## Case control studies

In cohort studies the denominator represents the exposure experience of the source population. If it is the exposure status as observed at the beginning of the cohort we will compute a risk. If we allow for exposure to vary overtime we will compute a rate which takes into account the time spent by each individual in the exposed and unexposed cohorts over time.
The main constraint in cohort studies is the necessity to collect information on exposure from large populations (to have denominators for the exposed and unexposed cohorts). We will see below that instead of collecting exposure information from the entire study population we can use a sample of it to calculate or estimate the risk ratio or the rate ratio. In other words, instead of using the entire cohort denominator we will use a sample of it. This sample is also frequently called a control group and it is used to represent the exposure experience of the source population.
The rationale behind using a sample of the denominator comes from the following formula for risk and rate ratio which can alternatively be expressed as follows:
For risk For rates From the above formula we already see that if we take an unbiased random sample of Ne and Nu the ratio of exposed to unexposed (Ne/Nu)  will not be modified and therefore the risk ratio will remain the same (Ne/Nu or a sample of it gives the same risk ratio if sampling is unbiased). The same applies if we use person years at risk (PT).

We have generally speaking three major ways to select a sampled control group which reflect three ways to estimate exposure experience in the source population.

1. Controls are selected  from people who are still free of the disease at the end of the study period (Ne-Ce and Nu-Cu). We will call the related study design a traditional case control study since it is the design most frequently used. The exposure measured reflects the exposure experience or status of people still free of disease at the end of the cohort.
2. Controls are randomly selected from the population present (at risk) at the beginning of the study (Ne and Nu in the above graphic). The related study design is called a case cohort study .The exposure measured reflects exposure status at the beginning of the cohort.
3. Controls are selected proportionally to the person-time contributed by exposed and unexposed cohorts (PTe and PTu). The related study design is called a density case control study. The exposure measured reflects the varying exposure of people at risk along the cohort.