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The Power of Pairing in Cluster Randomized Block Designs: A Monte Carlo Simulation. Nianbo Dong & Mark Lipsey 03/04/2010. Power Analysis for Group-Randomized Experiments. Two Big Design Families (Kirk, 1995) 1) Hierarchical Design 2) Cluster Randomized Block Design

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the power of pairing in cluster randomized block designs a monte carlo simulation
The Power of Pairing in Cluster Randomized Block Designs: A Monte Carlo Simulation
  • Nianbo Dong & Mark Lipsey
  • 03/04/2010
power analysis for group randomized experiments

Power Analysis for Group-Randomized Experiments

Two Big Design Families (Kirk, 1995)

1) Hierarchical Design

2) Cluster Randomized Block Design

Three Ways to do Power Analysis

1) Software, e.g., Optimal Design 2.0

(Spybrook, Raudenbush, Congdon, & Martinez, 2009)

2) MDES formula (Bloom, 2006; Schochet, 2008)

3) Power table using operational effect size

(Hedges, 2009; Konstantopoulos, 2009)

matched pair cluster randomized design 1

Matched-Pair Cluster-Randomized Design (1)

3. But, the gain in predictive power may outweigh the loss of degrees of freedom

(Billewicz, 1965; Bloom, 2007; Hedges, 2009; Martin, Diehr, Perrin, & Koepsell, 1993; Raudenbush, Martinez, & Spybrook, 2007)

4. Break-even point using MDES for fixed pair effect model (Bloom, 2007)

Advantages

1) Avoiding bad randomization, 2) Face validity

2. Cost: Loss of degree of freedom

matched pair cluster randomized design 2

Matched-Pair Cluster-Randomized Design (2)

  • MDES for 2-level hierarchical design, w/o covariance adjustment
  • (Bloom, 2006)

5. MDES Comparison

  • MDES for 3-level matched-pair cluster-randomized design, random pair effect model w/o covariance adjustment, VC

(SE from Raudenbush

& Liu, 2000)

: ICC for hierarchical design;

: Pair-level ICC for matched-pair cluster-randomized design

J: # of clusters; n: average # of individuals

matched pair cluster randomized design 25

Matched-Pair Cluster-Randomized Design (2)

  • MDES for 2-level hierarchical design, w/o covariance adjustment
  • (Bloom, 2006)

5. MDES Comparison

  • MDES for 3-level matched-pair cluster-randomized design, random pair effect model w/o covariance adjustment, VC

(SE from Raudenbush

& Liu, 2000)

: ICC for hierarchical design;

: Pair-level ICC for matched-pair cluster-randomized design

J: # of clusters; n: average # of individuals

research questions

Research Questions

The Overall Question

Are there design and analysis options other than increasing the sample size that might keep pre-randomization matching from degrading power relative to the analogous unmatched design?

four sub questions

How much difference does it make to statistical power:

    • 1. If we are able to make close matches or unable to do so?
    • 2. If we are treating the pairwise blocks as fixed effects vs. random effects?
    • 3. If we ignore the pairwise blocking entirely (and does this compromise the Type I error rate)?
    • 4. If we also use the blocking variable as a covariate in the analysis?

Four Sub-Questions

conclusions

Conclusions

  • The most important technique for maintaining power is to also use the matching variable as a covariate.

The advantages of pre-randomization matching do not have to come at the cost of reduced power– even when the matching is not very good.

  • The random effects model does not necessarily have less power than the fixed effects alternative.
  • Ignoring the pairwise blocking variable in the analysis, though not faithful to the actual design used, does not appear to cause problems with either the Type I or Type II error rate. (Consistent with Diehr, Martin, Koepsell, & Cheadle, 1995; Lynn & McCulloch, 1992; Proschan, 1996)