Estimating Complier Average Causal Effects for Clustered RCTs When the Treatment Affects the Service Population

RCTs sometimes test interventions that aim to improve existing services targeted to a subset of individuals identified after randomization. Accordingly, the treatment could affect the composition of service recipients and the offered services. With such bias, intention-to-treat estimates using data on service recipients and nonrecipients may be difficult to interpret. This article develops causal estimands and inverse probability weighting (IPW) estimators for complier populations in these settings, using a generalized estimating equation approach that adjusts the standard errors for estimation error in the IPW weights. While our focus is on more general clustered RCTs, the methods also apply (reduce) to non-clustered RCTs. Simulations show that the estimators achieve nominal confidence interval coverage under the assumed identification conditions. An empirical application demonstrates the methods using data from a large-scale RCT testing the effects of early childhood services on children's cognitive development scores.