13 Research methods, statistics, critical review and evidence-based practice13.2 Epidemiological studies
13.2 Quantitative study designs
12 min read4 figures
Written by Resident Doctor Committee · Published
Observational and experimental designs
Experimental studies have the investigator assign and control the exposure each participant receives.
Observational studies only record exposures that arise without investigator allocation.
A study's purpose is the comparison its method was designed to make, not the background need that prompted it or one of its individual results.
Case series
A case series describes a small cluster of patients who share an exposure and an outcome. It has no comparison group and gives no estimate of risk.
It is the quickest way to raise a signal and generate a hypothesis, such as a suspected new adverse drug effect.
The self-controlled case series design assumes that the outcome event does not change the probability of later exposure.
Cross-sectional studies
A cross-sectional study measures exposure and outcome together, once, in individual participants sampled without regard to either. There is no follow-up and no time order between them.
It measures prevalence at one point in time and cannot give incidence, because no one is followed. If 60 of 300 people surveyed are cases, prevalence is 60/300 (20%).
A cross-sectional survey that estimates the odds of an outcome for an exposure is analytical, but neither can be shown to come first. Depression found with unemployment could reflect causation in either direction or shared causes.
Some exposures, such as genotype, must precede the outcome, but confounding still needs consideration.
A study spanning several areas is still cross-sectional if it records individuals. It is ecological only if the data are aggregate area-level summaries.
Diagnostic accuracy
Cross-sectional is the design for diagnostic accuracy: the index test and the reference standard are applied to the same people at one time.
Cross-tabulating the two results gives sensitivity and specificity.
Ecological studies
An ecological study measures exposure and outcome only as group or area aggregates, never linked to individuals, so the population is the unit of analysis.
It is quick and cheap with routine data and generates hypotheses, for example comparing regional unemployment with regional suicide rates.
The ecological fallacy is carrying an association between population-level aggregates over to the individuals in those populations.
Durkheim's regional comparisons of Protestantism and suicide show the fallacy: regional rates cannot show the religion of those who died.
An area-level link between antidepressant prescribing and suicide may reflect underlying rates of depression, not an effect of treatment in treated individuals.
Case-control studies
A case-control study samples people by outcome and looks back for exposure, comparing cases with controls on past exposure.
Controls should represent the population that produced the cases, and exposure data come from recall or from records collected earlier.
Strengths
It is the efficient design for a rare outcome or one that appears long after exposure, because every case recruited is informative.
It avoids the huge samples, long follow-up and attrition that cohort studies and trials would need for such outcomes.
It is cheaper and quicker than a cohort study, because exposure is ascertained retrospectively and no one is followed forward.
It can examine many exposures for one disorder at once, whereas a cohort study examines several outcomes of one exposure.
Control selection and matching
Control selection and exposure measurement are the main appraisal issues.
Individual matching on confounders at the design stage suits a small case-control study best.
Hospital controls admitted with other diseases may share the exposure under study, which biases the odds ratio towards the null (1).
Overmatching occurs when controls come from the case's own family or household and share the exposure, such as cohabiting spouses. Matching then also matches on the exposure and masks its effect.
Nested case-control studies
A nested case-control study takes cases arising in a defined cohort and controls from the same cohort who are still at risk and lack the outcome at the index date.
It is a retrospective observational design even when it uses register data recorded prospectively, because cases are selected after the outcome and exposure is traced backwards.
Measures from a case-control table
Exposure | Cases | Controls |
|---|---|---|
Exposed | a | b |
Not exposed | c | d |
Measure | Calculation |
|---|---|
Odds of exposure in cases | a/c |
Odds of exposure in controls | b/d |
Odds ratio | (a/c) / (b/d) = ad/bc |
Case exposure rate | a / (a + c), exposed cases divided by all cases |
Odds are the number with a characteristic divided by the number without it in the same group, not divided by the total. An odds ratio compares the odds of two groups.
The odds ratio states how much higher the odds of exposure are in cases than in controls. It is not a risk.
The investigator samples on outcome and fixes the case-to-control ratio, so the table gives no incidence, risk or relative risk. Only the odds ratio is meaningful as an effect measure.
The table does give exposure proportions, odds, the odds ratio and its confidence interval.
