Case-Control Study: Design, Matching, and Odds Ratios

A case-control study is an observational design that starts from the outcome. You select people who have the disease or outcome of interest (cases) and comparable people who do not (controls), then compare how often each group was exposed to a possible cause in the past. The measure of association is the odds ratio.

Use a case-control design when the outcome is rare, when it takes a long time to develop, or when you want to screen several possible exposures for one outcome. It is often the only feasible design for rare diseases: following 100,000 people forward to observe 30 cases is expensive; finding 30 cases in hospital records and choosing controls is not.

How a case-control study works

1. Define the outcome precisely (diagnostic criteria, date of diagnosis).
2. Identify cases from a defined source: a hospital, registry, or a cohort.
3. Select controls from the same source population that produced the cases.
4. Measure past exposure in both groups, the same way, ideally without knowing who is a case.
5. Compare exposure odds between cases and controls.

Because the investigator decides how many cases and controls to include, the proportion of cases in the sample is artificial. That single fact explains most of the rules below.

Case-control vs cohort

Case-control studies are usually done with existing records or interviews, which makes them a common type of retrospective study. A retrospective study that samples by exposure, however, is a retrospective cohort, not a case-control study.

Choosing controls

Control selection makes or breaks a case-control study. The guiding principle: controls should represent the exposure distribution in the population that gave rise to the cases. Ask: if a control had developed the disease, would they have become a case in this study?

Common control sources:

• Population controls (random sample of residents): best representativeness, but lower participation.
• Hospital controls (patients with other conditions at the same hospital): convenient, but their conditions must not be related to the exposure. Smokers are overrepresented among many hospital patients, for example.
• Neighborhood, friend, or family controls: help match on social environment, but can overmatch on exposure.
• Controls sampled from a cohort (nested case-control): controls are drawn from cohort members still at risk at the time each case occurred. This design keeps the efficiency of case-control sampling inside a well-defined cohort.

Using several controls per case (up to about four) increases precision; beyond that the gain is small.

Matching

Matching makes controls similar to cases on chosen variables, usually strong confounders such as age and sex.

• Individual matching: each case gets one or more controls with the same values (for example, same sex and age within 5 years).
• Frequency matching: the control group has the same overall distribution of the matching variables as the cases.

Rules to remember:

1. Matching does not remove confounding by itself in a case-control study. It can introduce selection bias toward the null unless the analysis accounts for it. Analyze individually matched data with conditional logistic regression (or, for 1:1 pairs and one binary exposure, the matched-pairs odds ratio and McNemar's test). Analyze frequency-matched data with ordinary logistic regression that includes the matching variables.
2. You cannot study the effect of a matching variable, because you forced it to be equal between groups.
3. Do not overmatch. Matching on a variable that is caused by the exposure, or that is strongly related to exposure but not to the outcome, wastes information and can bias results.

Why the odds ratio, not relative risk

In a cohort, risk is cases divided by the number of people. In a case-control study you chose how many controls to include, so "cases / (cases + controls)" depends on your sampling, not on the population. The odds ratio does not.

You can see this directly. In the worked example below, the "risk ratio" you would naively compute is 1.56. Double the number of controls (keeping the same exposure proportions) and it becomes 1.71. The odds ratio stays at 2.00 either way.

The OR is symmetric: the odds ratio of exposure among cases vs controls equals the odds ratio of disease among exposed vs unexposed. When the disease is rare in the source population (a common rule of thumb is under 10%), the OR approximates the relative risk. With incidence density sampling (controls drawn from those at risk when each case occurs, as in nested designs), the OR estimates the incidence rate ratio without needing the rare disease assumption.

If you are comparing ratio measures across study designs, the hazard ratio guide has a side-by-side table of HR, RR, and OR.

Worked example: a 2×2 table

A hypothetical study recruits 200 patients with a liver disease (cases) and 400 controls without it from the same catchment area, and asks about past occupational solvent exposure.

Step 1: exposure odds in each group.

• Cases: 80 / 120 = 0.667
• Controls: 100 / 300 = 0.333

Step 2: the odds ratio.

OR = (a × d) / (b × c) = (80 × 300) / (120 × 100) = 24,000 / 12,000 = 2.00

Cases had twice the odds of past solvent exposure compared with controls.

Step 3: the 95% confidence interval (Woolf / log method).

