Graduation Year


Document Type




Degree Granting Department

Epidemiology and Biostatistics

Major Professor

Hendricks Brown, Ph.D.

Co-Major Professor

Yiliang Zhu, Ph.D.


Causal effect, CACE, Multi-level randomized trials, Noncompliance, Rubin causal model


The Principal Stratification method estimates a causal intervention effect by taking account of subjects' differences in participation, adherence or compliance. The current Principal Stratification method has been mostly used in randomized intervention trials with randomization at a single (individual) level with subjects who were randomly assigned to either intervention or control condition. However, randomized intervention trials have been conducted at group level instead of individual level in many scientific fields. This is so called "two-level randomization", where randomization is conducted at a group (second) level, above an individual level but outcome is often observed at individual level within each group. The incorrect inferences may result from the causal modeling if one only considers the compliance from individual level, but ignores it or be determine it from group level for a two-level randomized trial.

The Principal Stratification method thus needs to be further developed to address this issue. To extend application of the Principal Stratification method, this research developed a new methodology for causal inferences in two-level intervention trials which principal stratification can be formed by both group level and individual level compliance. Built on the original Principal Stratification method, the new method incorporates a range of alternative methods to assess causal effects on a population when data on exposure at the group level are incomplete or limited, and are data at individual level. We use the Gatekeeper Training Trial, as a motivating example as well as for illustration. This study is focused on how to examine the intervention causal effect for schools that varied by level of adoption of the intervention program (Early-adopter vs. Later-adopter). In our case, the traditional Exclusion Restriction Assumption for Principal Stratification method is no longer hold.

The results show that the intervention had a stronger impact on Later-Adopter group than Early-Adopter group for all participated schools. These impacts were larger for later trained schools than earlier trained schools. The study also shows that the intervention has a different impact on middle and high schools.