Invited Commentary: Where Do the Causal DAGs Come From?

How do we construct our causal DAGs, e.g. for life course modelling 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. In conclusion I find that expert- or theory-driven model building might benefit from some more checking against the data and causal discovery could bring new ideas into old theories.

The role of psychosocial well-being and emotion-driven impulsiveness in food choices of European adolescents.

BACKGROUND: It is unclear whether a hypothetical intervention targeting either psychosocial well-being or emotion-driven impulsiveness is more effective in reducing unhealthy food choices. Therefore, we aimed to compare the (separate) causal effects of psychosocial well-being and emotion-driven impulsiveness on European adolescents' sweet and fat propensity. METHODS: We included 2,065 participants of the IDEFICS/I.Family cohort (mean age: 13.4) providing self-reported data on sweet propensity (score range: 0 to 68.4), fat propensity (range: 0 to 72.6), emotion-driven impulsiveness using the UPPS-P negative urgency subscale, and psychosocial well-being using the KINDLR Questionnaire. We estimated, separately, the average causal effects of psychosocial well-being and emotion-driven impulsiveness on sweet and fat propensity applying a semi-parametric doubly robust method (targeted maximum likelihood estimation). Further, we investigated a potential indirect effect of psychosocial well-being on sweet and fat propensity mediated via emotion-driven impulsiveness using a causal mediation analysis. RESULTS: If all adolescents, hypothetically, had high levels of psychosocial well-being, compared to low levels, we estimated a decrease in average sweet propensity by 1.43 [95%-confidence interval: 0.25 to 2.61]. A smaller effect was estimated for fat propensity. Similarly, if all adolescents had high levels of emotion-driven impulsiveness, compared to low levels, average sweet propensity would be decreased by 2.07 [0.87 to 3.26] and average fat propensity by 1.85 [0.81 to 2.88]. The indirect effect of psychosocial well-being via emotion-driven impulsiveness was 0.61 [0.24 to 1.09] for average sweet propensity and 0.55 [0.13 to 0.86] for average fat propensity. CONCLUSIONS: An intervention targeting emotion-driven impulsiveness, compared to psychosocial well-being, would be marginally more effective in reducing sweet and fat propensity in adolescents.

Variable selection in linear regression models: Choosing the best subset is not always the best choice.

We consider the question of variable selection in linear regressions, in the sense of identifying the correct direct predictors (those variables that have nonzero coefficients given all candidate predictors). Best subset selection (BSS) is often considered the "gold standard," with its use being restricted only by its NP-hard nature. Alternatives such as the least absolute shrinkage and selection operator (Lasso) or the Elastic net (Enet) have become methods of choice in high-dimensional settings. A recent proposal represents BSS as a mixed-integer optimization problem so that large problems have become computationally feasible. We present an extensive neutral comparison assessing the ability to select the correct direct predictors of BSS compared to forward stepwise selection (FSS), Lasso, and Enet. The simulation considers a range of settings that are challenging regarding dimensionality (number of observations and variables), signal-to-noise ratios, and correlations between predictors. As fair measure of performance, we primarily used the best possible F1-score for each method, and results were confirmed by alternative performance measures and practical criteria for choosing the tuning parameters and subset sizes. Surprisingly, it was only in settings where the signal-to-noise ratio was high and the variables were uncorrelated that BSS reliably outperformed the other methods, even in low-dimensional settings. Furthermore, FSS performed almost identically to BSS. Our results shed new light on the usual presumption of BSS being, in principle, the best choice for selecting the correct direct predictors. Especially for correlated variables, alternatives like Enet are faster and appear to perform better in practical settings.

Considering Questions Before Methods in Dementia Research With Competing Events and Causal Goals.

Studying causal exposure effects on dementia is challenging when death is a competing event. Researchers often interpret death as a potential source of bias, although bias cannot be defined or assessed if the causal question is not explicitly specified. Here we discuss 2 possible notions of a causal effect on dementia risk: the "controlled direct effect" and the "total effect." We provide definitions and discuss the "censoring" assumptions needed for identification in either case and their link to familiar statistical methods. We illustrate concepts in a hypothetical randomized trial on smoking cessation in late midlife, and emulate such a trial using observational data from the Rotterdam Study, the Netherlands, 1990-2015. We estimated a total effect of smoking cessation (compared with continued smoking) on 20-year dementia risk of 2.1 (95% confidence interval: -0.1, 4.2) percentage points and a controlled direct effect of smoking cessation on 20-year dementia risk had death been prevented of -2.7 (95% confidence interval: -6.1, 0.8) percentage points. Our study highlights how analyses corresponding to different causal questions can have different results, here with point estimates on opposite sides of the null. Having a clear causal question in view of the competing event and transparent and explicit assumptions are essential to interpreting results and potential bias.

