  In observational studies of treatment effects, matched samples are created so
treated and control groups are similar in terms of observable covariates.
Traditionally such matched samples consist of matched pairs. If a pair match
fails to make treated and control units sufficiently comparable, alternative
forms of matching may be necessary. One general strategy to improve balance is
to match a variable number of control units to each treated unit. A more
tailored strategy is to adopt a fine balance constraint. Under a fine balance
constraint, a nominal covariate is exactly balanced, but it does not require
individually matched treated and control subjects for this variable. In the
example, we seek to construct a matched sample for an ongoing evaluation of
Peer Health Exchange, an intervention in schools designed to decrease risky
health behaviors among youth. We find that an optimal pair match that minimizes
distances between pairs creates a matched sample where balance is poor. Here we
propose a method to allow for fine balance constraints when each treated unit
is matched to a variable number of control units, which is not currently
possible using existing matching algorithms. Our approach uses the entire
number to first determine the optimal number of controls for each treated unit.
For each strata of matched treated units, we can then apply a fine balance
constraint. We then demonstrate that a matched sample for the evaluation of the
Peer Health Exchange based on a variable number of controls and fine balance
constraint is superior to simply using a variable-ratio match.
