Invited commentary: where do the causal DAGS come from?

How do we construct our causal directed acyclic graphs (DAGs)-for example, for life-course modeling and analysis? In this commentary, I review how the data-driven construction of causal DAGs (causal discovery) has evolved, what promises it holds, and what limitations or caveats must be considered. I find that expert- or theory-driven model-building might benefit from some more checking against the data and that causal discovery could bring new ideas to old theories.

Causal relationships between pain, medical treatments, and knee osteoarthritis: A graphical causal model to guide analyses.

OBJECTIVE: Randomized controlled trials (RCTs) are a gold standard for estimating the benefits of clinical interventions, but their decision-making utility can be limited by relatively short follow-up time. Longer-term follow-up of RCT participants is essential to support treatment decisions. However, as time from randomization accrues, loss to follow-up and competing events can introduce biases and require covariate adjustment even for intention-to-treat effects. We describe a process for synthesizing expert knowledge and apply this to long-term follow-up of an RCT of treatments for meniscal tears in patients with knee osteoarthritis (OA). METHODS: We identified 2 post-randomization events likely to impact accurate assessment of pain outcomes beyond 5 years in trial participants: loss to follow-up and total knee replacement (TKR). We conducted literature searches for covariates related to pain and TKR in individuals with knee OA and combined these with expert input. We synthesized the evidence into graphical models. RESULTS: We identified 94 potential covariates potentially related to pain and/or TKR among individuals with knee OA. Of these, 46 were identified in the literature review and 48 by expert panelists. We determined that adjustment for 50 covariates may be required to estimate the long-term effects of knee OA treatments on pain. CONCLUSION: We present a process for combining literature reviews with expert input to synthesize existing knowledge and improve covariate selection. We apply this process to the long-term follow-up of a randomized trial and show that expert input provides additional information not obtainable from literature reviews alone.

The Paradox of Time in Dynamic Causal Systems.

Recent work has shown that people use temporal information including order, delay, and variability to infer causality between events. In this study, we build on this work by investigating the role of time in dynamic systems, where causes take continuous values and also continually influence their effects. Recent studies of learning in these systems explored short interactions in a setting with rapidly evolving dynamics and modeled people as relying on simpler, resource-limited strategies to grapple with the stream of information. A natural question that arises from such an account is whether interacting with systems that unfold more slowly might reduce the systematic errors that result from these strategies. Paradoxically, we find that slowing the task indeed reduced the frequency of one type of error, albeit at the cost of increasing the overall error rate. To explain these results we posit that human learners analyze continuous dynamics into discrete events and use the observed relationships between events to draw conclusions about causal structure. We formalize this intuition in terms of a novel Causal Event Abstraction model and show that this model indeed captures the observed pattern of errors. We comment on the implications these results have for causal cognition.

Assessing knowledge, attitudes, and practices towards causal directed acyclic graphs: a qualitative research project.

Causal graphs provide a key tool for optimizing the validity of causal effect estimates. Although a large literature exists on the mathematical theory underlying the use of causal graphs, less literature exists to aid applied researchers in understanding how best to develop and use causal graphs in their research projects. We sought to understand why researchers do or do not regularly use DAGs by surveying practicing epidemiologists and medical researchers on their knowledge, level of interest, attitudes, and practices towards the use of causal graphs in applied epidemiology and health research. We used Twitter and the Society for Epidemiologic Research to disseminate the survey. Overall, a majority of participants reported being comfortable with using causal graphs and reported using them 'sometimes', 'often', or 'always' in their research. Having received training appeared to improve comprehension of the assumptions displayed in causal graphs. Many of the respondents who did not use causal graphs reported lack of knowledge as a barrier to using DAGs in their research. Causal graphs are of interest to epidemiologists and medical researchers, but there are several barriers to their uptake. Additional training and clearer guidance are needed. In addition, methodological developments regarding visualization of effect measure modification and interaction on causal graphs is needed.

Curie's principle and causal graphs.

Curie's Principle says that any symmetry property of a cause must be found in its effect. In this article, I consider Curie's Principle from the point of view of graphical causal models, and demonstrate that, under one definition of a symmetry transformation, the causal modeling framework does not require anything like Curie's Principle to be true. On another definition of a symmetry transformation, the graphical causal modeling formalism does imply a version of Curie's Principle. These results yield a better understanding of the logical landscape with respect to the relationship between Curie's Principle and graphical causal modeling.

Causal graphs for the analysis of genetic cohort data.

The increasing availability of genetic cohort data has led to many genome-wide association studies (GWAS) successfully identifying genetic associations with an ever-expanding list of phenotypic traits. Association, however, does not imply causation, and therefore methods have been developed to study the issue of causality. Under additional assumptions, Mendelian randomization (MR) studies have proved popular in identifying causal effects between two phenotypes, often using GWAS summary statistics. Given the widespread use of these methods, it is more important than ever to understand, and communicate, the causal assumptions upon which they are based, so that methods are transparent, and findings are clinically relevant. Causal graphs can be used to represent causal assumptions graphically and provide insights into the limitations associated with different analysis methods. Here we review GWAS and MR from a causal perspective, to build up intuition for causal diagrams in genetic problems. We also examine issues of confounding by ancestry and comment on approaches for dealing with such confounding, as well as discussing approaches for dealing with selection biases arising from study design.

