a person with a positive test truly has the disease: TP / (TP + FP). Negative predictive value (NPV) is the probability that a person with a negative test is truly disease-free: TN / (FN + TN). Unlike sensitivity and specificity, PPV and NPV depend heavily on disease prevalence.

Question 4

What are likelihood ratios?

Accepted Answer

The positive likelihood ratio (LR+) is the factor by which the odds of disease increase after a positive test: LR+ = sensitivity / (1 − specificity). The negative likelihood ratio (LR−) is the factor after a negative test: LR− = (1 − sensitivity) / specificity. An LR+ > 10 or LR− < 0.1 is generally considered strong evidence. LRs are independent of prevalence, making them more portable across populations than PPV/NPV.

Question 5

What is the diagnostic odds ratio?

Accepted Answer

The diagnostic odds ratio (DOR) is a single summary measure of test accuracy: DOR = (TP $	imes$ TN) / (FP $	imes$ FN), or equivalently DOR = LR+ / LR−. Values > 1 indicate discriminating ability; higher is better. DOR is useful for meta-analysis but does not distinguish between sensitivity and specificity trade-offs.

Question 6

What is Shannon entropy in diagnostic testing?

Accepted Answer

Shannon entropy $H(p) = -p \cdot \log_2(p) - (1-p) \cdot \log_2(1-p)$ quantifies diagnostic uncertainty in bits. Before testing, uncertainty equals H(prevalence). After testing, each outcome has its own posterior uncertainty. The information gain — the reduction in expected entropy — measures how much the test reduces diagnostic uncertainty. This is a rigorous, information-theoretic complement to traditional accuracy metrics.

Question 7

When should I use Wilson vs Clopper-Pearson confidence intervals?

Accepted Answer

Wilson score intervals are the recommended default — they have better coverage properties and are never degenerate (unlike Wald intervals). Clopper-Pearson "exact" intervals are conservative (always $\geq$ nominal coverage) and preferred when strict coverage guarantees are required, such as regulatory submissions. For most research purposes, Wilson intervals are preferred.

Question 8

What is the Haldane-Anscombe correction?

Accepted Answer

When any cell of the 2×2 table is zero, likelihood ratios and the DOR become undefined (0 or ∞). The Haldane-Anscombe correction adds 0.5 to all four cells before computing ratios and their confidence intervals. This produces finite estimates with valid CIs. The correction is widely used in meta-analysis and is enabled by default in this tool.

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