Traditional case-control studies

Let suppose that we are at the end of the follow up period and have respectively Ce and Cu cases, and Ne-Ce and Nu-Cu persons still free of disease (non cases), in the two cohorts. If the disease is rare it is obvious that persons free of disease at the end of the study period reflect the exposure experience of the source population. If the disease is frequent, exposure among persons free of disease at the end of the study may be lower than in the source population (since exposure increases the risk of disease).

If the disease is rare  we can use a sample of non cases at the end of the study period to estimate the risk ratio. Using non cases to estimate the source population exposure experience is the principle of traditional case control studies.

Let’s call “c” and “d” respectively the number of exposed and unexposed in the sample. If sampling is done independently from the exposure status we would expect if the disease is rare

    

 or equivalently

 

If the above is true the risk ratio estimated from a traditional case control study can be represented as:

 

The quantity ad/bc is the odds ratio. It represents the ratio of the odds of disease among exposed divided by the odds of disease among unexposed.

 

However if the disease is not rare a large part of Ne/Nu is represented by future cases who are more likely to be exposed than non cases. Consequently, the odds ratio may dramatically overestimate the risk ratio.

 

To illustrate this point let’s now move to the example of a food borne outbreak in a nursing home with 200 residents and 74 cases of gastroenteritis. The epidemic curve is consistent with a point common source of infection and example 4 shows the results of a retrospective cohort study. It suggests that the risk of gastroenteritis is 3.4 times higher among residents who consumed a specific food item compared to those who did not.

 

Example 1: Occurrence of gastroenteritis among residents of nursing home A according to consumption of a specific food item.

 

Specific food item  Total Cases  Risk Risk ratio
Yes 60 44 73.3% 3.4
No 140 30 21.4% Reference
Total 200 74 37.5%

Let’s suppose investigators would have preferred to conduct a traditional case control study (case – non cases study) rather than a retrospective cohort. In a traditional case control study controls are selected from people who are free of the disease at the end of the stuy period. The OR is a good estimate of the risk ratio if the disease is rare.

 

Example 2: Consumption of a specific food item among cases and various samples of residents of a nursing home

Consumption  Cases  50% sample of non cases OR 50% sample of source population RR
Yes 44 8 10.1 30 3.4
NO 30 55 70

Using as controls a 50% sample of the non cases the odds ratio equals 10.1, overestimating the risk ratio by a factor of three. This should not come as a surprise, though. When selecting controls from non-cases, and since the disease is frequent (the overall risk of gastroenteritis is 37.5%), the control group is no longer representing the distribution of exposure in the source population. The frequency of exposure in the control group selected from non cases is 7.3% and was 30% in the source population.

If instead we had done a case cohort study and chosen a 50% random sample of the source population, the sample (if unbiased and ignoring random variation) would be likely to provide the same proportion of exposed (30%) than in the source population. The risk ratio obtained (3.4) would again be similar to the risk ratio observed in the cohort study.

When to use a traditional case control study?

Traditional case control studies are an easy and very convenient way to conduct epidemiological studies when the disease is rare. Because of its simplicity it is the most popular method. It has been extremely useful to epidemiologists in the past 50 years. Provided that the disease is rare the odds ratio provides a good estimate of the risk ratio. However, it should not be used when disease incidence is high. This particularly applies to investigations of food borne outbreaks with very high incidence.

NB. "Traditional case-control studies" are a type of case-control studies, where controls are simply non-cases. For this reason, you may find them quoted as "case-non-case studies" in literature.