# Case Control Odds Ratio

## Case Control Odds Ratio

Odds ratio (OR) of exposure in cases and controls is the measure of association in case-control studes

Since the case-control design starts with the cases and controls and fixes the ratio of the two by selecting one or more controls per case,
OR of exposure = OR of disease

The odds ratio is the OR of exposure,
• BUT the OR of exposure equals the OR of disease (OR we want)
To understand the OR in a case-control study we need to look at how the OR approximates the risk ratio and approximates the rate ratio.

## Case-control Design Notation

To switch from the notation of a cohort to case-control design, the events (diagnoses) in a case-control study are the cases.

1 = EXPOSED and 0 = NOT EXPOSED

• Some of the cases will be discovered to have been exposed = E1
• And some of the cases will be discovered to have been unexposed = E0

With this notation we can look at how the OR estimates other ratio measures.

## Capturing Events with a Case-Control Study Design

The goal of the case-control design:
• Obtain all the cases that occur during a defined time period (or a random sample of those cases)
Easily achievable if all, or nearly all the cases are diagnosed and registered:
• In a disease registry
• Kaiser’s system of record keeping.
Use a primary study base such as
• participants in a cohort
• residents of California
• members of Kaiser Permanente
Getting an unbiased estimate of this ratio is not a problem in a case-control design.

In case control design, Case Control Design: OR estimates Risk Ratio and Case Control Design: OR estimates Rate Ratio.

## Rare Disease Assumption

The rare disease assumption says that if the incidence of the disease under study is very low
• the OR from a case-control study even with sampling prevalent controls approximates the risk ratio.
Although there is no absolute number, less than 10% is often given as a definition of what is meant by rare.

• Rare disease assumption if disease incidence low in unexposed and exposed (<10%).
• OR approximately equals RR
• Exposure in controls approximately equals exposure in whole cohort