The width of the confidence interval and the p value relate to the confidence level and the sample size.
With conventional sampling, the odds ratio approximates the risk ratio when the outcome is rare.
In an exposure-stratified analysis, odds ratios are estimated against a reference category fixed at 1, which has no estimate or interval of its own.
Cohort studies
A cohort study selects people by exposure, or by a characteristic present at entry such as a diagnosis, and follows them forward to count later outcomes. Investigators allocate nothing.
Cohorts study rare exposures efficiently but need very large samples for rare outcomes, and selective loss to follow-up can distort results.
Prospective cohort studies
A prospective cohort study measures exposure at entry in people free of the outcome and follows them forward as outcomes accrue.
It records exposure before the outcome is known, which secures time order and avoids recall bias. Prospective longitudinal designs reduce recall bias generally.
It is the design for an early-life exposure with a later outcome, and for an exposure that cannot ethically be assigned. It gives the incidence of several outcomes and shows that exposure came before illness.
Its strength over a retrospective cohort is control over the quality and method of measuring exposure and confounders at the time.
It is usually costlier and slower than a case-control study, and its main drawback is the years of follow-up before outcomes accrue.
Retrospective cohort studies
A retrospective (historical) cohort study groups people by exposure recorded in the past and reads the later outcome from existing records. Both had already happened when the research began.
It has the same structure as a prospective cohort, analysed forward from exposure to outcome, and differs only in when the data are collected. Incidence can still be calculated.
It suits exposure recorded long ago with a long lag to outcome, giving incidence and relative risk without waiting years.
Its genuine weakness is record quality.
Measures from cohort data
Incidence counts new cases arising over time and is measured by following a disease-free cohort forward.
Cohort data give the risk in exposed and unexposed people, so relative risk can be calculated. The odds ratio overstates relative risk when the outcome is common.
Measure | Definition |
|---|---|
Relative risk (RR) | Risk in the exposed divided by risk in the unexposed; 1.0 means equal risk, so no raised risk with exposure |
Attributable risk (risk difference) | Incidence in the exposed minus incidence in the unexposed |
Attributable risk per cent (attributable fraction in the exposed) | The share of cases among exposed people that is due to the exposure |
Population attributable risk | Attributable risk multiplied by the prevalence of exposure in the population |
Population attributable fraction (Levin's formula) | p(RR - 1) / [1 + p(RR - 1)], where p is the prevalence of exposure |
Time-to-event outcomes
Among observational designs, only a cohort can generate a Kaplan-Meier survival curve. Individuals are free of the outcome at a defined start and followed forward with dates of events or censoring.
The group that reaches the event sooner, shown by medians or survival curves, is the one at higher risk of it.
A composite outcome counts only the events named in its definition, such as admission, suicide attempt, discontinuation, switch or addition of treatment, or death.
Non-randomised and historical comparisons
A non-randomised controlled trial allocates by a fixed, predictable rule (alternation, odd or even numbers, dates) or by patient choice. Its concurrent comparison arm makes it controlled, but not randomised.
A quasi-experimental study resembles a trial, because an intervention is deliberately introduced and compared, but it lacks random assignment.
A historical controlled trial compares people receiving a new intervention with a different group who received the comparator at an earlier, non-concurrent time.
A before-and-after design differs by using the same participants' earlier data.
Historical comparisons can blur: older cohorts who rated an old system stayed on after a new system began, so they met both, while the new intake met only the new system.
Randomised controlled trials
Randomisation sets a randomised controlled trial apart from observational designs. Chance allocation makes arms comparable on average in measured and unmeasured characteristics.
A study is still a randomised controlled trial when the investigator randomly allocates participants to blinded active or placebo arms after an uncontrolled open-label phase.
A treatment as usual (TAU) arm continues standard care unmodified, with nothing added by the study.
In an add-on (augmentation) trial, both arms keep the background treatment and only the added agent differs. The control arm is background treatment plus placebo.
An active-drug run-in before randomisation identifies and excludes participants who will not adhere, so those randomised are more compliant.
An open-label extension offers the active drug to all completers and follows them unblinded. It respects ethical limits on continuing placebo and can reveal delayed harms.
