Case-Control Design - Incidence Density Sampling- CUT

Lead Author(s): Jeff Martin, MD

Summary of Case-Control Sampling
Definition: Incidence Density Sampling Within a Cohort
- Case-control Incidence Density Sampling
Diagram: Incidence Density Sampling Within a Cohort
Details of Incidence Density Sampling Within a Cohort
Controls in Incidence Density Sampling in a Fixed Cohort Study Base
Case-Control Incidence Density Sampling in a Dynamic Primary Study Base
How OR = Rate Ratio in a Case-Control Study with Incidence Density Sampling
- Sampling Using Estimate of Rate Ratio
- Estimate of Rate Ratio Calculation
Examples of Incidence Density Sampling

Summary of Case-Control Sampling

Design	Sampling	Measure of Association
Case-cohort	Entire cohort at baseline	risk ratio
Incidence-density	Non-cases at time of diagnosis	rate ratio
Prevalent Case Control	Non-cases at single point in time	odds ratio

A random sample of the cohort baseline = case-cohort design
- (Sampling Controls - Random Sample at Baseline)

At time each case is diagnosed = incidence density sampling

From persons without disease at the end of follow-up = prevalent controls design
- (Sampling Controls at Follow-up)

Definition: Incidence Density Sampling Within a Cohort

In incidence density sampling the selection of controls is governed by the diagnoses of cases.

Every time a case is diagnosed one or more controls are selected
from other members of the cohort who, at that time, do not have the diagnosis.

The term incidence density comes from

The time of follow-up and
The incidence of new disease are involved in determining eligible controls.

Case-control Incidence Density Sampling

Controls are sampled from the risk set at the time each case is diagnosed

Samples person-time experience of the subjects at risk each time a case is diagnosed

Odds ratio estimates the rate ratio

A case-control study with incidence density sampling

gives an odds ratio that estimates the rate ratio
because the sampling method is based on person-time of exposure.

Every time a case is diagnosed the person-time of the subjects at risk in the study base (cohort) is sampled randomly.

Diagram: Incidence Density Sampling Within a Cohort

In the diagram below, you can see incidence sampling within a cohort study.

The study base is the cohort.
In this example, controls are sampled each time a case is diagnosed.

Details of Incidence Density Sampling Within a Cohort

In the above diagram, 4 cases occur at 4 different points in time giving rise to 4 risk sets of cases and controls.

Controls for each case are selected at random in each risk set from cohort subjects under follow-up at the time (called incidence density sampling).

It follows from the random selection, that a control can later become a case.

Results can be just as valid as using entire cohort.

Because the controls are selected randomly from those still under follow-up at the time a case is diagnosed, the sample of controls provides the same estimate of an association between a predictor and the outcome that one would obtain if all of those still under follow-up were used.

The schematic illustrates how matching on follow-up time would be sampling the person-time follow-up of the cohort as time progresses.

Imagine ending the study after the first event occurs.
A random sample of those still at risk at that time will give a ratio of exposed and unexposed person-time that is the same as the ratio obtained using everyone in the cohort at that time point (give or take random sampling error).

The same reasoning applies to each subsequent event. The sum of all those person-time samplings will approximate the total person-time follow-up of the cohort in the exposed and unexposed provided the control samples were taken independently of exposure (always the key issue).

Controls in Incidence Density Sampling in a Fixed Cohort Study Base

The key point is that with incidence density sampling in a fixed cohort study base

The controls are matched to cases on time at risk - on the amount of follow-up time

You are sampling both persons and time when you pick the controls

You can conceptualize it as sampling the person-time of the cohort each time a diagnosis is made.
In other words, you are sampling non-cases (controls) at each time case occurs.

As with the case-cohort design,

Someone who is a control can later become a case and /or control again

Case-Control Incidence Density Sampling in a Dynamic Primary Study Base

In case-control incidence density sampling in a dynamic primary study base

you use a population-based disease registry to identify all new cases of disease during a defined time period.

How OR = Rate Ratio in a Case-Control Study with Incidence Density Sampling

So analogously to showing how the OR in a case-cohort design estimates the risk ratio, using the graphic below shows how the OR in a case-control design with incidence density sampling estimates the rate ratio because

the controls are providing an estimate of the proportion of exposed to unexposed person-time.

EXPOSURE ODDS IN CASES = a/c

EXPOSURE ODDS IN CONTROLS = b/d

Sampling Using Estimate of Rate Ratio

In obtaining a risk ratio, we estimated the propotion of exposed and unexposed persons.

For calculating a rate ratio in a case control study, we estimate the proportion of exposed and unexposed person-time.

When we talk about rates, we are talking about person-time

When we talk about measures of association, we are talking about incidence rates within the groups of exposed and unexposed persons.

CALCULATIONS:

To calculate the risk ratio in a case-control setting we need to get an unbiased estimate of the proportion of persons with and without the exposure.
For the rate ratio we need an analogous estimate of exposed and unexposed person-time.

Estimate of Rate Ratio Calculation

As you can see in the calculation below if we can estimate the proportion of unexposed person-time to exposed person-time in a case- control study, we can estimate the rate ratio.

Rate ratio (person-time) in cohort

where exposed =

and unexposed =

So analogous to estimating risk ratio, we need to estimate the proportion:

THUS, OR in a case-control design with incidence density sampling estimates the rate ratio because

the controls are providing an estimate of the proportion of exposed to unexposed person-time.

Examples of Incidence Density Sampling

These are examples of incident density in a dynamic primary study base.

An additional example of incidence density sampling as well as selection bias can be seen on the Coffee and Pancreatic Cancer Study in Selection Bias.