Defining causal mediation with a longitudinal mediator and a survival outcome.

In the context of causal mediation analysis, prevailing notions of direct and indirect effects are based on nested counterfactuals. These can be problematic regarding interpretation and identifiability especially when the mediator is a time-dependent process and the outcome is survival or, more generally, a time-to-event outcome. We propose and discuss an alternative definition of mediated effects that does not suffer from these problems, and is more transparent than the current alternatives. Our proposal is based on the extended graphical approach of Robins and Richardson (in: Shrout (ed) Causality and psychopathology: finding the determinants of disorders and their cures, Oxford University Press, Oxford, 2011), where treatment is decomposed into different components, or aspects, along different causal paths corresponding to real world mechanisms. This is an interesting alternative motivation for any causal mediation setting, but especially for survival outcomes. We give assumptions allowing identifiability of such alternative mediated effects leading to the familiar mediation g-formula (Robins in Math Model 7:1393, 1986); this implies that a number of available methods of estimation can be applied.

Modernizing the Bradford Hill criteria for assessing causal relationships in observational data.

Perhaps no other topic in risk analysis is more difficult, more controversial, or more important to risk management policy analysts and decision-makers than how to draw valid, correctly qualified causal conclusions from observational data. Statistical methods can readily quantify associations between observed variables using measures such as relative risk (RR) ratios, odds ratios (OR), slope coefficients for exposure or treatment variables in regression models, and quantities derived from these measures. Textbooks of epidemiology explain how to calculate population attributable fractions, attributable risks, burden-of-disease estimates, and probabilities of causation from relative risk (RR) ratios. Despite their suggestive names, these association-based measures have no necessary connection to causation if the associations on which they are based arise from bias, confounding, p-hacking, coincident historical trends, or other noncausal sources. But policy analysts and decision makers need something more: trustworthy predictions - and, later, evaluations - of the changes in outcomes caused by changes in policy variables. This concept of manipulative causation differs from the more familiar concepts of associational and attributive causation most widely used in epidemiology. Drawing on modern literature on causal discovery and inference principles and algorithms for drawing limited but useful causal conclusions from observational data, we propose seven criteria for assessing consistency of data with a manipulative causal exposure-response relationship - mutual information, directed dependence, internal and external consistency, coherent causal explanation of biological plausibility, causal mediation confirmation, and refutation of non-causal explanations - and discuss to what extent it is now possible to automate discovery of manipulative causal dependencies and quantification of causal effects from observational data. We compare our proposed principles for causal discovery and inference to the traditional Bradford Hill considerations from 1965. Understanding how old and new principles are related can clarify and enrich both.

Graphical Models for Quasi-experimental Designs.

Randomized controlled trials (RCTs) and quasi-experimental designs like regression discontinuity (RD) designs, instrumental variable (IV) designs, and matching and propensity score (PS) designs are frequently used for inferring causal effects. It is well known that the features of these designs facilitate the identification of a causal estimand and, thus, warrant a causal interpretation of the estimated effect. In this article, we discuss and compare the identifying assumptions of quasi-experiments using causal graphs. The increasing complexity of the causal graphs as one switches from an RCT to RD, IV, or PS designs reveals that the assumptions become stronger as the researcher's control over treatment selection diminishes. We introduce limiting graphs for the RD design and conditional graphs for the latent subgroups of com-pliers, always takers, and never takers of the IV design, and argue that the PS is a collider that offsets confounding bias via collider bias.

Limitations of individual causal models, causal graphs, and ignorability assumptions, as illustrated by random confounding and design unfaithfulness.

We describe how ordinary interpretations of causal models and causal graphs fail to capture important distinctions among ignorable allocation mechanisms for subject selection or allocation. We illustrate these limitations in the case of random confounding and designs that prevent such confounding. In many experimental designs individual treatment allocations are dependent, and explicit population models are needed to show this dependency. In particular, certain designs impose unfaithful covariate-treatment distributions to prevent random confounding, yet ordinary causal graphs cannot discriminate between these unconfounded designs and confounded studies. Causal models for populations are better suited for displaying these phenomena than are individual-level models, because they allow representation of allocation dependencies as well as outcome dependencies across individuals. Nonetheless, even with this extension, ordinary graphical models still fail to capture distinctions between hypothetical superpopulations (sampling distributions) and observed populations (actual distributions), although potential-outcome models can be adapted to show these distinctions and their consequences.

Improving causal inferences in risk analysis.