Multiple imputation and test-wise deletion for causal discovery with incomplete cohort data.

Causal discovery algorithms estimate causal graphs from observational data. This can provide a valuable complement to analyses focusing on the causal relation between individual treatment-outcome pairs. Constraint-based causal discovery algorithms rely on conditional independence testing when building the graph. Until recently, these algorithms have been unable to handle missing values. In this article, we investigate two alternative solutions: test-wise deletion and multiple imputation. We establish necessary and sufficient conditions for the recoverability of causal structures under test-wise deletion, and argue that multiple imputation is more challenging in the context of causal discovery than for estimation. We conduct an extensive comparison by simulating from benchmark causal graphs: as one might expect, we find that test-wise deletion and multiple imputation both clearly outperform list-wise deletion and single imputation. Crucially, our results further suggest that multiple imputation is especially useful in settings with a small number of either Gaussian or discrete variables, but when the dataset contains a mix of both neither method is uniformly best. The methods we compare include random forest imputation and a hybrid procedure combining test-wise deletion and multiple imputation. An application to data from the IDEFICS cohort study on diet- and lifestyle-related diseases in European children serves as an illustrating example.

Insights into the Cross-world Independence Assumption of Causal Mediation Analysis.

Causal mediation analysis is a useful tool for epidemiologic research, but it has been criticized for relying on a "cross-world" independence assumption that counterfactual outcome and mediator values are independent even in causal worlds where the exposure assignments for the outcome and mediator differ. This assumption is empirically difficult to verify and problematic to justify based on background knowledge. In the present article, we aim to assist the applied researcher in understanding this assumption. Synthesizing what is known about the cross-world independence assumption, we discuss the relationship between assumptions for causal mediation analyses, causal models, and nonparametric identification of natural direct and indirect effects. In particular, we give a practical example of an applied setting where the cross-world independence assumption is violated even without any post-treatment confounding. Further, we review possible alternatives to the cross-world independence assumption, including the use of bounds that avoid the assumption altogether. Finally, we carry out a numeric study in which the cross-world independence assumption is violated to assess the ensuing bias in estimating natural direct and indirect effects. We conclude with recommendations for carrying out causal mediation analyses.

Discussion on "Causal mediation of semicompeting risks" by Yen-Tsung Huang.

Huang proposes a method for assessing the impact of a point treatment on mortality either directly or mediated by occurrence of a nonterminal health event, based on data from a prospective cohort study in which the occurrence of the nonterminal health event may be preemptied by death but not vice versa. The author uses a causal mediation framework to formally define causal quantities known as natural (in)direct effects. The novelty consists of adapting these concepts to a continuous-time modeling framework based on counting processes. In an effort to posit "scientifically interpretable estimands," statistical and causal assumptions are introduced for identification. In this commentary, we argue that these assumptions are not only difficult to interpret and justify, but are also likely violated in the hepatitis B motivating example and other survival/time to event settings as well.

[Secondary Data for Pharmacoepidemiological Research - Making the Best of It!] / Nutzung von Sekundärdaten für die pharmakoepidemiologische Forschung ­ machen wir das Beste draus!

Studies using secondary data such as health care claims data are often faced with methodological challenges due to the time-dependence of key quantities or unmeasured confounding. In the present paper, we discuss approaches to avoid or suitably address various sources of potential bias. In particular, we illustrate the target trial principle, marginal structural models, and instrumental variables with examples from the "GePaRD" database. Finally, we discuss the strengths and limitations of record linkage which can sometimes be used to supply missing information.

A generalized theory of separable effects in competing event settings.

In competing event settings, a counterfactual contrast of cause-specific cumulative incidences quantifies the total causal effect of a treatment on the event of interest. However, effects of treatment on the competing event may indirectly contribute to this total effect, complicating its interpretation. We previously proposed the separable effects to define direct and indirect effects of the treatment on the event of interest. This definition was given in a simple setting, where the treatment was decomposed into two components acting along two separate causal pathways. Here we generalize the notion of separable effects, allowing for interpretation, identification and estimation in a wide variety of settings. We propose and discuss a definition of separable effects that is applicable to general time-varying structures, where the separable effects can still be meaningfully interpreted as effects of modified treatments, even when they cannot be regarded as direct and indirect effects. For these settings we derive weaker conditions for identification of separable effects in studies where decomposed, or otherwise modified, treatments are not yet available; in particular, these conditions allow for time-varying common causes of the event of interest, the competing events and loss to follow-up. We also propose semi-parametric weighted estimators that are straightforward to implement. We stress that unlike previous definitions of direct and indirect effects, the separable effects can be subject to empirical scrutiny in future studies.

