Community Medicine — Biostatistics and Demography, NMC MBBS licence examination syllabus (Nepal Medical Council).
A drug "halves your risk". Of what, from what, and how many people must take it for one to benefit?
Two headlines describe the same trial. The first says the treatment halves the risk of death. The second says it reduces deaths from 0.4% to 0.2%. Both are accurate. One sells the drug; the other tells you that 500 people must take it for one life to be saved.
Learning to move between those two descriptions is most of what biostatistics is for in clinical practice. The epidemiology chapter covered how studies are designed and how a diagnostic test is judged. This chapter starts after the study is finished: the result is on the page — what does it actually mean?
The p-value is the most quoted and most misunderstood number in medicine, so it is worth being precise about what it asks.
The p-value answers exactly one question: if there were truly no effect, how often would chance alone produce a result at least this extreme? A small p-value means the data would be surprising in a world where the treatment did nothing.
Notice what that does not say. It is not the probability that the finding is true. It is not the probability that chance produced it. And it says nothing whatever about how large the effect is.
The conventional cut-off of 0.05 is a convention, not a law of nature — there is no meaningful difference between p = 0.049 and p = 0.051, and treating one as a discovery and the other as nothing is a mistake with a long history. Report the effect and its confidence interval; let the p-value support the argument rather than carry it.Why does study size matter so much here? Because with a large enough sample, a difference far too small to matter to any patient will still be statistically significant. Significance tells you an effect is probably not zero. It does not tell you the effect is worth having.
Where a p-value gives a verdict, a confidence interval gives a range — and the range is usually the more useful thing.
A 95% confidence interval gives the range of effect sizes reasonably compatible with the data. Two features matter when you read one:
Once you accept an effect is real, the next question is how big it is — and there are several ways to express that, which do not mean the same thing.
Relative riskRisk in the exposed divided by risk in the unexposed. Needs incidence, so it comes from cohort studies and trials. Answers "how many times more likely?"
Odds ratioUsed in case-control studies, where incidence cannot be measured because the investigator chose how many cases and controls to recruit. Approximates the relative risk when the disease is rare.
Absolute risk reductionThe plain difference between the two risks. This is the number that tells you whether the effect matters to a person.
Number needed to treat1 ÷ ARR. How many patients must be treated for one to benefit. Small is good; a large NNT means most people treated get nothing.
This is the single most useful idea in the chapter, and it is worth seeing with numbers.
Take a treatment that halves risk. In a common disease, risk might fall from 40% to 20% — an absolute reduction of 20 percentage points, so the NNT is 1 ÷ 0.20 = 5. Treat five patients, help one. That is a good treatment.
Now the same 50% reduction in a rare disease: risk falls from 0.4% to 0.2%. The absolute reduction is 0.2 percentage points, so the NNT is 1 ÷ 0.002 = 500. Treat five hundred patients, help one — and expose all five hundred to the side effects and the cost.
Both scenarios are honestly described as "a 50% risk reduction". The relative figure is identical; the clinical meaning is not remotely the same. This is why benefits are advertised in relative terms and harms in absolute ones — and why you should ask for the other number before you are persuaded.(Those figures are arithmetic illustrations chosen to make the point clearly. They are not data about any particular disease or drug.)
Before any test is applied, data has to be summarised — and the right summary depends on the shape of the distribution.
Mean, median and mode. The mean is the arithmetic average and uses every value, which is also its weakness: it is dragged by extreme values. The median is the middle value when data are ordered, and is barely affected by outliers. The mode is the commonest value.
Why does this matter clinically? Consider hospital length of stay, where most patients leave within days but a few stay months. The mean is pulled upward by those few and describes almost nobody. The median describes the typical patient. Skewed data are better summarised by the median — and income, length of stay and parasite counts are all skewed.
Spread. The standard deviation summarises how far values typically fall from the mean. In a normal distribution, a predictable proportion of observations lie within one, two and three standard deviations of the mean — which is where reference ranges come from.
Do not confuse the standard deviation with the standard error. The standard deviation describes how much individuals vary. The standard error describes how precisely you have estimated the mean, and it shrinks as the sample grows. A large study can have a small standard error and still show wide individual variation — the two answer different questions.Public health measures are ratios, and almost every exam error with them is a denominator error rather than an arithmetic one.
The pattern is mostly regular. Rates concerning babies are expressed per 1000 live births: infant mortality (deaths under one year), neonatal mortality (first 28 days), and under-5 mortality. Crude birth and death rates are per 1000 mid-year population.
The exception is the one examiners like. The maternal mortality ratio is expressed per 100,000 live births — a different multiplier, because maternal deaths are far rarer, and a figure per 1000 would be an unhelpful decimal.
Why is "crude" called crude? Because it ignores age structure. A country with many older people will have a higher crude death rate than a country with a young population even if health care is identical, simply because more of its population is at an age when people die. Comparing two populations fairly requires standardising for age.
Two further ideas complete the demographic picture.
Total fertility rate is the average number of children a woman would have if she experienced current age-specific fertility rates throughout her reproductive life. Replacement level is slightly above two — slightly, because not every child survives to reproduce and slightly more boys are born than girls.
The demographic transition describes what happens as a country develops. Death rates fall first, driven by sanitation, nutrition and infection control, while birth rates stay high — so the population grows quickly. Birth rates fall later, as child survival improves, women's education rises and family planning becomes available. The gap between the two falls is where population growth happens.
The order matters and explains a common confusion: rapid population growth in a developing country is usually a sign that mortality has improved ahead of fertility, not that fertility has risen. The population pyramid shows the same story in a picture — a broad base means a young, growing population; a narrowing base means fertility has fallen.For any current national or global figure, use your own up-to-date source. This chapter deliberately quotes none, because such figures change with each survey round.
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