I have become accustomed to matching groups with each other (a treatment group with a created control group) and I do this in R, but I would like to know if each individual case in the treatment could be acceptably paired with a case in the control.
For example, if you have a treatment group of those who took the drug, and you create a control group using a series of reasonable variables, then one could quite easily have two groups that are balanced. However, say we were also interested in the time (i.e. date) when the people in the treatment group took the drug. Could I then match, on a one to one basis, each case from the treatment with a case from the non-treatment and essentially give the non-treatment cases the same time (i.e. date) as their matched treatment counterpart?
Another way of asking this question is, would it be theoretically sound for me to move away from comparing groups to actually comparing individuals in the groups (matched VS non-matched)?
Thanks a lot.
Michael
Seems you are describing a standard example of propensity score matching.
While you can match subjects for a control group using individual cases, it should not be done without considering the characteristics of the populations from which they come. Matched cases should come from the same general proximity of the respective distributions. The danger is that is you take a matched case from either the extreme low or high end of a distribution, there is a very high chance the error of measurement is high unless the measurement was perfect (without error). A very detailed explanation of this and evaluation of suggested corrections can be found at Article An empirical examination of analysis of covariance with and ...
The root of the problem is the threat to validity known as regression to the mean.
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