Estimating marginal treatment effect in cluster randomized trials with multi-level missing outcomes

Analyses of cluster randomized trials (CRTs) can be complicated by informative missing outcome data. Methods such as inverse probability weighted generalized estimating equations have been proposed to account for informative missingness by weighing the observed individual outcome data in each cluster. These existing methods have focused on settings where missingness occurs at the individual level and each cluster has partially or fully observed individual outcomes. In the presence of missing clusters, for example, all outcomes from a cluster are missing due to drop-out of the cluster, these approaches ignore this cluster-level missingness and can lead to biased inference if the cluster-level missingness is informative. Informative missingness at multiple levels can also occur in CRTs with a multi-level structure where study participants are nested in subclusters such as healthcare providers, and the subclusters are nested in clusters such as clinics. In this paper, we propose new estimators for estimating the marginal treatment effect in CRTs accounting for missing outcome data at multiple levels based on weighted generalized estimating equations. We show that the proposed multi-level multiply robust estimator is consistent and asymptotically normally distributed provided that one of the multiple propensity score models postulated at each clustering level is correctly specified. We evaluate the performance of the proposed method through extensive simulations and illustrate its use with a CRT evaluating a Malaria risk-reduction intervention in rural Madagascar.