Professional Role · Topic 23 of 26

Research Statistics for Clinicians

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Professional role · research statistics

Research Statistics for Clinicians

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

01 · Benefit per patientNNT = 1 ÷ ARR, rounded up

02 · Not significant95% CI crosses 1 (ratio) or 0 (difference)

03 · The trapLower prevalence: PPV falls, NPV rises

Diagnostic test formulas

TP/FP = true/false positives · TN/FN = true/false negatives

Sensitivity = TP ÷ (TP + FN) — everyone with the disease

Specificity = TN ÷ (TN + FP) — everyone without the disease

PPV = TP ÷ (TP + FP) — everyone with a positive test

NPV = TN ÷ (TN + FN) — everyone with a negative test

LR+ = sensitivity ÷ (1 − specificity)

LR− = (1 − sensitivity) ÷ specificity

Sensitivity and specificity are properties of the test; PPV and NPV depend on prevalence (pretest probability).

What the test numbers mean

High sensitivity: few false negatives — a negative helps rule out

High specificity: few false positives — a positive helps rule in

Moving the cutoff trades sensitivity against specificity (ROC curve)

Screening uses a sensitive cutoff; confirming uses a specific one

LR+ over 10: strong evidence for disease

LR− under 0.1: strong evidence against disease

LR = 1 adds nothing

Likelihood ratios convert pretest probability into post-test probability.

Worked example: same test, two prevalences

Example test: sensitivity 71% · specificity 85%, 2,000 patients

30% prevalence: 600 with disease → TP 426, FN 174

1,400 without disease → TN 1,190, FP 210

PPV = 426 ÷ 636 = 67% · NPV = 1,190 ÷ 1,364 = 87%

5% prevalence: 100 with disease → TP 71, FN 29

1,900 without disease → TN 1,615, FP 285

PPV = 71 ÷ 356 = 20% · NPV = 1,615 ÷ 1,644 = 98%

LR+ = 0.71 ÷ 0.15 = 4.73 · LR− = 0.29 ÷ 0.85 = 0.34

Sensitivity, specificity and the likelihood ratios are identical at both prevalences; only the predictive values move.

Treatment effect formulas

ARR = control event rate − treatment event rate

RRR = ARR ÷ control event rate = 1 − RR

NNT = 1 ÷ ARR, rounded up to the next whole number

NNH = 1 ÷ absolute risk increase, rounded up

Cochrane now prefers 'NNT for an additional harmful outcome' (NNTH) to 'NNH'. Absolute differences vary with baseline risk while relative effects are more stable, so an NNT applies only to a stated comparator, outcome, time frame and baseline risk.

Worked example: NNT and NNH

Example trial: death 10% on placebo · 6% on drug

ARR = 0.10 − 0.06 = 0.04 (4 percentage points)

NNT = 1 ÷ 0.04 = 25 treated to prevent 1 death

RRR = 0.04 ÷ 0.10 = 40%

Bleeding 3% vs 1%: ARI = 0.02 → NNH = 1 ÷ 0.02 = 50

Death 4% → 3%: RRR 25%, but ARR 1 point → NNT 100

Confidence intervals and p-values

The null value: 1 for ratios (RR, OR, HR), 0 for differences

95% CI excludes the null exactly when p < 0.05

Ratio CI 0.8–1.3 crosses 1: not significant

p-value: chance of a result at least this extreme if the null is true

p < 0.05 is a conventional, arbitrary cutoff

p > 0.05 does not prove there is no effect

Very large studies can make a trivial difference significant

Judge clinical importance by the effect size and its CI

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

Type I · type II error

Type I error (α)

Rejects a true null hypothesis

A false-positive finding: an effect that is not there

α (significance level) usually 0.05

Type II error (β)

Fails to reject a false null hypothesis

Misses a real effect — typical of small studies

Power = 1 − β, conventionally 0.80 (β = 0.20)

Larger samples raise power

Which ratio a design gives

Cohort studies and RCTs: risk and relative risk

Case-control studies: odds ratio only

A ratio of 1 means no association

Sensitivity/specificity or predictive value?

	Sensitivity & specificity	PPV & NPV
Question answered	If disease is present (or absent), how often is the test positive (or negative)?	If the test is positive (or negative), how likely is disease present (or absent)?
Denominator	Everyone with (or without) the disease	Everyone with a positive (or negative) test
Changes with prevalence	No — a property of the test	Yes — PPV falls and NPV rises as prevalence falls
Best use	Choosing a test and its cutoff	Interpreting one patient's result

Common errors

Applying a PPV from a study to a lower-prevalence population

Trusting the relative risk reduction without the absolute numbers

Rounding an NNT or NNH down — always round up

Reading p > 0.05 as proof of no effect

Equating statistical significance with clinical importance

Reporting relative risk from a case-control study

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 · Cochrane Handbook, Chapter 15: Interpreting results and drawing conclusions · Banerjee A et al. Hypothesis testing, type I and type II errors, Ind Psychiatry J 2009 · Ranganathan P, Aggarwal R. Study designs: Part 3 — Analytical observational studies · Ranganathan P, Aggarwal R. Study designs: Part 5 — Interventional studies (III) · Follow your institution's protocols.