Toward identifiability of total effects in summary causal graphs with latent confounders: an extension of the front-door criterion

Conducting experiments to estimate total effects can be challenging due to cost, ethical concerns, or practical limitations. As an alternative, researchers often rely on causal graphs to determine if it is possible to identify these effects from observational data. Identifying total effects in fully specified non-temporal causal graphs has garnered considerable attention, with Pearl's front-door criterion enabling the identification of total effects in the presence of latent confounding even when no variable set is sufficient for adjustment. However, specifying a complete causal graph is challenging in many domains. Extending these identifiability results to partially specified graphs is crucial, particularly in dynamic systems where causal relationships evolve over time. This paper addresses the challenge of identifying total effects using a specific and well-known partially specified graph in dynamic systems called a summary causal graph, which does not specify the temporal lag between causal relations and can contain cycles. In particular, this paper presents sufficient graphical conditions for identifying total effects from observational data, even in the presence of hidden confounding and when no variable set is sufficient for adjustment, contributing to the ongoing effort to understand and estimate causal effects from observational data using summary causal graphs.