Constrained instruments and their application to Mendelian randomization with pleiotropy.

In Mendelian randomization (MR), inference about causal relationship between a phenotype of interest and a response or disease outcome can be obtained by constructing instrumental variables from genetic variants. However, MR inference requires three assumptions, one of which is that the genetic variants only influence the outcome through phenotype of interest. Pleiotropy, that is, the situation in which some genetic variants affect more than one phenotype, can invalidate these genetic variants for use as instrumental variables; thus a naive analysis will give biased estimates of the causal relation. Here, we present new methods (constrained instrumental variable [CIV] methods) to construct valid instrumental variables and perform adjusted causal effect estimation when pleiotropy exists and when the pleiotropic phenotypes are available. We demonstrate that a smoothed version of CIV performs approximate selection of genetic variants that are valid instruments, and provides unbiased estimates of the causal effects. We provide details on a number of existing methods, together with a comparison of their performance in a large series of simulations. CIV performs robustly across different pleiotropic violations of the MR assumptions. We also analyzed the data from the Alzheimer's disease (AD) neuroimaging initiative (ADNI; Mueller et al., 2005. Alzheimer's Dementia, 11(1), 55-66) to disentangle causal relationships of several biomarkers with AD progression.

Epidemiology, genetic epidemiology and Mendelian randomisation: more need than ever to attend to detail.

In the current era, with increasing availability of results from genetic association studies, finding genetic instruments for inferring causality in observational epidemiology has become apparently simple. Mendelian randomisation (MR) analyses are hence growing in popularity and, in particular, methods that can incorporate multiple instruments are being rapidly developed for these applications. Such analyses have enormous potential, but they all rely on strong, different, and inherently untestable assumptions. These have to be clearly stated and carefully justified for every application in order to avoid conclusions that cannot be replicated. In this article, we review the instrumental variable assumptions and discuss the popular linear additive structural model. We advocate the use of tests for the null hypothesis of 'no causal effect' and calculation of the bounds for a causal effect, whenever possible, as these do not rely on parametric modelling assumptions. We clarify the difference between a randomised trial and an MR study and we comment on the importance of validating instruments, especially when considering them for joint use in an analysis. We urge researchers to stand by their convictions, if satisfied that the relevant assumptions hold, and to interpret their results causally since that is the only reason for performing an MR analysis in the first place.

Time-dependent mediators in survival analysis: Modeling direct and indirect effects with the additive hazards model.

We discuss causal mediation analyses for survival data and propose a new approach based on the additive hazards model. The emphasis is on a dynamic point of view, that is, understanding how the direct and indirect effects develop over time. Hence, importantly, we allow for a time varying mediator. To define direct and indirect effects in such a longitudinal survival setting we take an interventional approach (Didelez, 2018) where treatment is separated into one aspect affecting the mediator and a different aspect affecting survival. In general, this leads to a version of the nonparametric g-formula (Robins, 1986). In the present paper, we demonstrate that combining the g-formula with the additive hazards model and a sequential linear model for the mediator process results in simple and interpretable expressions for direct and indirect effects in terms of relative survival as well as cumulative hazards. Our results generalize and formalize the method of dynamic path analysis (Fosen, Ferkingstad, Borgan, & Aalen, 2006; Strohmaier et al., 2015). An application to data from a clinical trial on blood pressure medication is given.

Covariate selection strategies for causal inference: Classification and comparison.

When causal effects are to be estimated from observational data, we have to adjust for confounding. A central aim of covariate selection for causal inference is therefore to determine a set that is sufficient for confounding adjustment, but other aims such as efficiency or robustness can be important as well. In this paper, we review six general approaches to covariate selection that differ in the targeted type of adjustment set. We discuss and illustrate their advantages and disadvantages using causal diagrams. Moreover, the approaches and different ways of implementing them are compared empirically in an extensive simulation study. We conclude that there are considerable differences between the approaches but none of them is uniformly best, with performance depending on the chosen adjustment method as well as the true confounding structure. Any prior structural knowledge on the causal relations is helpful to choose the most appropriate method.

