# 5.5 - Analysis

## Analytic Methods for Non-Matched Case-Control Studies Section

With case-control studies, we essentially work down the columns of the 2 × 2 table. Cases are identified first, then controls. The investigator then determines whether cases and controls were exposed or not exposed to the risk factor.

2 × 2 Table for Non-Matched Case-Control Data:
Category Case
(Number)
Controls
(Number)
Total Exposure
(Number)
Exposed A B TotalExposed
Not Exposed C D TotalNotExposed
Total TotalCases TotalControls Total

We calculate the odds of exposure among cases (A/C) and the odds of exposure among controls (B/D). The odds ratio is then (A/C)/(B/D), which simplifies after cross-multiplication to (A*D)/(B*C).

For case-control studies, since the ratio of cases to controls is not necessarily representative of the ratio in the population, the odds ratio must be used as the summary measure.  The relative risk is not an accurate measure in this type of study.

Analytic methods for non-matched case-control studies include:

• Chi-square 2 × 2 analysis;
• Mantel-Hanszel statistic (This test takes into account the possibility that there are different effects for the different strata (e.g., effect modification))
• Fisher’s Exact test (This test is used if the expected cell size is <5)
• Unconditional logistic regression (The method is used to simultaneously adjust for multiple confounders; a multivariable analysis).

### Example

For the obesity and microscopic colitis example (Obesity is associated with decreased risk of microscopic colitis in women), the data from table 2 can be used to construct this 2x2 table for the comparison of microscopic colitis between those with low and high BMI.

Comparison of Microscopic Colitis between those with Low and High BMI
Category Case
(Number)
Controls
(Number)
Total Exposure
(Number)
Exposed
(BMI >=30)
22 105 TotalExposed (127)
Not Exposed
(BMI < 25)
50 73 TotalNotExposed (123)
Total TotalCases
(72)
TotalControls
(178)
Total (250)

OR = (22*73)/(50*105) = 0.31
As we see in the text: As shown in Table Table2, the risk for microscopic colitis was lower for … BMI > 30 kg/m2 (OR 0.31, 95%CI: 0.17-0.55) compared to under- or healthy weight (BMI < 25 kg/m2) as the reference.

To review, for a simple non-matched case-control study, you find a case, then determine whether the person is exposed or not. Find a control; determine their exposure status.

## Analytic Methods of Matched Case-Control Studies Section

In an analysis of a matched study design, only discordant pairs are used. A discordant pair occurs when the exposure status of the case is different from the exposure status of the control. The most commonly used analytic method for matched case-control studies is conditional logistic regression, conditioned upon the matching.

The matched case-control study has linked a case to a control based on the matching of one or more variables. The summary table will differ for a matched case-control study

2 × 2 Table for Matched Case-Control Data:
Controls Cases
Exposed
(Number)
Not-Exposed
(Number)
Total
(Number)
Exposed
(Number)
A
(Concordant Pair)
B
(Discordant Pair)
TotalExposedControls
Not-Exposed
(Number)
C
(Discordant Pair)
D
(Concordant Pair)
TotalNot ExposedControls
Total TotalExposedCases TotalNot ExposedCases Total

### Example

Let's look at an example. Suppose we plan to match cases to controls by gender and age (+/- 5 years). We first identify the following case:

#### Case:

Male, 45 years of age (Patient 1);
Exposure status: Exposed
If this was a non-matched study, the case would be counted in cell A in the non matched 2x2 table because he is exposed. However, in the age- and gender-matched case-control study we must also find a male control within five years of age. Searching in the appropriate control population, we locate the following control:

#### Control:

Male 48 years of age (Person 47);
Exposure status: Exposed
If Person 47 were counted in an unmatched study, he would belong in cell B of the preceding table. In a matched case-control study, however, we are interested in results for the matched pair. The data from Patient 1 and Person 47 are linked for the duration of the study. The appropriate table for the matched study is depicted below. Where do Patient 1 and Person 47 belong?

Patient 1 is a case and he is exposed so he fits into either cell A or cell C. Based upon his control's status we determine which cell is the correct placement for this pair. Patient 1's control is exposed, therefore Patient 1 and Person 47 fit into cell A as a pair. This is a concordant pair because both are exposed. Concordancy is based upon exposure status. In a matched case-control study, the cell counts represent pairs, not individuals. In the statistical analysis, only the discordant pairs are important. Cells B and C contribute to the odds ratio in a matched design. Cells A and D do not contribute to the odds ratio. If the risk for disease is increased due to exposure, C will be greater than B. The odds ratio is then (B/C).

## Comparing Matched and Non-Matched Case-Control Studies Section

### Stop and Think!

Come up with an answer to the questions and then click on the button below to reveal the answer.

1. Can you think of more than one reason why a matched case-control study could take longer to complete than an unmatched study?

First, you must identify matched controls, sometimes more than one per case. Second, since only the discordant pairs contribute to the statistical analysis, achieving a desired statistical power depends on obtaining a particular number of discordant pairs.
2. Why bother with matching if it means a longer case-control study?

When performing statistical analysis, the matched variables are not included in the statistical model.
(In a cohort study, confounding is dealt with by including the terms in the model to adjust for their effects. In a matched case-control study, the adjustment for this confounding can be made through the matching.)