Causal inference in randomized trials with partial clustering

Abstract

Background:

Participant dependence, if present, must be accounted for in the analysis of randomized trials. This dependence, also referred to as “clustering,” can occur in one or more trial arms. This dependence may predate randomization or arise after randomization. We examine three trial designs: one “fully clustered” (where all participants are dependent within clusters or groups) and two “partially clustered” (where some participants are dependent within clusters and some participants are completely independent of all others).

Methods:

For these three designs, we (1) use causal models to non-parametrically describe the data generating process and formalize the dependence in the observed data distribution; (2) develop a novel implementation of targeted minimum loss-based estimation for analysis; (3) evaluate the finite-sample performance of targeted minimum loss-based estimation and common alternatives via a simulation study; and (4) apply the methods to real-data from the SEARCH-IPT trial.

Results:

We show that the two randomization schemes resulting in partially clustered trials have the same dependence structure, enabling use of the same statistical methods for estimation and inference of causal effects. Our novel targeted minimum loss-based estimation approach leverages covariate adjustment and machine learning to improve precision and facilitates estimation of a large set of causal effects. In simulations, we demonstrate that targeted minimum loss-based estimation achieves comparable or markedly higher statistical power than common alternatives for these partially clustered designs. Finally, application of targeted minimum loss-based estimation to real data from the SEARCH-IPT trial resulted in 20%–57% efficiency gains, demonstrating the real-world consequences of our proposed approach.

Conclusions

Partially clustered trial analysis can be made more efficient by implementing targeted minimum loss-based estimation, assuming care is taken to account for the dependent nature of the observed data.