Recent headlines and scientific articles projecting significant human health benefits from changes in exposures too often depend on unvalidated subjective expert judgments and modeling assumptions, especially about the causal interpretation of statistical associations. Some of these assessments are demonstrably biased toward false positives and inflated effects estimates. More objective, data-driven methods of causal analysis are available to risk analysts. These can help to reduce bias and increase the credibility and realism of health effects risk assessments and causal claims. For example, quasi-experimental designs and analysis allow alternative (noncausal) explanations for associations to be tested, and refuted if appropriate. Panel data studies examine empirical relations between changes in hypothesized causes and effects. Intervention and change-point analyses identify effects (e.g., significant changes in health effects time series) and estimate their sizes. Granger causality tests, conditional independence tests, and counterfactual causality models test whether a hypothesized cause helps to predict its presumed effects, and quantify exposure-specific contributions to response rates in differently exposed groups, even in the presence of confounders. Causal graph models let causal mechanistic hypotheses be tested and refined using biomarker data. These methods can potentially revolutionize the study of exposure-induced health effects, helping to overcome pervasive false-positive biases and move the health risk assessment scientific community toward more accurate assessments of the impacts of exposures and interventions on public health.

A case study and proposal for publishing directed acyclic graphs: The effectiveness of the quadrivalent human papillomavirus vaccine in perinatally HIV Infected girls.

BACKGROUND: Developing a causal graph is an important step in etiologic research planning and can be used to highlight data flaws and irreparable bias and confounding. As a case study, we consider recent findings that suggest human papillomavirus (HPV) vaccine is less effective against HPV-associated disease among girls living with HIV compared to girls without HIV. OBJECTIVES: To understand the relationship between HIV status and HPV vaccine effectiveness, it is important to outline the key assumptions of the causal mechanisms before designing a study to investigate the effect of the HPV vaccine in girls living with HIV infection. METHODS: We present a causal graph to describe our assumptions and proposed approach to explore this relationship. We hope to obtain feedback on our assumptions before data analysis and exemplify the process for designing causal graphs to inform an etiologic study. CONCLUSION: The approach we lay out in this paper may be useful for other researchers who have an interest in using causal graphs to describe and assess assumptions in their own research before undergoing data collection and/or analysis.

How subgroup analyses can miss the trees for the forest plots: A simulation study.

OBJECTIVES: Subgroup analyses of clinical trial data can be an important tool for understanding when treatment effects differ across populations. That said, even effect estimates from prespecified subgroups in well-conducted trials may not apply to corresponding subgroups in the source population. While this divergence may simply reflect statistical imprecision, there has been less discussion of systematic or structural sources of misleading subgroup estimates. STUDY DESIGN AND SETTING: We use directed acyclic graphs to show how selection bias caused by associations between effect measure modifiers and trial selection, whether explicit (e.g., eligibility criteria) or implicit (e.g., self-selection based on race), can result in subgroup estimates that do not correspond to subgroup effects in the source population. To demonstrate this point, we provide a hypothetical example illustrating the sorts of erroneous conclusions that can result, as well as their potential consequences. We also provide a tool for readers to explore additional cases. CONCLUSION: Treating subgroups within a trial essentially as random samples of the corresponding subgroups in the wider population can be misleading, even when analyses are conducted rigorously and all findings are internally valid. Researchers should carefully examine associations between (and consider adjusting for) variables when attempting to identify heterogeneous treatment effects.

Causal Learning via Manifold Regularization.

This paper frames causal structure estimation as a machine learning task. The idea is to treat indicators of causal relationships between variables as 'labels' and to exploit available data on the variables of interest to provide features for the labelling task. Background scientific knowledge or any available interventional data provide labels on some causal relationships and the remainder are treated as unlabelled. To illustrate the key ideas, we develop a distance-based approach (based on bivariate histograms) within a manifold regularization framework. We present empirical results on three different biological data sets (including examples where causal effects can be verified by experimental intervention), that together demonstrate the efficacy and general nature of the approach as well as its simplicity from a user's point of view.

Causal inference algorithms can be useful in life course epidemiology.

OBJECTIVES: Life course epidemiology attempts to unravel causal relationships between variables observed over time. Causal relationships can be represented as directed acyclic graphs. This article explains the theoretical concepts of the search algorithms used for finding such representations, discusses various types of such algorithms, and exemplifies their use in the context of obesity and insulin resistance. STUDY DESIGN AND SETTING: We investigated possible causal relations between gender, birth weight, waist circumference, and blood glucose level of 4,081 adult participants of the Prevention of REnal and Vascular ENd-stage Disease study. The latter two variables were measured at three time points at intervals of about 3 years. RESULTS: We present the resulting causal graphs, estimate parameters of the corresponding structural equation models, and discuss usefulness and limitations of this methodology. CONCLUSION: As an exploratory method, causal graphs and the associated theory can help construct possible causal models underlying observational data. In this way, the causal search algorithms provide a valuable statistical tool for life course epidemiological research.