Step 2 CK · Ethics, Biostatistics & Patient Safety

Biostatistics & Evidence Interpretation (Clinical)

Name: Biostatistics & Evidence Interpretation (Clinical)
Creator: Veli Bakalov, MD

Turning RR, OR, NNT, CIs, and test performance into bedside decisions

Ethics, Biostatistics & Patient Safety·Biostatistics·5 min read·9 high-yield points·Reviewed by Veli Bakalov, MD @HemeOncBuddy

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High-yield

Sensitivity = TP/(TP+FN) and specificity = TN/(TN+FP) are intrinsic to the test: SnNout (screen with a sensitive test), SpPin (confirm with a specific test).
PPV and NPV depend on prevalence: higher prevalence raises PPV and lowers NPV; at 1% prevalence even a 99%/99% test has a PPV of only 50%.
LR+ = sens/(1 − spec), LR− = (1 − sens)/spec; posttest odds = pretest odds × LR; LR+ >10 or LR− <0.1 is decisive, LR = 1 is useless.
RR (risk exposed ÷ unexposed) comes from RCTs and cohorts; OR comes from case-control studies and approximates RR only for rare disease; HR comes from survival analysis.
ARR = control rate − treatment rate; NNT = 1/ARR rounded up (10% → 5% gives NNT 20); RRR = 1 − RR and can hide a tiny absolute benefit.
A 95% CI crossing 1 (ratios) or 0 (differences) means not statistically significant; narrower CIs come from larger samples.
p <0.05 means the result is unlikely if the null were true; it is not the probability that the null is true and says nothing about effect size.
Type I error (α) = false positive; type II error (β) = false negative; power = 1 − β, raised chiefly by sample size.
Screening: lead-time bias (earlier diagnosis only appears to lengthen survival) and length-time bias (catches indolent disease); evidence ranks meta-analysis > RCT > cohort > case-control > case series > expert opinion.

Diagnostic tests: the 2×2 table

Set up every test the same way. Rows are the test result and columns are true disease status, giving true positives (TP), false positives (FP), false negatives (FN), and true negatives (TN). Sensitivity and specificity are read down the disease columns; predictive values are read across the test-result rows.

The 2×2 table

Test result	Disease present	Disease absent	Read across
Positive	TP	FP	PPV = TP/(TP+FP)
Negative	FN	TN	NPV = TN/(TN+FN)
Read down	Sensitivity = TP/(TP+FN)	Specificity = TN/(TN+FP)

SnNout and SpPin. Sensitivity is the ability to detect disease: a highly Sensitive test that is Negative rules disease OUT. Specificity is the ability to identify the healthy: a highly Specific test that is Positive rules disease IN. Both are intrinsic to the test and independent of prevalence. Use sensitive tests to screen and specific tests to confirm. Moving a test's cutoff trades one against the other: a lower positivity threshold raises sensitivity and lowers specificity.

Predictive values depend on prevalence. As disease prevalence (pretest probability) rises, PPV rises and NPV falls. In a low-prevalence population, even an excellent test yields many false positives, so PPV is low.

Population10,000 people, 1% prevalence: 100 diseased, 9,900 healthy.
Test is 99% sensitive and 99% specific99 true positives; 1% of 9,900 = 99 false positives.
PPV99/(99+99) = 50%: half of all positive results are false alarms.

Worked example: why a positive screen for a rare disease is often wrong

Likelihood ratios. LR+ = sensitivity/(1 − specificity), and LR− = (1 − sensitivity)/specificity. They convert pretest to posttest probability: posttest odds = pretest odds × LR. An LR+ above 10 or an LR− below 0.1 shifts probability substantially, whereas an LR of 1 means the test changes nothing. Like sensitivity and specificity, LRs are independent of prevalence.

