Case-control studies

Learning goals

After this lesson, you should be able to:

  • Explain why one might one prefer to conduct a case-control study over a cohort study
  • Explain why odds ratios rather than relative risks are used as a measure of association in case-control studies
  • Compute an interpret an odds ratio from study data





Recap of video material

Cohort vs. case-control studies

Nature of sampling

  • Cohort: Sample by exposure status
  • Case-control: Sample by disease status

Resources needed

  • Cohort:
    • If using a prospective cohort study, a lot of time might be needed for the disease to develop
    • Might need to enroll a large number of patients if the disease is rare
  • Case-control:
    • All data on outcomes and exposures are available without having to wait for follow up (like a retrospective cohort study)

Other considerations

Odds

Odds are, when someone talks about odds, they’re not talking about odds.

If pp is the probability of an event (say, the risk of disease in an exposed group), the odds of that event is:

odds=p1−p\mathrm{odds} = \frac{p}{1-p}

In other words, the odds tells us how much more likely an event is to happen than not happen.

  • Unlike probability, it is not between 0 and 1. Odds can go from 0 to infinity.
  • Increasing odds does mean increasing probability.
    • If Event A has higher odds than Event B, Event A is indeed more likely than Event B.

Quick exercise: Jump to Moodle, and open the PDF titled 06_case_control_studies_activity. Let’s do Exercise 1.

Odds ratios as measures of association

Jump to Moodle, and open the PDF titled OR_RR_handout. We’ll walk through this handout together.

Potential biases in selection of cases and controls

Study: Tuberculosis and cancer

  • Context and study design
    • 1929 study investigated whether tuberculosis protects against cancer
    • Autopsies at Johns Hopkins Hospital were examined and this led to the identification of 816 cancer patients
    • 816 controls were identified from the remaining autopsies
  • Results:
    • In the 816 cancer patients, 54 had tuberculosis (6.6%)
    • In the 816 controls, 133 had tuberculosis (16.3%)
    • Because tuberculosis was more common in the controls, it appeared that tuberculosis was protective
  • Problems with control selection
    • Tuberculosis was a major cause of being admitted to Johns Hopkins Hospital at the time
    • The prevalence of tuberculosis among both cases and controls was likely over-represented but likely more so in the controls. Why? If one did not have cancer, there had to be SOME reason for being in the hospital. At the time, that reason was very commonly tuberculosis.
  • Possible better approaches
    • Guiding goal: Want the controls to accurately represent the people in the population who don’t have disease
    • Survey Baltimore neighborhoods to find controls and ascertain their tuberculosis exposure

Exploring cohort and case-control studies via simulation

The interactive application available at https://lesliemyint.shinyapps.io/cohort_case_control/ allows for exploration of the properties of relative risks and odds ratios in cohort and case-control studies. (If you are interested in coding in R and data science, the application is an example of something that you could create in going through the Data Science curriculum in MSCS.)

  1. By default, the simulation shows a population of 1 million people in which the disease is rare.
    1. Check the calculations for the relative risk and odds ratio. (These are labeled as “True” values because they are computed in the whole population.)
    2. Are the true RR and OR close? Briefly explain why or why not.
    3. Now click the “Common (30%)” button under “Rarity of disease”. How do the RR and OR compare now? Briefly explain.

The advantage of simulations is that we know the true values of the quantities that we’re trying to estimate (here: ORs and RRs). We can use that knowledge to examine how well our study designs “work” - that is, how well they estimate the truth when we don’t have access to the whole population.

  1. Clicking the “Perform each study once” button carries out both a cohort and a case-control study in the population with the selected disease rarity. That is, for a cohort study, the selected number of exposed individuals are drawn from the population of exposed individuals, and the same for unexposed individuals. For a case-control study, the same is done for people with the disease and people without the disease.
    1. How close are the studies’ OR and RR to the true OR and RR from the population? Why might we expect the studies’ OR and RR to be a bit different from the truth?
  2. You can perform 100 cohort and 100 case-control studies by clicking the “Perform each study 100 times” button. Results are summarized in boxplots at the bottom of the page. The thick black line in the middle of rectangle give the median value. The red horizontal dashed lines indicate the true population values.
    1. Conduct studies for the range of sample sizes for both rare and common diseases. In what situations did the studies tend to estimate the true population values well?
    2. The height of the boxplots is a direct indicator of the variation in estimates from study to study. What do you notice about this variation as sample size increases?





Activity

Navigate to Moodle, and open the PDF titled 06_case_control_studies_activity.