Depicting deterministic variables within directed acyclic graphs (DAGs): An aid for identifying and interpreting causal effects involving derived variables and compositional data.

Deterministic variables are variables that are functionally determined by one or more parent variables. They commonly arise when a variable has been functionally created from one or more parent variables, as with derived variables, and in compositional data, where the 'whole' variable is determined from its 'parts'. This article introduces how deterministic variables may be depicted within directed acyclic graphs (DAGs) to help with identifying and interpreting causal effects involving derived variables and/or compositional data. We propose a two-step approach in which all variables are initially considered, and a choice is made whether to focus on the deterministic variable or its determining parents. Depicting deterministic variables within DAGs brings several benefits. It is easier to identify and avoid misinterpreting tautological associations, i.e., self-fulfilling associations between deterministic variables and their parents, or between sibling variables with shared parents. In compositional data, it is easier to understand the consequences of conditioning on the 'whole' variable, and correctly identify total and relative causal effects. For derived variables, it encourages greater consideration of the target estimand and greater scrutiny of the consistency and exchangeability assumptions. DAGs with deterministic variables are a useful aid for planning and interpreting analyses involving derived variables and/or compositional data.

The Association Between Childhood Leukemia and Population Mixing: An Artifact of Focusing on Clusters?

BACKGROUND: Studies investigating the population-mixing hypothesis in childhood leukemia principally use two analytical approaches: (1) nonrandom selection of areas according to specific characteristics, followed by comparisons of their incidence of childhood leukemia with that expected based on the national average; and (2) regression analyses of region-wide data to identify characteristics associated with the incidence of childhood leukemia. These approaches have generated contradictory results. We compare these approaches using observed and simulated data. METHODS: We generated 10,000 simulated regions using the correlation structure and distributions from a United Kingdom dataset. We simulated cases using a Poisson distribution with the incidence rate set to the national average assuming the null hypothesis that only population size drives the number of cases. Selection of areas within each simulated region was based on characteristics considered responsible for elevated infection rates (population density and inward migration) and/or elevated leukemia rates. We calculated effect estimates for 10,000 simulations and compared results to corresponding observed data analyses. RESULTS: When the selection of areas for analysis is based on apparent clusters of childhood leukemia, biased assessments occur; the estimated 5-year incidence of childhood leukemia ranged between zero and eight per 10,000 children in contrast to the simulated two cases per 10,000 children, similar to the observed data. Performing analyses on region-wide data avoids these biases. CONCLUSIONS: Studies using nonrandom selection to investigate the association between childhood leukemia and population mixing are likely to have generated biased findings. Future studies can avoid such bias using a region-wide analytical strategy. See video abstract at, http://links.lww.com/EDE/B431.

Does cycle commuting reduce the risk of mental ill-health? An instrumental variable analysis using distance to nearest cycle path.

BACKGROUND: Previous studies have linked cycling with improved mental wellbeing but these studies tend to use cross-sectional survey data that have small sample sizes and self-reported health measures, and are potentially susceptible to omitted-variable bias and reverse causation. We use an instrumental variable approach and an objective measure of mental ill-health taken from linked administrative data to ask: 'Does cycle commuting reduce the risk of mental ill-health?' METHODS: Our study links data on commuting in Edinburgh and Glasgow from the Scottish population census with mental health prescriptions from the National Health Service Prescribing Information System records. We use road distance from home to nearest cycle path as an instrumental variable for cycle commuting. RESULTS: In total, 378 253 people aged 16-74 years living and working in the City of Edinburgh and Glasgow City council areas at the 2011 census were included in our study; 1.85% of commuters in Glasgow and 4.8% of commuters in Edinburgh cycled to work. Amongst cyclists, 9% had a prescription for mental health compared with 14% amongst non-cyclists. Using a bivariate probit model, we estimate a mean average reduction in prescriptions for antidepressants and/or anxiolytics in the 5 years following the census of -15.1% (95% CI: -15.3% to -15.0%) amongst cycle commuters compared with those who use any other mode to commute. CONCLUSIONS: This work suggests that cycle commuting is causally related to reduced mental ill-health and provides further evidence in support of the promotion of active travel to encourage commuters travelling shorter distances to shift to cycle commutes.

Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: review and recommendations.

BACKGROUND: Directed acyclic graphs (DAGs) are an increasingly popular approach for identifying confounding variables that require conditioning when estimating causal effects. This review examined the use of DAGs in applied health research to inform recommendations for improving their transparency and utility in future research. METHODS: Original health research articles published during 1999-2017 mentioning 'directed acyclic graphs' (or similar) or citing DAGitty were identified from Scopus, Web of Science, Medline and Embase. Data were extracted on the reporting of: estimands, DAGs and adjustment sets, alongside the characteristics of each article's largest DAG. RESULTS: A total of 234 articles were identified that reported using DAGs. A fifth (n = 48, 21%) reported their target estimand(s) and half (n = 115, 48%) reported the adjustment set(s) implied by their DAG(s). Two-thirds of the articles (n = 144, 62%) made at least one DAG available. DAGs varied in size but averaged 12 nodes [interquartile range (IQR): 9-16, range: 3-28] and 29 arcs (IQR: 19-42, range: 3-99). The median saturation (i.e. percentage of total possible arcs) was 46% (IQR: 31-67, range: 12-100). 37% (n = 53) of the DAGs included unobserved variables, 17% (n = 25) included 'super-nodes' (i.e. nodes containing more than one variable) and 34% (n = 49) were visually arranged so that the constituent arcs flowed in the same direction (e.g. top-to-bottom). CONCLUSION: There is substantial variation in the use and reporting of DAGs in applied health research. Although this partly reflects their flexibility, it also highlights some potential areas for improvement. This review hence offers several recommendations to improve the reporting and use of DAGs in future research.

A causal inference perspective on the analysis of compositional data.

BACKGROUND: Compositional data comprise the parts of some whole, for which all parts sum to that whole. They are prevalent in many epidemiological contexts. Although many of the challenges associated with analysing compositional data have been discussed previously, we do so within a formal causal framework by utilizing directed acyclic graphs (DAGs). METHODS: We depict compositional data using DAGs and identify two distinct effect estimands in the generic case: (i) the total effect, and (ii) the relative effect. We consider each in the context of three specific example scenarios involving compositional data: (1) the relationship between the economically active population and area-level gross domestic product; (2) the relationship between fat consumption and body weight; and (3) the relationship between time spent sedentary and body weight. For each, we consider the distinct interpretation of each effect, and the resulting implications for related analyses. RESULTS: For scenarios (1) and (2), both the total and relative effects may be identifiable and causally meaningful, depending upon the specific question of interest. For scenario (3), only the relative effect is identifiable. In all scenarios, the relative effect represents a joint effect, and thus requires careful interpretation. CONCLUSIONS: DAGs are useful for considering causal effects for compositional data. In all analyses involving compositional data, researchers should explicitly consider and declare which causal effect is sought and how it should be interpreted.