13 Research methods, statistics, critical review and evidence-based practice13.2 Epidemiological studies
13.2.1 Probability sampling
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Written by Resident Doctor Committee · Published
Populations, frames and samples
Term | Meaning |
|---|---|
Target population | The whole group the results are meant to generalise to |
Sampling frame | The list the sample is actually drawn from |
Sample | The units drawn from the frame |
Participants | The people in the sample who actually take part |
Parameter | A numerical property of the whole population |
A census includes every member of the target population, so the sample size equals the population size.
Sampling with replacement puts each selected unit back before the next draw, so it can be selected again and appear more than once.
Coverage error arises when the frame misses part of the target population; household surveys miss people living in institutions and people who are homeless.
Probability and non-probability sampling
Probability sampling gives every member of the population a known, non-zero chance of selection through a random step. In non-probability methods that chance cannot be calculated.
Non-probability method | How people are chosen |
|---|---|
Convenience | Patients are taken only because they are close at hand, with no frame and no random step |
Purposive | The researcher chooses who to include |
Quota | Preset numbers per subgroup, such as sex and age, are filled with whoever is approached first |
Snowball | Participants recruit further participants from their contacts |
A sample is most representative when a probability method draws it from a complete frame, which removes selection bias, and it is large enough to keep random sampling error small.
Random sampling error shrinks as the sample grows, but coverage error and non-response bias are systematic, so a larger sample does not remove them.
Simple random sampling
Simple random sampling gives every member of the frame the same independent chance of selection, and every possible set of the chosen size the same chance of being the sample.
It uses no subgroups, clusters or fixed interval, and it needs a complete list of the frame.
Without replacement, each unit's chance of selection is n/N, where n is the sample size and N the frame size.
Systematic sampling
Systematic sampling takes one random start, then every kth unit through an ordered list, where k = N/n.
It also works on a stream of arrivals, such as every tenth attender.
It spreads the sample evenly through the list and is easy to carry out.
Periodicity is its weakness: a cycle in the list that matches the interval biases the sample. With one admission a day, taking every seventh admission samples a single weekday.
Stratified and quota sampling
Stratified random sampling divides the frame into mutually exclusive subgroups (strata) on a defined characteristic, such as age, sex or region, then selects at random within every stratum.
This guarantees that smaller groups are represented, and it improves precision when strata differ on the outcome.
Allocation | Sampling fraction | Consequence |
|---|---|---|
Proportional | The same in every stratum | The sample mirrors population proportions |
Disproportionate | Higher in a chosen stratum, for example over-sampling a small group | The sample does not mirror the population, so the analysis must weight it |
Quota sampling differs from stratified sampling only in its last step: it fills each subgroup with whoever comes first, not by random selection.
Cluster and multistage sampling
Cluster sampling draws whole naturally occurring groups at random, such as care homes, schools or general practices, and includes everyone in each chosen group.
It saves travel and listing costs and works where no list of individuals exists.
It loses precision because members of a group resemble each other, so each extra person adds less independent information.
Multistage random sampling makes random draws at successive nested levels, such as areas, then institutions, then individuals, so individuals inside the chosen groups are themselves sampled.
It makes national surveys feasible when no single list of the population exists.
Selecting 20 wards and every inpatient is cluster sampling; selecting 10 patients within each ward is two-stage sampling.
The Adult Psychiatric Morbidity Survey selects addresses by stratified multistage random sampling, then a randomly selected adult; it covers people aged 16 and over in private households in England.
The design effect measures the precision lost to clustering: design effect = 1 + (m - 1) x rho, where m is the average number sampled per cluster and rho the intracluster correlation.
Adding clusters usually helps precision more than adding people to existing clusters, and the analysis must allow for clustering or its confidence intervals will be too narrow.
Nested case-control studies
Incidence density (risk-set) sampling selects controls at the time each case arises, from cohort members still at risk, matched on time at risk.
When exposure data come from records written before the outcome existed, recall bias is the error least likely to affect the study.
Such a study can still suffer residual confounding, loss of cases, incomplete capture of exposure and low power for rare exposures.