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Principles of matching

Last modified at 9/3/2014 5:04 PM by Arnold Bosman

Confounding implies that the confounding factor (which is one of the exposures) is not evenly distributed between cases and controls (or between exposed and unexposed). Therefore in order to prevent confounding the simplest solution would be to design a study in which cases and controls (or exposed and unexposed) would have an equal distribution of the confounding factor. This process is called matching.

Matching is  most often applied in to  case controls studies, however  matching may be performed also in cohort studies [1].

We usually identify two types of matching process, individual matching and frequency matching. Both individual and frequency matching have the same consequence: matching will have to be taken into account during the analysis.

Individual matching

In this first method, matching is performed subject by subject. This is called individual matching. For example, if age is a confounding factor, for each case age 30 years, one control of the same age will be selected, and so far and so on for all cases included in the study. The results are pairs of individuals belonging to the same study population and sharing one common characteristic (in this example, a specific age).

In individual matching, we may also consider to select more than one control per case. Then two or more controls have then the same characteristic of the case. We have then constituted triplets (one case and 2 controls), quadruplets (one case and 3 controls), etc.

Frequency matching

In a second type of matching process, matching is no longer done individually but for groups of subjects. In such instance a group of controls is matched to a group of cases with respect to a particular characteristic (the confounding factor). For example if in a case control study with 50 cases there are 20 men and 30 women, we would select a control group having the same gender distribution. We would first select 20 men from the male study population and then 30 women from the female study population.

Why matching?

Matching controls to cases is nothing more than stratifying in advance of analysis. Instead of constituting strata at the time of the study analysis we prepare them before the study is done, at the time of controls selection. When we select one control per case, each stratum will include one case and one control. We will therefore have as many strata as pairs in the study. The objective of matching is to prepare the analysis. Matching optimizes the number of cases and controls per stratum. It avoids having no case or no control in a stratum, as could happen when doing a stratified analysis afterwards (The biggest inefficiency in a stratified analysis done afterward would occur when in a stratum there is either no case or no control). This is why matching is frequently mentioned as a way to improve the efficiency of an analysis by better distributing cases and controls between strata.


1. Rothman KJ, Greenland S; Modern Epidemiology, second edition. Lippincott Williams & Wilkins 1998, 147-161.