A Darwinian version of the Leslie logistic model for age-structured populations.

In this review, we explore the advances, setbacks, and future possibilities of directed acyclic graphs (DAGs) as conceptual and analytical tools in applied and theoretical epidemiology. DAGs are literal, theoretical or speculative, and diagrammatic representations of known, uncertain, or unknown data generating mechanisms (and dataset generating processes) in which the causal relationships between variables are determined on the basis of two over-riding principles-"directionality" and "acyclicity". Among the many strengths of DAGs are their transparency, simplicity, flexibility, methodological utility, and epistemological credibility. All these strengths can help applied epidemiological studies better mitigate (and acknowledge) the impact of avoidable (and unavoidable) biases in causal inference analyses based on observational/non-experimental data. They can also strengthen the credibility and utility of theoretical studies that use DAGs to identify and explore hitherto hidden sources of analytical and inferential bias. Nonetheless, and despite their apparent simplicity, the application of DAGs has suffered a number of setbacks due to weaknesses in understanding, practice, and reporting. These include a failure to include all possible (conceivable and inconceivable) unmeasured covariates when developing and specifying DAGs; and weaknesses in the reporting of DAGs containing more than a handful of variables and paths, and where the intended application(s) and rationale(s) involved is necessary for appreciating, evaluating, and exploiting any causal insights they might offer. We proposed two additional principles to address these weaknesses and identify a number of opportunities where DAGs might lead to further advancements: The critical appraisal and synthesis of observational studies; the external validity and portability of causality-informed prediction; the identification of novel sources of bias; and the application of DAG-dataset consistency assessment to resolve pervasive uncertainty in the temporal positioning of time-variant and time-invariant exposures, outcomes, and covariates.