Understanding risk and benefit figures

Medical statistics are presented in ways that are technically accurate and practically misleading. A few concepts protect against this.

Relative versus absolute risk

• Relative risk compares two groups.
• Absolute risk states the actual chance.
• A large relative change can be a tiny absolute one.
• Marketing and headlines favour relative figures.
• Always ask for the absolute numbers.

Consider a treatment halving a risk. If the risk was one in a thousand, one person in two thousand benefits. If it was one in ten, one in twenty benefits. The same relative figure describes very different situations.

Number needed to treat

• How many people must be treated for one to benefit.
• A low number means a large effect.
• A high number means most treated people gain nothing.
• The same calculation applies to harm.
• Comparing both gives a balanced picture.

This is one of the most usable concepts available to patients, and clinicians can often supply the figure if asked.

Five-year survival figures

• The proportion alive five years after diagnosis.
• Sensitive to when diagnosis occurred.
• Earlier diagnosis increases the figure even if nothing changes.
• Mortality rates are a better measure of whether treatment helps.

The third point explains why comparing survival rates between countries or eras can mislead: the difference may reflect detection practices rather than better treatment.

Screening statistics

• Screening finds conditions earlier.
• Some of those would never have caused harm.
• Treating them counts as a success but may not be one.
• Screening also produces false positives with real consequences.
• Benefit is real for some programmes and modest in others.

Screening decisions are genuinely more complicated than they appear, and asking about both benefits and harms is appropriate.

False positives and false negatives

• No test is perfect.
• False positives cause anxiety and further investigation.
• False negatives cause false reassurance.
• The rarer a condition, the more false positives relative to true ones.

The last point is counterintuitive. For rare conditions, most positive results from a good test can still be false positives, which is why confirmatory testing exists.

Confidence intervals

• A range within which the true value likely lies.
• A wide interval means substantial uncertainty.
• An interval crossing zero means the effect may not exist.
• Point estimates without intervals hide this.

Statistical and clinical significance

• Statistical significance means an effect is unlikely to be chance.
• It says nothing about whether the effect is large enough to matter.
• Large studies detect trivial differences.
• Ask about effect size, not only significance.

Surrogate outcomes

• Studies sometimes measure a marker instead of an outcome.
• Improving the marker does not always improve the outcome.
• There are historical examples where it did not.
• Ask what was actually measured.

A treatment that improves a blood test result has not necessarily improved anything a patient would notice or care about.

Who was studied

• Trial participants are often healthier than average patients.
• Older people and those with several conditions are underrepresented.
• Results may not transfer to you.
• Ask whether the evidence applies to your situation.

Applying figures to yourself

• Population figures describe averages, not individuals.
• Your baseline risk may differ substantially.
• Ask what your personal risk is estimated to be.
• Ask how that estimate was reached.

Risk over different time horizons

• A risk over ten years sounds different from the same risk annually.
• Ask what period a figure refers to.
• Lifetime risk figures can sound alarming and be misleading.
• Ask for risk over a horizon that matters to your decision.

Lifetime risk figures are commonly quoted and rarely the relevant number for a decision being made now. Asking for the figure over the next five or ten years usually produces something far more useful for weighing an immediate choice.

Reading about treatments online

• Patient forums describe experiences, not typical outcomes.
• People with unusual experiences post more often.
• Commercial sites present selected evidence.
• Prefer sources that state uncertainty.
• Bring what you find to your clinician rather than acting on it.

Forums are valuable for practical advice about living with a condition and unreliable as a guide to how common outcomes are. Keeping those two uses separate makes them much more useful than either dismissing them or treating them as evidence.

Framing effects

• The same figure described as survival or mortality feels different.
• Ninety per cent survival and ten per cent mortality are identical.
• People choose differently depending on the framing.
• Ask for both formulations.

This effect is robust and affects clinicians as well as patients. Asking for the number stated both ways is a simple defence against being steered by presentation rather than substance.

Lead time and length bias

• Lead time bias: earlier diagnosis lengthens measured survival without changing death.
• Length bias: screening preferentially finds slower-growing disease.
• Both make screening look more effective than it is.
• Mortality comparisons avoid these problems.

These two effects are the main reason why screening evaluation relies on randomised mortality data rather than survival comparisons, and why enthusiastic survival statistics should be read cautiously.

Overdiagnosis

• Finding conditions that would never have caused symptoms.
• Treating them creates harm without benefit.
• It is impossible to know in an individual case.
• It is measurable at population level.
• It is the main harm of screening programmes.

This is a genuinely difficult concept because the individual patient can never know whether they were overdiagnosed, which is why the discussion has to happen before screening rather than after.

A workable approach

• Ask for absolute numbers.
• Ask for the number needed to treat and to harm.
• Ask what was actually measured.
• Ask whether the evidence applies to people like you.
• Then decide what matters to you.

Summary

Relative figures overstate effects, so always ask for absolute numbers and for the number needed to treat. Five-year survival is sensitive to when diagnosis occurred, which is why it can improve without treatment improving. For rare conditions, most positive test results can still be false positives. And statistical significance says nothing about whether an effect is large enough to matter.

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