# Cluster Unit Randomized Trials

## 5. Pair-Matching

### When is Pair-matching Worthwhile

The main attraction of pair-matching on strongly predictive baseline risk factors is the potential increase it brings in statistical efficiency and trial power. Dealing first with the case of a quantitative outcome measure, let denote the difference in means for the jth pair of clusters, j =1,2,...k. Then the variance of dj is given by 2σ^{2}(1- ρ_{M}), where v denotes the variance of the outcome measure and the “matching correlation” ρ_{M}_{ }denotes the Pearson product-moment correlation between and . This simple result shows that the matched-pair design will always be more powerful than a completely randomized design provided ρ_{M} is positive. However this result ignores the difference in degrees of freedom used to test the effect of intervention in the two designs. Thus in the completely randomized design the analysis would typically take the form of a two-sample t-test with 2(k-1) degrees of freedom, while for a pair-matched design, it would typically take the form of a paired t-test with only k-1 degrees of freedom.

This discrepancy will have little impact on power in trials enrolling, say, 30 or more matched pairs. However logistical and cost considerations dictate that many CRTs, particularly those designed to evaluate community-based interventions, are forced to enroll far fewer pairs. The question then arises as to what point the gain in efficiency due to pair-matching on important baseline risk factors outweighs the loss in efficiency resulting from halving the available degrees of freedom. This question was addressed by Martin et al., 1993, who used numerical evaluation to conclude that if the number of pairs k is 10 or less, the pair-matched design should only be used if the investigators are confident that the value of ρ_{M} is at least 0.20. More generally they stated "It is unlikely that effective matching would be possible for small studies. Matching may be overused as a design tool." This point was also made by LaPrelle et al., 1992, who stated that matching on variables poorly related to outcome will "do little but reduce power by shifting the unit of analysis from the individual community to the pair of communities."