Blinding
Type | Who is unaware of allocation |
|---|---|
Single-blind | One party, such as the patient |
Double-blind | Two parties, such as patients and outcome raters |
Triple-blind | Also the analyst, who works on coded groups |
Trial designs
Design | How it works | Use or limit |
|---|---|---|
Parallel-group | Each participant receives one intervention; groups are compared side by side | Needed when the outcome is a one-off event such as relapse, or when effects carry over |
Cross-over | Every participant receives both treatments in randomised order, usually with a washout to limit carry-over | Suits only a stable condition and a quickly reversible drug effect |
Factorial | Tests two interventions alone and in combination, in a two-by-two grid of arms | Estimates each effect and whether they interact |
Cluster randomised | Allocates whole groups such as schools, wards or units, not individuals | For interventions delivered to groups such as a class; stops control participants picking up the intervention |
Sequential | No fixed sample size; results are reviewed as each pair completes, stopping when a pre-specified boundary is crossed | Can answer with fewer participants |
A cross-over trial needs fewer participants than a parallel design because each participant is their own control. Fixed personal characteristics cannot confound the comparison, whereas a parallel-group trial depends on randomisation for baseline balance.
Outcomes within a cluster are correlated, measured by the intraclass correlation coefficient (ICC), so the analysis and sample size must allow for clustering.
With clusters of roughly equal size, the design effect is 1 + (m - 1) x ICC, where m is the average cluster size. The effective sample size is the actual size divided by the design effect.
n-of-1 trials
An n-of-1 trial is a blinded randomised comparison of active treatment and placebo, or of two treatments, in repeated periods within a single patient.
It aims to optimise that patient's own treatment, not to give a generalisable result.
It suits a stable chronic condition treated with a fast-acting, reversible drug of uncertain benefit in this patient, with washout and attention to time trends and carry-over.
It is unsuitable for a potentially curative treatment with a lasting effect.
Superiority, equivalence and non-inferiority
Trial type | Question | Conclusion rule |
|---|---|---|
Superiority | Does treatment A beat treatment B? | A non-significant result shows only that superiority was not demonstrated |
Equivalence | Are the treatments similarly effective? | The whole confidence interval of the difference must lie inside both margins |
Non-inferiority | Is the new treatment not unacceptably worse? | Only the bound on the worse side must clear one pre-specified margin; silent on superiority |
Failing to show superiority does not show equivalence, because an imprecise trial may miss an important difference.
Intention-to-treat analysis
Intention-to-treat analysis compares participants in their allocated groups regardless of adherence, which preserves the randomised comparison.
Non-adherence dilutes differences, which in a non-inferiority trial can falsely favour similarity. Per-protocol analysis excludes non-adherers and can itself introduce selection bias.
Trial phases
Phase | Role |
|---|---|
0 to II | Too small or early to establish comparative benefit |
III | Large pre-licensing randomised comparison against placebo or standard treatment that supports a marketing authorisation |
IV | Follows licensing |
Systematic reviews and meta-analysis
A systematic review synthesises existing evidence with a protocol, an explicit search, eligibility criteria, structured extraction and appraisal.
A meta-analysis pools the results of existing studies, shown on a forest plot as separate studies plus a pooled diamond. It is secondary research and collects no new data.
Meta-analysis is optional within a review and needs comparable studies.
Systematic methods make decisions auditable but do not guarantee validity, since incomplete searches and biased primary studies still limit a review.
Qualitative research and audit
A qualitative study uses purposive sampling, open interviews and thematic analysis to understand experience and meaning. Recruitment stops when no new themes emerge.
Clinical audit measures current practice against an explicit standard, acts on the shortfall and repeats the measurement to close the loop. It is quality improvement, not research.
Designs in schizophrenia research
Design | What it shows | Example |
|---|---|---|
Adoption study | Separates genes from rearing environment, because adoptees share genes with biological relatives but a home with adoptive relatives | Danish adoption studies |
Archived childhood home movies rated blind against sibling controls | Early neuromotor abnormalities in those who later develop schizophrenia | Walker and Lewine |
Army conscript cohorts | Near-universal standardised testing before illness shows lower premorbid IQ in those later diagnosed | Swedish and Israeli studies |
Prospective follow-up of never-treated patients | The natural course of schizophrenia free of drug effects | Rural China; the pre-antipsychotic era |