Bagged random causal networks for interventional queries on observational biomedical datasets.

Learning causal effects from observational data, e.g. estimating the effect of a treatment on survival by data-mining electronic health records (EHRs), can be biased due to unmeasured confounders, mediators, and colliders. When the causal dependencies among features/covariates are expressed in the form of a directed acyclic graph, using do-calculus it is possible to identify one or more adjustment sets for eliminating the bias on a given causal query under certain assumptions. However, prior knowledge of the causal structure might be only partial; algorithms for causal structure discovery often provide ambiguous solutions, and their computational complexity becomes practically intractable when the feature sets grow large. We hypothesize that the estimation of the true causal effect of a causal query on to an outcome can be approximated as an ensemble of lower complexity estimators, namely bagged random causal networks. A bagged random causal network is an ensemble of subnetworks constructed by sampling the feature subspaces (with the query, the outcome, and a random number of other features), drawing conditional dependencies among the features, and inferring the corresponding adjustment sets. The causal effect can be then estimated by any regression function of the outcome by the query paired with the adjustment sets. Through simulations and a real-world clinical dataset (class III malocclusion data), we show that the bagged estimator is -in most cases- consistent with the true causal effect if the structure is known, has a good variance/bias trade-off when the structure is unknown (estimated using heuristics), has lower computational complexity than learning a full network, and outperforms boosted regression. In conclusion, the bagged random causal network is well-suited to estimate query-target causal effects from observational studies on EHR and other high-dimensional biomedical databases.