Compliance Mixture Modelling with a Zero-Effect Complier Class and Missing Data
Version of Record online: 17 SEP 2012
© 2012, The International Biometric Society
Volume 68, Issue 4, pages 1037–1045, December 2012
How to Cite
Sobel, M. E. and Muthén, B. (2012), Compliance Mixture Modelling with a Zero-Effect Complier Class and Missing Data. Biometrics, 68: 1037–1045. doi: 10.1111/j.1541-0420.2012.01791.x
- Issue online: 21 DEC 2012
- Version of Record online: 17 SEP 2012
- Received April 2011. Revised April 2012. Accepted April 2012.
- Causal inference;
- Latent ignorability;
- Missing data;
- Mixture distributions
Summary Randomized experiments are the gold standard for evaluating proposed treatments. The intent to treat estimand measures the effect of treatment assignment, but not the effect of treatment if subjects take treatments to which they are not assigned. The desire to estimate the efficacy of the treatment in this case has been the impetus for a substantial literature on compliance over the last 15 years. In papers dealing with this issue, it is typically assumed there are different types of subjects, for example, those who will follow treatment assignment (compliers), and those who will always take a particular treatment irrespective of treatment assignment. The estimands of primary interest are the complier proportion and the complier average treatment effect (CACE). To estimate CACE, researchers have used various methods, for example, instrumental variables and parametric mixture models, treating compliers as a single class. However, it is often unreasonable to believe all compliers will be affected. This article therefore treats compliers as a mixture of two types, those belonging to a zero-effect class, others to an effect class. Second, in most experiments, some subjects drop out or simply do not report the value of the outcome variable, and the failure to take into account missing data can lead to biased estimates of treatment effects. Recent work on compliance in randomized experiments has addressed this issue by assuming missing data are missing at random or latently ignorable. We extend this work to the case where compliers are a mixture of types and also examine alternative types of nonignorable missing data assumptions.