Editing Epidemiology (section)

=== Case-control studies ===
[[case-control study|Case-control studies]] select subjects based on their disease status. It is a retrospective study. A group of individuals that are disease positive (the "case" group) is compared with a group of disease negative individuals (the "control" group). The control group should ideally come from the same population that gave rise to the cases. The case-control study looks back through time at potential exposures that both groups (cases and controls) may have encountered. A 2×2 table is constructed, displaying exposed cases (A), exposed controls (B), unexposed cases (C) and unexposed controls (D). The statistic generated to measure association is the [[odds ratio]] (OR),<ref>{{Cite journal |last1=Bewick |first1=Viv |last2=Cheek |first2=Liz |last3=Ball |first3=Jonathan |date=February 2004 |title=Statistics review 8: Qualitative data – tests of association |journal=Critical Care |volume=8 |issue=1 |pages=46–53 |doi=10.1186/cc2428 |doi-access=free |issn=1466-609X |pmid=14975045|pmc=420070 }}</ref> which is the ratio of the odds of exposure in the cases (A/C) to the odds of exposure in the controls (B/D), i.e. OR = (AD/BC).{{citation needed|date=March 2023}}

{| class="wikitable"
|-
!
! Cases
! Controls
|-
| Exposed
| A
| B
|-
| Unexposed
| C
| D
|}

If the OR is significantly greater than 1, then the conclusion is "those with the disease are more likely to have been exposed", whereas if it is close to 1 then the exposure and disease are not likely associated. If the OR is far less than one, then this suggests that the exposure is a protective factor in the causation of the disease.
Case-control studies are usually faster and more cost-effective than [[cohort studies]] but are sensitive to bias (such as [[recall bias]] and [[selection bias]]). The main challenge is to identify the appropriate control group; the distribution of exposure among the control group should be representative of the distribution in the population that gave rise to the cases. This can be achieved by drawing a random sample from the original population at risk. This has as a consequence that the control group can contain people with the disease under study when the disease has a high attack rate in a population.{{citation needed|date=March 2023}}

A major drawback for case control studies is that, in order to be considered to be statistically significant, the minimum number of cases required at the 95% confidence interval is related to the odds ratio by the equation:

:<math>\text{total cases} = A+C = 1.96^2 (1+N) \left(\frac{1}{\ln(OR)}\right)^2 \left(\frac{OR+2\sqrt{OR}+1}{\sqrt{OR}}\right) \approx 15.5 (1+N) \left(\frac{1}{\ln(OR)}\right)^2</math>

where N is the ratio of cases to controls.
As the odds ratio approaches 1, the number of cases required for statistical significance grows towards infinity; rendering case-control studies all but useless for low odds ratios. For instance, for an odds ratio of 1.5 and cases = controls, the table shown above would look like this:

{| class="wikitable"
|-
!
! Cases
! Controls
|-
| Exposed
| 103
| 84
|-
| Unexposed
| 84
| 103
|}

For an odds ratio of 1.1:

{| class="wikitable"
|-
!
! Cases
! Controls
|-
| Exposed
| 1732
| 1652
|-
| Unexposed
| 1652
| 1732
|}