• ln(OR) = ln(2.00) = 0.693
• SE of ln(OR) = sqrt(1/a + 1/b + 1/c + 1/d) = sqrt(1/80 + 1/120 + 1/100 + 1/300) = 0.185
• ln(OR) ± 1.96 × SE = 0.693 ± 0.362 → 0.331 to 1.055
• Exponentiate: 95% CI 1.39 to 2.87

Step 4: test of association. Pearson chi-square (no continuity correction) gives χ²(1, N = 600) = 14.29, p < .001. The Wald z for ln(OR) is 0.693 / 0.185 = 3.75, which agrees.

You can reproduce the OR and CI with the odds ratio calculator and the test with the chi-square calculator. If any expected cell count is below 5, use the Fisher exact test instead.

The naive "risk ratio" trap. Computing (80/180) / (120/420) gives 1.56. Double the controls to 200 exposed and 600 unexposed and the same formula gives (80/280) / (120/720) = 1.71, while the OR is still (80 × 600) / (120 × 200) = 2.00. Only the OR is meaningful here.

Matched-pairs example

In a 1:1 individually matched study, only discordant pairs carry information. Suppose there are 25 pairs where the case was exposed and the control was not, and 10 pairs where the control was exposed and the case was not.

• Matched OR = 25 / 10 = 2.50
• SE of ln(OR) = sqrt(1/25 + 1/10) = 0.374, giving 95% CI 1.20 to 5.21
• McNemar's test: (25 − 10)² / (25 + 10) = 6.43, χ²(1) = 6.43, p = .011

Concordant pairs (both exposed or both unexposed) do not enter the calculation.

Adjusting for confounders

The crude OR above ignores age, sex, alcohol use, and other factors. In practice you would fit a logistic regression (or conditional logistic regression for matched sets) with the exposure and selected confounders, and report both crude and adjusted ORs. The adjusted OR is exp(B) for the exposure coefficient, with CI exp(B ± 1.96 × SE).

How to report a case-control study (APA 7 and STROBE)

Follow the STROBE checklist for case-control studies. In particular, describe:

• How cases were defined, identified, and ascertained, and the time period
• The source of controls and the rationale for choosing them
• Matching criteria and the number of controls per case
• How exposure was measured and whether assessors were blinded to case status
• Participation rates for cases and controls
• The analysis, including how matching was handled

Results sentence (APA 7):

With adjustment:

Matched analysis:

Keep the leading zero on ORs and CIs, drop it on p values, and give exact p values unless smaller than .001.

Common biases and mistakes

1. Controls from the wrong population. If controls would not have been cases had they developed the disease, the OR is biased.
2. Recall bias. Cases often remember exposures more thoroughly. Use records where possible, structured questionnaires, and blinded interviewers.
3. Interviewer bias. An interviewer who knows case status may probe harder. Blind them when feasible.
4. Calling the OR a relative risk, especially when the disease is common.
5. Ignoring matching in the analysis, or matching on too many variables.
6. Reverse causation. Early disease can change exposure (people with early symptoms change their diet). Define an exposure window that ends before symptom onset.
7. Too few cases for the number of confounders. Logistic regression needs enough cases (and controls) per parameter; plan sample size in advance with a power analysis.

FAQ

Is a case-control study prospective or retrospective?

Most are retrospective with respect to exposure, because exposure is measured after the outcome has occurred. Cases can still be enrolled prospectively as they are diagnosed (an incident case-control design).

What is a nested case-control study?

A case-control study drawn from an existing cohort: all cases in the cohort are included, and controls are sampled from cohort members at risk when each case occurred. It saves cost when measuring exposure is expensive, such as assaying stored blood samples.

Can a case-control study prove causation?

No single observational study proves causation. A well-designed case-control study can provide strong evidence of association, which, with consistency across studies, temporal order, and dose-response, supports causal inference.

How many controls per case should I use?

One to four. Precision improves noticeably up to about four controls per case and only slightly after that.

What test should I use for a case-control 2×2 table?

The chi-square test for unmatched data with adequate expected counts, Fisher's exact test for small counts, and McNemar's test for 1:1 matched pairs. Report the odds ratio and its 95% CI in all cases.

From your case-control dataset to a draft

If your data are already in a spreadsheet with case status, exposures, and covariates, Data2Paper's Generate Paper can run the descriptive tables, crude and adjusted odds ratios, and draft the Methods and Results sections. The first half of the paper is free to generate and preview; the full draft is a one-time $19.90. It is an AI-generated draft without expert review, so check the analysis choices (especially how matching was handled) and every number before submission. The clinical data analysis guide covers the wider workflow.