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. 2019 Aug 14;74(9):849–857. doi: 10.1136/thoraxjnl-2018-212979

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© Author(s) (or their employer(s)) 2019. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.

This is an open access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited, appropriate credit is given, any changes made indicated, and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/.

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DAG demonstrating causal relationships and potential biasing pathways affecting the association between housing quality and ARI hospitalisation (produced using DAGitty V.2.3 software). In this conceptual diagram, each circle represents an individual exposure (‘node’) of theoretical relevance to this hypothesis; each node is interconnected by directional arrows (‘edges’) that represent theoretical associations based on the researchers’ assessment of a priori literature and determination of biological plausibility. Housing quality (RHI and/or Damp–Mould index as proxy) is the exposure of interest (green node with black border), with ARI hospitalisation (blue node with black border) as the outcome of interest. The association of interest, therefore, is the edge represented by the green arrow connecting the exposure and outcome. Age, gender, secondhand smoke exposure and BMI (blue nodes with blue borders) are theoretically causally associated with (ie, ancestors of) the outcome alone. In this instance, all the other exposures (‘nodes’) are theoretically causally associated with (ie, ancestors of) both the exposure and the outcome. To adjust for confounding in the association of interest, it is necessary to close all ‘backdoor pathways’ between the exposure and outcome (ie, any pathway (consisting of a series of one or more edges and nodes) that provides an alternate route between the exposure and outcome); this is accomplished by adjusting for at least one node on that path. The minimally sufficient adjustment set is the combination of the fewest nodes that, being ancestors of both the exposure and outcome, if selected, effectively block all backdoor pathways between the exposure and the outcome (white nodes with black borders). These ‘adjusted variables’ are then introduced into the multivariate modelling as potential confounders. No other ancestors (blue, red or green nodes) are necessary (or appropriate) to include in the model as potential confounders. ARI, acute respiratory infection; BMI, body mass index; CNOS, Canadian National Occupancy Standard; DAG, directed acyclic graph; NZiDep, New Zealand Index of Socioeconomic Deprivation; RHI, Respiratory Hazard Index.