Estimation of marginal causal effects in the presence of confounding by cluster

A popular way to control for unmeasured confounders is to utilize clusters (e.g. sets of siblings), in which a potentially large set of confounders are constant. By estimating the exposure-outcome association within clusters, rather than between unrelated subjects, all cluster-constant confounders are implicitly controlled for. To analyze such clustered data, it is common to use fixed effects models, which absorb all cluster-constant confounders into a cluster-specific intercept. In this article, we show how linear and log-linear fixed effects models can be used to estimate marginal counterfactual means. These counterfactual means can be estimated and presented for each exposure level separately, or contrasted to form a wide range of marginal causal effects. For binary outcomes, we propose to estimate marginal causal effects with marginal logistic between-within models. These models include a constant intercept common for all clusters, and control for unmeasured cluster-constant confounders by adding the mean exposure level in each cluster to the model. We illustrate the proposed methods by re-analyzing data from a co-twin control study on birth weight and Attention-Deficit/Hyperactivity Disorder.