Matching in Case-Control Designs

EPID 712

Lecture 13

02/23/00

Megan O’Brien

Objectives

• Discuss methods of matching in case-control studies

• Discuss advantages and disadvantages of matching in case-control studies

• Discuss methods of analyzing matched case-control data

• Recommended reading: Szklo and Nieto pgs: 40-48

277314-317328-331

• Further reading: See Rothman and Greenland. Modern Epidemiology

What is matching?

• The process of making a study group and a comparison group comparable with respect to extraneous factors (Last JM. A Dictionary of Epidemiology. 3rd Ed. New York, NY: Oxford University Press; 1995)

• In case-control studies, we match to make cases and controls as similar as possible with regard to potentially important confounding factors

Types of matching

• Individual (paired) matching: for each case, one (or more) controls with the relevant characteristics matching the case are chosen

– For continuous variables such as age or weight, controls may be selected if they are within a specified range of the control value

• Example: Age ± 2 years

• Example: Weight ± 5 pounds

• When matching on a variety of characteristics, including continuous variables, it may be very difficult to individually match on all characteristics

• Minimum Euclidean distance: identify the individual who is the closest match with regard to all of the variables.

– We usually do this using mathematical modeling techniques

• Frequency matching: Controls are selected such that the distribution of the relevant characteristic in the controls is similar to the distribution in the cases

• Example: If 30% of cases are smokers, then select a control group in such a way that 30% of controls are smokers

Advantages of Matching• May be the best way to control for a strong

confounder when there is little overlap of the confounder between the cases and controls– Example: If the cases tend to be older (CHD, prostate

cancer) and a random sample of controls would result in a much younger control group, then there may not be much overlap of age between cases and controls

– This lack of overlap makes adjustment for confounding difficult. Why?

• When the confounder is strong, matching increases the efficiency of the study (by decreasing the width of the confidence intervals around an estimate)

• Matching can be a useful method of sampling controls when cases and controls are identified from a reference population for which there is no available sampling frame (list).– Example: Reference population is patients at a clinic or

hospital

Disadvantages of Matching

• It may difficult (and expensive) to identify a matched control

• When you match on a characteristic, you create an equal distribution in the cases and controls. Therefore, you cannot examine the association between the matched characteristic and the outcome

• You cannot assess additive interaction between the matching variable and the exposure of interest

• You must account for matching in the data analysis

• You may create groups that are no longer representative of the reference population, thus decreasing your ability to generalize your findings

• If you match on a characteristic that is a weak confounder, you may decrease the statistical power of your study

• If you match on a characteristic that is strongly correlated with the exposure of interest, you may overmatch

• If you categorize continous variables too broadly, you may still have residual confounding

Overmatching• Overmatching occurs when you match on a variable

that is strongly correlated with the exposure of interest

• By setting the distribution of the matching variable to be equal between cases and controls, you are effectively setting the distribution of the exposure variable to be equal between cases and controls

• In doing so, you will be unable to detect a difference in exposure between cases and controls

Residual confounding• Occurs when you categorize continuous

variables

• Ex. Create age categories for matching20-2525-3030-35

For each case between 20 and 25, select a control who is also between 20 and 25

• Now your cases and controls are comparable with respect to age right?

Age category Case subjects Control subjects

20-25 20 22 23

23 25 25

Mean age 21.67 24.33

Are these two groups really comparable?

Analysis of matched data

• Mantel-Haenszel OR (pg. 277)

– If we pair-match cases and controls, we keep them in pairs for the calculation of the odds ratio

– What combinations will be possible with regard to exposure?

• Concordant pairs: • Both case and control are exposed

• Neither case nor control are exposed

• Discordant pairs• Case is exposed, control is not

• Control is exposed, case is not

• What do the concordant pairs tell us?

– Nothing

• We are interested in the discordant pairs

Control Exposed Not exposed

Case Exposed a b

Not exposed c d

c

bORMH

Note that each cell contains pairs. So the OR is a ratio of the discordant pairs.

See pg. 280 for the derivation of this formula.

How do you interpret the MH OR?

Just as usual.

Control Exposed Not exposed

Case Exposed 42 115

Not exposed 17 165

76.617

115ORMH

Cases are 6.76 times more likely to be exposed than controls.

Multivariate analysis of matched data

• Conditional logistic regression (pg. 314)

– Use when you have individual matching

– Analogous to logistic regression, but the model takes into account the pairing of cases and controls

• Logistic regression

– Use when you have frequency matching

– Simply include the matching variables in the model