Measures of association

RR vs OR vs HR

Measure	Typical design	Meaning	Key point
Relative risk (RR)	RCTs and cohort studies	Risk in the exposed ÷ risk in the unexposed	Needs incidence, so the study must follow people forward
Odds ratio (OR)	Case-control studies	Odds of exposure in cases ÷ odds in controls	Approximates RR only when the disease is rare
Hazard ratio (HR)	Survival analysis (Cox proportional hazards, Kaplan-Meier curves)	Ratio of instantaneous event rates over time	HR 0.7 = 30% lower instantaneous event rate with treatment

For any ratio, 1 means no association; below 1 means lower risk, above 1 means higher risk.

Why case-control studies give odds ratios. A case-control study starts from outcome status and looks back at exposure, so the investigator sets the number of cases and controls and disease incidence cannot be calculated. Cohort studies and RCTs follow exposure forward and measure incidence directly.

Effect size: ARR, RRR, NNT, and NNH

Absolute risk reduction (ARR) = control event rate − treatment event rate.
Relative risk reduction (RRR) = ARR ÷ control event rate = 1 − RR.
Number needed to treat (NNT) = 1/ARR, rounded up: the number of patients treated to prevent one event. A lower NNT means a more effective therapy.
Number needed to harm (NNH) = 1/attributable risk (risk in the exposed − risk in the unexposed).

10% → 5%ARR 0.05 → NNT 20

8% → 6%ARR 0.02 → NNT 50

2% → 1%50% RRR but only 1% ARR → NNT 100

A large relative risk reduction can conceal a tiny absolute benefit. The same 50% RRR means an NNT of 5 when baseline risk is 40% but an NNT of 100 when it is 2%. Always ask for the absolute numbers.

Statistical inference: confidence intervals and p-values

Confidence intervals. A 95% confidence interval (CI) is a range of plausible values for the true effect: if the study were repeated many times, 95% of intervals built this way would capture the true effect. For a ratio (RR, OR, HR), a CI that crosses 1 is not statistically significant; for a difference (ARR, mean difference), a CI that crosses 0 is not significant. An RR of 0.8 with a 95% CI of 0.6–1.1, or an OR of 1.5 with a CI of 0.9–2.4, is not significant. A narrower CI, usually from a larger sample, is more precise.

p-values. The p-value is the probability of a result at least this extreme if the null hypothesis is true; below 0.05 is the usual cutoff. It is not the probability that the null is true, and it says nothing about the size of the effect.

Hypothesis-testing errors

Study conclusion	Null actually true	Null actually false
Reject the null (finds a difference)	Type I error (α): false positive	Correct; probability = power (1 − β)
Fail to reject (no difference found)	Correct	Type II error (β): false negative

Power rises chiefly with larger sample size, and also with a larger true effect and less variability.

Statistical is not clinical significance. With a large enough sample, a trivial difference can reach p < 0.05 yet be clinically irrelevant. Judge clinical significance by the effect size (ARR, NNT) and the confidence interval, not by the p-value alone.

Screening and the evidence hierarchy

Principles of screening (Wilson-Jungner). Screen for an important, common or serious disease with a detectable preclinical phase and an effective early treatment. Use a test with high sensitivity (few false negatives) that is acceptable to patients, and confirm a positive screen with a highly specific test.

Lead-time bias: earlier detection starts the survival clock sooner, so survival appears longer even though death is not delayed. Mortality rates avoid this bias.
Length-time bias: screening preferentially catches slow-growing, indolent disease with a long preclinical phase, which makes screen-detected cases look more benign.
Overdiagnosis: detecting disease that would never have caused symptoms, an extreme form of length-time bias.

Systematic review / meta-analysisStatistically pools multiple RCTs.
Randomized controlled trialRandomization balances known and unknown confounders; best design for causation.
Cohort studyFollows exposure forward; gives RR.
Case-control studyStarts from outcome, looks back; gives OR.
Case series or report, expert opinionWeakest evidence.

Strength of evidence, strongest first

Randomization protects against confounding only if it is preserved: intention-to-treat analysis keeps every patient in the group they were assigned to.