Variability in Causal Effects, Moderation, and Noncompliance from Data MAR in a Multisite Trial

Music City Center 

We extend methods for estimating hierarchical linear models with incomplete data to study complier-average causal effects (CACE) in a multi-site trial. Individuals at each site are assigned to either treatment or control. Compliers adhere to their assigned condition and would have done so had they been assigned to the other. Under the assumptions of monotonicity (treatment assignment does not decrease participation), random treatment assignment, and treatment affecting outcomes only if participants comply, compliance is missing at random. We study the mean and variance of CACE across sites, site-specific average CACE, and the association between site-level and within-site covariates and CACE. To estimate these, we factorize the complete data likelihood into the distribution of the outcome and compliance, conditional on selected random effects, and the marginal distribution of these random effects. Assuming the random effects are provisionally known, we integrate out the missing data, then numerically integrate out the random effects, maximizing the likelihood using the EM algorithm. We illustrate this approach with data from a large-scale study on charter school effectiveness.

Complier average causal effects (CACE)

Site-specific average CACE

mean and variance of CACE across sites

provisionally known random effects

the EM algorithm

adaptive Gauss Hermite quadrature 

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