HC5: Case control studies

Case-control study

In a case control study, instead of a census (information about everybody), sampling is done. The cases are compared to a sample of the entire population. This happens as follows:

1. Case detection
2. Sample of the controls
3. Exposure status assessment among cases and among controls
   • E.g. comparison between the smoking status among the population and the smoking status among the population
4. Exposure-outcome relation estimation

Case-control versus cohort:

A case-control study is very efficient compared to a cohort study:

• Cohort: requires information about the entire study population
• Case-control: requires information about part of the controls
  • Advantage: practical efficiency, particularly when:
    • Disease is rare
    • There is a long/unknown latency period
    • Assessment exposure is expensive
  • Disadvantage: it is not possible to estimate absolute disease frequencies (risk/rate)

Case-control studies do not allow for:

• Randomization
• Absolute measures of disease frequency

Odds ratio

The odds ratio is the ratio of odds of exposure among cases and odds of exposure among controls. It is the only measure that can be estimated with a case control study.

The following calculations can be done:

• Odds ratio (OR) = (a/b)/(c/d) = ad/bc

Interpretation:

The interpretation of the odds ratio depends on how the control study is done and what the controls represent. How this can be interpreted depends on the moment of sampling controls. Moments of sampling controls are:

• At the end of the follow-up → sampling from non-cases
• At the start of the follow-up → case-cohort
• During the follow-up (each time a case occurs) → incidence density sampling
  • Each time a case is identified, a control is sampled from the cohort

Controls can represent various things, such as:

• Non-cases
• Total number of subjects
• Person time

Sampling of non-cases:

In this case, non-cases (those who did not develop the outcome of interest) are sampled → the controls represent the non-cases in the cohort study:

• c = k x C
• d = k x D
  • OR = ad/bc = (a/(k x C))/(b/(k x D))
  • RR = (A/(A+C))/(B/(B+D)) = (A/C)/(B/D) = AD/BC = OR
    • This only is the case if A ≪C and B ≪D → in case of a rare outcome
      • If the outcome is <10%
      • The odds ratio can be interpreted as the risk ratio

Sampling at baseline:

In this case, sampling at baseline (a case-cohort study) is done → controls represent the total number of subjects:

• c = k x (A+C)
• d = k x (B+D)
• OR = (a/(k x (A+C))/(b/k x (B+D)) = (a/(A+C))/(b/(B+D)) = RR

At the start of follow-up, the OR can be interpreted as the RR.

Incidence density sampling:

In this case, incidence density sampling is done → controls represent person time:

• c = k x T1
• d = k x T0
• OR = (a(k x T0))/(b(k x T1)) = (a/T1)/(b/T0) = RR

Each time a case is identified at a moment in time, information about the controls received. At every time point, someone can act as a control who does not have the outcome of interest yet. The OR is numerically the same as the RR in a cohort study.

Summarized:

In short, in a case-control study, exposure among the cases is compared to exposure among the controls. Depending on when the controls are sampled, the interpretation of the odds ratio changes → the odds ratio can show the (estimated) risk ratio in several samples:

• Sampling from non-cases: OR = OR ≈ RR
• Sampling at baseline (case-cohort): OR = RR (risk ratio)
• Incidence density sampling: OR = RR (rate ratio)

Important facts

Who to sample:

Controls should be representative in terms of exposure of the “source population”. The “source population” is the population within which the study is conducted (the cohort/region). In case of smoking and lung cancer, controls consist of the subjects without lung cancer. These can be:

• Hospital controls
  • Often not representative of the source population
• Friends, family or neighbor controls
  • Often not representative of the source population
• Population controls
  • More representative of the source population
  • Downside: individuals might not want to participate

Amount of controls per case:

The more controls there are per case, the more narrow the confidence interval will be and the more precise the OR. How many controls there are per case refers to precision, not to validity:

• 1 control per case is often optimal, notably when:
  • Data collection is expensive
  • Many cases are detected
• >4 controls per case are of little added value
  • Increases the precision only marginally

Cohort or case control?

Whether there is a cohort or a case-control depends on the situation:

• A study in which patients with a genetic polymorphism are compared to control subjects with respect to their risk of developing osteoarthritis → cohort
  • Individuals with a certain exposure are compared to individuals with a different exposure type
• A study in which patients with a deep venous thrombosis are compared to their healthy relatives (controls) with respect to their risk of developing an ischemic stroke → cohort
  • Individuals who have a disease are compared to individuals without a disease, but the risk of another disease is calculated
• A study in which patients with esophagus cancer are compared to their healthy relatives (controls) with respect to their cigarette smoking behavior → case-control
  • Individuals who are exposed are compared to non-exposed
• A randomized controlled trial of the cholesterol lowering effect of statin therapy (vs. placebo) → cohort
  • RCTs can never be case-control studies

Study design

In short, a study design is built up as follows:

• Experimental study
  • Cohort
• Observational study
  • Cohort
  • Case-control