A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.

Number Needed to Treat and Number Needed to Harm

Graduate Depth 247 in the knowledge graph ☐ I know this ☆ Set as goal
1,512prerequisites beneath it
See this on the map →
Attributable Risk and Population Attributable Fraction→
intervention-effectiveness clinical-significance decision-making

Core Idea

Number needed to treat (NNT) is the reciprocal of attributable risk in a trial: NNT = 1 / AR. It expresses how many people must receive an intervention to prevent one adverse outcome. Number needed to harm (NNH) applies the same logic to adverse effects. These metrics translate relative measures into absolute, clinically interpretable terms for individual patients.

Explainer

From your study of attributable risk, you know that absolute risk measures — unlike relative ones — answer the question of how much a risk actually changes. A relative risk reduction of 50% sounds identical whether the risk drops from 20% to 10% or from 0.002% to 0.001%, but the public health and clinical significance of those two scenarios are vastly different. The number needed to treat (NNT) is the tool that makes this concreteness automatic, by converting the absolute risk difference into the language of individual patients: how many people must receive this treatment to prevent one adverse outcome?

The calculation flows directly from your attributable risk knowledge. In a randomized trial, the absolute risk reduction (ARR) is simply the event rate in the control group minus the event rate in the treatment group: ARR = Risk_control − Risk_treatment. NNT = 1 / ARR. A concrete example: a trial of a cholesterol-lowering drug finds that over 5 years, 8% of patients in the placebo group had a heart attack, compared to 5% in the treated group. ARR = 0.08 − 0.05 = 0.03. NNT = 1/0.03 ≈ 33. You must treat 33 patients for 5 years to prevent one heart attack. Number needed to harm (NNH) is calculated identically but for adverse events: if the drug causes a serious side effect in 2% of treated patients and 0.5% of controls, ARR_harm = 0.015, NNH = 67.

The clinical power of these metrics lies in enabling direct comparison between benefit and risk. The NNT of 33 and NNH of 67 in this example mean that for every two patients harmed by the drug, roughly four are protected from a heart attack — a favorable ratio. The formal version of this comparison is the likelihood of being helped vs. harmed (LHH), calculated as NNH / NNT. Values above 1 favor treatment; below 1, the harm exceeds the benefit. For patient communication, framing as "1 in 33 patients benefits from this drug" is often more intuitive and honest than "the drug reduces your heart attack risk by 38%" — the relative measure that pharmaceutical marketing typically emphasizes because it sounds more impressive.

One critical limitation is that NNT is not a fixed property of a drug — it depends on the population's baseline risk and the time horizon of the trial. The NNT above applies only to patients with 8% five-year MI risk treated for five years. Applied to a lower-risk population (say, 2% five-year risk) with the same relative risk reduction, ARR would be approximately 0.008 and NNT would jump to 125. The treatment is three to four times less efficient in absolute terms, even though the same trial's relative risk reduction still applies. This is why applying published NNTs uncritically to patients who differ from the trial population can be systematically misleading — the absolute benefit scales with baseline risk, so the same drug can range from highly efficient prevention to marginal benefit depending entirely on who is receiving it.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → One-to-One Correspondence → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Making 10 as an Addition Strategy → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Iterated Integrals and Fubini's Theorem → Double Integrals in Cartesian Coordinates → Double Integrals in Polar Coordinates → Double Integrals in Polar Coordinates → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → The Measurement Problem → Interpretations of Quantum Mechanics → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → VSEPR Theory and Molecular Geometry → Molecular Geometry and Electron Pair Geometry → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Heat Capacity and Calorimetry → Entropy and Molecular Disorder → Spontaneity and ΔG → Entropy and Gibbs Free Energy → Chemical Equilibrium → Acid-Base Chemistry → Weak Acid Ionization → Weak Base Ionization → Acid and Base Strength: Ka, Kb, and Ionization → Leaving Groups and Nucleofugality → SN2 Substitution Reactions → SN1 Substitution Reactions → E1 Elimination Reactions → Alcohols and Ethers: Structure, Properties, and Nomenclature → Reactions of Alcohols → Aldehydes and Ketones: Structure and Reactivity → Oxidation Reactions in Organic Chemistry → Oxidation of Alcohols to Aldehydes and Ketones → Aldehyde and Ketone Structure and Nomenclature → Nucleophilic Addition to Aldehydes and Ketones → Carboxylic Acids and Their Derivatives → IUPAC Nomenclature of Carbonyls and Carboxylic Acids → IUPAC Nomenclature of Alkenes → Electrophilic Addition to Alkenes → Aromaticity and Benzene → Electrophilic Aromatic Substitution (EAS) → Nucleophilic Aromatic Substitution (SNAr) → Nucleophilic Acyl Substitution → Amines: Structure, Basicity, and Reactions → Amine Reactivity: Nucleophilicity and Basicity → Amino Acid Structure and Properties → Peptide Bonds and Polypeptide Formation → Protein Primary Structure → Protein Secondary Structure → Protein Tertiary Structure → Enzyme Structure and Function → Transcription: DNA to RNA → RNA Types and Structure → RNA Structure and Intramolecular Base Pairing → RNA Processing and Splicing → Translation: RNA to Protein → Ribosomes: Protein Synthesis Machines → Translation: Initiation and Elongation → Post-Translational Modifications → Proteasomal Degradation and Ubiquitin-Mediated Marking → Cell Cycle Regulation and Checkpoints → Mitosis → Cytokinesis → Meiosis → Chromosomal Theory of Inheritance → Mendelian Genetics → Dominance, Recessiveness, and Allelic Interactions → Sex-Linked Inheritance → Non-Mendelian Inheritance Patterns → Population Genetics and Hardy-Weinberg Equilibrium → Natural Selection → Adaptation and Fitness → Life History Strategies: r- and K-Selection → Predator-Prey Dynamics and the Lotka-Volterra Model → Community Ecology: Structure and Organization → Species Interactions: Competition, Predation, Mutualism, and Parasitism → Trophic Levels and Food Webs → Energy Flow and Ecological Efficiency → Biogeochemical Cycles: Carbon, Nitrogen, and Phosphorus → Microbial Ecology and Biogeochemical Cycling → Symbiosis, Commensalism, and Parasitism in Microbes → Human Microbiome → Emerging Infectious Diseases → Infectious Disease Surveillance Systems → Outbreak Investigation → Epidemic Curve Interpretation and Outbreak Analysis → Temporal Clustering and Seasonality Analysis → Interrupted Time Series Design → Natural Experiments and Quasi-Experimental Design → Difference-in-Differences Analysis → Synthetic Control and Comparative Case Studies → Matching in Case-Control Studies → Odds Ratio and Case-Control Study Analysis → Attributable Risk and Population Attributable Fraction → Number Needed to Treat and Number Needed to Harm

Longest path: 248 steps · 1512 total prerequisite topics

Prerequisites (1)

Leads To (0)

No topics depend on this one yet.