Professional Role · Topic 18 of 21

Research Statistics for Clinicians

Professional role · research statistics

Research Statistics for Clinicians

Sensitivity and specificity describe the test; predictive values shift with prevalence; NNT = 1/ARR; a 95% CI crossing the null means not significant.

Key numbers

Sensitivity = TP ÷ (TP + FN)TP ÷ (TP + FN)

Specificity = TN ÷ (TN + FP)TN ÷ (TN + FP)

NNT = 1 ÷ absolute risk reductionNNT = 1 ÷ ARR

95% CI crossing null: not significantcrosses null = p ≥ 0.05

Same test, lower prevalence: PPV collapsesPPV 67% → 20%

01 · CalculateNNT = 1 ÷ absolute risk reduction

NNT = 1 ÷ ARR, rounded up. Example: death 10% on placebo vs 6% on drug → ARR = 0.04 → NNT = 1 ÷ 0.04 = 25; RRR = 0.04 ÷ 0.10 = 40%.

02 · The rule95% CI crossing null: not significant

A 95% CI excludes the null — 1 for ratios (RR, OR, HR), 0 for differences — exactly when p < 0.05. A ratio CI of 0.8–1.3 crosses 1, so the result is not significant.

03 · CalculatePredictive values change with prevalence

PPV = TP ÷ (TP + FP) and NPV = TN ÷ (TN + FN). Unlike sensitivity and specificity, they depend on prevalence (pretest probability): as prevalence falls, PPV falls and NPV rises.

What it is

Core idea

p-value: chance of the result if no effectThe p-value is the probability of a result at least this extreme if the null hypothesis is true; p < 0.05 is a conventional, arbitrary cutoff, and p > 0.05 does not prove no effect.

Type I error (α): a false-positive findingA type I error (α) is rejecting a null hypothesis that is true — concluding there is an effect when there is none; α, the significance level, is usually set at 0.05.

Type II error (β): a missed real effectA type II error (β) is failing to reject a false null — missing a real effect, typical of small studies. Power = 1 − β, conventionally 0.80 (β = 0.20); larger samples raise power.

Diagnosis & monitoring

Work-up

Sensitivity = TP ÷ (TP + FN) must knowSensitivity = true positives ÷ all patients with the disease (TP + FN): how well the test detects disease. A highly sensitive test has few false negatives, so a negative result helps rule disease out.

Specificity = TN ÷ (TN + FP) must knowSpecificity = true negatives ÷ all patients without the disease (TN + FP). A highly specific test has few false positives, so a positive result helps rule disease in; confirmatory tests favor specificity.

Same test, lower prevalence: PPV collapsesWorked example: a test with sensitivity 71% and specificity 85% has PPV 67% and NPV 87% at 30% prevalence; at 5% prevalence PPV falls to 20% and NPV rises to 98%.

Likelihood ratios from sensitivity and specificityLR+ = sensitivity ÷ (1 − specificity); LR− = (1 − sensitivity) ÷ specificity. Example (sensitivity 0.71, specificity 0.85): LR+ = 0.71 ÷ 0.15 = 4.73; LR− = 0.29 ÷ 0.85 = 0.34.

NNH = 1 ÷ absolute risk increaseNumber needed to harm = 1 ÷ absolute risk increase for an adverse outcome (e.g., bleeding 3% vs 1% → ARI 0.02 → NNH 50); NNTs are always rounded up to the next whole number.

The rules

Know these

Strong LRs: LR+ over 10, LR− under 0.1A positive result with LR+ > 10 is strong evidence for disease; a negative result with LR− < 0.1 is strong evidence against it; LR = 1 adds nothing. LRs convert pretest into post-test probability.

Cutoff choice trades sensitivity against specificityMoving a test's cutoff trades sensitivity against specificity; a ROC curve plots this trade-off. Screening tests use a sensitive cutoff; tests meant to confirm a diagnosis use a specific one.

Sensitivity/specificity or predictive value?

Commonly confused

Question answered	If disease is present (or absent), how often is the test positive (or negative)?
Denominator	Everyone with (or without) the disease
Changes with prevalence	No — a property of the test
Best use	Choosing a test and its cutoff

Commonly confused

Tell apart

Relative risk reduction exaggerates small benefitsRRR = 1 − RR = ARR ÷ control event rate. Death falling from 4% to 3% is a 25% RRR but only a 1-percentage-point ARR (NNT 100) — always look for the absolute numbers.

Statistical significance is not clinical importanceA very large study can make a trivial difference statistically significant; judge clinical importance by whether the effect and its confidence interval include a difference large enough to matter to patients.

Case-control gives odds ratios, cohorts give relative riskCohort studies and RCTs follow people forward from exposure, yielding risk and relative risk; case-control studies start from the outcome, so only an odds ratio can be estimated. A ratio of 1 means no association.

More detail

Reference

Show 3 reference facts

Because absolute risk differences vary with baseline risk while relative effects are more stable, an NNT applies only to a stated comparator, outcome, time frame and baseline risk.

Testing many outcomes, subgroups or interim analyses inflates the chance of a spuriously significant result unless the analysis corrects for multiple comparisons.

Larger samples give narrower confidence intervals and smaller p-values for an effect of the same size; a 99% CI excludes the null only when p < 0.01.

Pearl

SnNout and SpPin: a negative result on a highly Sensitive test rules disease out; a positive result on a highly Specific test rules it in.

Sources · Merck Manual Professional — Understanding Medical Tests and Test Results (sensitivity, specificity, predictive values, likelihood ratios; leukocyte esterase worked example) · Cochrane Handbook for Systematic Reviews of Interventions, Chapter 15: Interpreting results and drawing conclusions (RRR, ARR, NNT, P values and confidence intervals) · Banerjee A et al. Hypothesis testing, type I and type II errors. Ind Psychiatry J 2009;18:127–131 · Ranganathan P, Aggarwal R. Study designs: Part 3 — Analytical observational studies. Perspect Clin Res 2019;10:91–94 · Ranganathan P, Aggarwal R. Study designs: Part 5 — Interventional studies (III). Perspect Clin Res 2020;11:47–50 · Starter sheet built from the verified AGACNP fact map (facts reviewed 2026-10-15).