Understanding health research: probability, risk and uncertainty

Identify the people, event, and time frame

“Ten people developed a disease” is incomplete. Were they ten out of a hundred or ten thousand? Were they followed for a year, a decade, or a lifetime? Was the event a new diagnosis, a symptom, admission to hospital, or death? These choices determine what the number means. Before comparing studies, align the denominator, outcome definition, and observation period; a yearly risk cannot be compared directly with a lifetime risk.

Begin with the simplest setting: people initially free of a particular disease are followed for a fixed period, and new cases are counted. In real studies, follow-up may differ between participants, so investigators may report events per person-year. An incidence rate relates to risk over time but is not the same quantity. A headline giving only a multiplier has left essential interpretation unfinished.

Absolute and relative changes describe the same comparison

All numbers here are invented for teaching and describe no actual treatment. Suppose two comparable groups of 100 people complete one year of observation. The target event occurs in 10 controls and 5 people receiving an intervention. Their absolute risks are 10% and 5%. The absolute reduction is 5 percentage points: 5 fewer people with the event per 100.

Relative risk is 5% divided by 10%, or 0.5, giving a 50% relative reduction. “Risk halved” and “5 fewer per 100” therefore describe the same result. If another population started at 2 events per 1,000, the same hypothetical relative reduction would mean 1 fewer per 1,000. Actual relative effects need not remain constant across populations; this example illustrates arithmetic. Decisions also require evidence about credibility, duration, and adverse outcomes, not just an impressive percentage.

Draw the example as two grids of 100 squares, shading 10 in one and 5 in the other, using the same scale. The five fewer shaded squares show the absolute difference. A chart whose vertical axis starts near the observed values can create a different visual impression from one starting at zero. Check axes and scales as well as the height of bars.

A sample estimates a probability, not an individual future

Even a well-conducted study might count a different number of events with a different sample. An observed 5% estimates risk in a relevant population; it is neither an unchanging constant nor a way of identifying which five individuals will become ill. Small samples and few events usually make estimates less stable. Participant numbers matter, but so does the number of events actually observed.

A confidence interval expresses statistical uncertainty as a range. Under the specified model assumptions, repeatedly sampling and constructing 95% confidence intervals in the same way would produce intervals that cover the true parameter about 95% of the time. It does not contain 95% of individual people or predict one person's symptoms. A narrow interval suggests precision, but systematic recruitment or measurement errors can still produce a precise estimate of the wrong target. Precision and credibility require separate judgments.

Statistical reference: Office for National Statistics

Statistical significance does not settle practical importance

P values are frequently reported in papers. First identify the null hypothesis being tested, such as no difference in effect between two interventions. A P value concerns the probability of results at least as extreme as those observed, assuming that null hypothesis and the specified statistical model. It is not the probability that the conclusion is wrong or that a treatment works. Treating 0.05 as an absolute dividing line can make nearly similar findings sound contradictory.

Read effect size, interval width, study quality, and practical importance together. A very large study can detect a difference too small to matter in daily life. A small study may leave a meaningful effect unresolved. If researchers examine many outcomes and advertise only the most favorable one, multiple testing and selective reporting also matter. “Not statistically significant” does not prove no effect, just as “significant” does not prove a useful benefit for every person.

Why a positive test still needs interpretation

Tests can miss disease or flag it when it is absent. Sensitivity is the proportion of people with the target condition who test positive. Specificity is the proportion without it who test negative. A person usually asks a different question: given my positive result, how likely is the condition? That also depends on how common it was in the tested population and why testing was done.

Here is another invented illustration. Among 1,000 people, 10 have a condition. A test detects 9 of them, while approximately 50 of the other 990 receive false-positive results. Of about 59 positive results, only 9 are true positives. This describes no real test; it shows how false positives can outnumber true positives when disease is uncommon. Symptoms, exposure history, examination, and appropriate confirmation help interpretation. A positive result is not automatically a diagnosis, and one negative result does not erase concerning symptoms.

Testing reference: National Cancer Institute

Turn statistics into an understandable statement

To explain a study to someone else, use a consistent sequence: who was studied, what was compared, for how long, how many events occurred in each group, how large the difference was, and how uncertain the estimate remains. Keep a common denominator such as per 100 or per 1,000. List benefits and harms separately rather than compressing them into a single “success rate.”

If a number was not reported, say so instead of filling the gap. Applicability requires comparing age, existing illness, concurrent treatment, starting risk, and the outcome that matters. One person may prioritize symptom relief; another may place more weight on adverse effects or treatment burden. The same evidence can therefore inform different choices. Statistics should clarify what is known and unknown, allowing a more concrete discussion rather than replacing judgment with an apparently precise score.

When comparing reports, temporarily remove words such as breakthrough or dramatic and retain the population, numbers, time frame, and outcomes. Retell the finding in your own words. If those essentials are missing, identify the gap. Leaving a judgment open is a useful response to uncertainty.

Bilingual terms

绝对风险 · Absolute risk

The probability of an event in a defined population over a stated period.

绝对风险差 · Absolute risk difference

The difference between two comparable risks, expressed in percentage points when subtracting percentages.

阳性预测值 · Positive predictive value

The proportion of positive test results that are true positives; it depends in part on disease prevalence in the tested population.

Sources and further reading

• NCI：绝对风险的定义
• NCI：癌症统计与个人解释的边界
• Cochrane：效果量与估计
• Cochrane：解释结果与结论
• 英国国家统计局：调查的不确定性
• MedlinePlus：怎样理解化验结果
• CDC：资料分析与解释
• NCI：筛查检测的敏感度、特异度与预测值
• 美国统计学会：P值的使用与解释声明

Original course source-check record: 9 September 2026. Full Chinese and English sentence-by-sentence language review: 14 September 2026. AI editing and language review are not human clinical review. Linked institutions have not participated in or endorsed this course.