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.

Comparison of statistical methods for finding network motifs.

There has been much recent interest in systems biology for investigating the structure of gene regulatory systems. Such networks are often formed of specific patterns, or network motifs, that are interesting from a biological point of view. Our aim in the present paper is to compare statistical methods specifically with regard to the question of how well they can detect such motifs. One popular approach is by network analysis with Gaussian graphical models (GGMs), which are statistical models associated with undirected graphs, where vertices of the graph represent genes and edges indicate regulatory interactions. Gene expression microarray data allow us to observe the amount of mRNA simultaneously for a large number of genes p under different experimental conditions n, where p is usually much larger than n prohibiting the use of standard methods. We therefore compare the performance of a number of procedures that have been specifically designed to address this large p-small n issue: G-Lasso estimation, Neighbourhood selection, Shrinkage estimation using empirical Bayes for model selection, and PC-algorithm. We found that all approaches performed poorly on the benchmark E. coli network. Hence we systematically studied their ability to detect specific network motifs, pairs, hubs and cascades, in extensive simulations. We conclude that all methods have difficulty detecting hubs, but the PC-algorithm is most promising.

Lack of identification in semiparametric instrumental variable models with binary outcomes.

A parameter in a statistical model is identified if its value can be uniquely determined from the distribution of the observable data. We consider the context of an instrumental variable analysis with a binary outcome for estimating a causal risk ratio. The semiparametric generalized method of moments and structural mean model frameworks use estimating equations for parameter estimation. In this paper, we demonstrate that lack of identification can occur in either of these frameworks, especially if the instrument is weak. In particular, the estimating equations may have no solution or multiple solutions. We investigate the relationship between the strength of the instrument and the proportion of simulated data sets for which there is a unique solution of the estimating equations. We see that this proportion does not appear to depend greatly on the sample size, particularly for weak instruments (ρ(2) ≤ 0.01). Poor identification was observed in a considerable proportion of simulated data sets for instruments explaining up to 10% of the variance in the exposure with sample sizes up to 1 million. In an applied example considering the causal effect of body mass index (weight (kg)/height (m)(2)) on the probability of early menarche, estimates and standard errors from an automated optimization routine were misleading.

A longitudinal causal graph analysis investigating modifiable risk factors and obesity in a European cohort of children and adolescents.

Childhood obesity is a complex disorder that appears to be influenced by an interacting system of many factors. Taking this complexity into account, we aim to investigate the causal structure underlying childhood obesity. Our focus is on identifying potential early, direct or indirect, causes of obesity which may be promising targets for prevention strategies. Using a causal discovery algorithm, we estimate a cohort causal graph (CCG) over the life course from childhood to adolescence. We adapt a popular method, the so-called PC-algorithm, to deal with missing values by multiple imputation, with mixed discrete and continuous variables, and that takes background knowledge such as the time-structure of cohort data into account. The algorithm is then applied to learn the causal structure among 51 variables including obesity, early life factors, diet, lifestyle, insulin resistance, puberty stage and cultural background of 5112 children from the European IDEFICS/I.Family cohort across three waves (2007-2014). The robustness of the learned causal structure is addressed in a series of alternative and sensitivity analyses; in particular, we use bootstrap resamples to assess the stability of aspects of the learned CCG. Our results suggest some but only indirect possible causal paths from early modifiable risk factors, such as audio-visual media consumption and physical activity, to obesity (measured by age- and sex-adjusted BMI z-scores) 6 years later.

Severity of bias of a simple estimator of the causal odds ratio in Mendelian randomization studies.

Mendelian randomization studies estimate causal effects using genetic variants as instruments. Instrumental variable methods are straightforward for linear models, but epidemiologists often use odds ratios to quantify effects. Also, odds ratios are often the quantities reported in meta-analyses. Many applications of Mendelian randomization dichotomize genotype and estimate the population causal log odds ratio for unit increase in exposure by dividing the genotype-disease log odds ratio by the difference in mean exposure between genotypes. This 'Wald-type' estimator is biased even in large samples, but whether the magnitude of bias is of practical importance is unclear. We study the large-sample bias of this estimator in a simple model with a continuous normally distributed exposure, a single unobserved confounder that is not an effect modifier, and interpretable parameters. We focus on parameter values that reflect scenarios in which we apply Mendelian randomization, including realistic values for the degree of confounding and strength of the causal effect. We evaluate this estimator and the causal odds ratio using numerical integration and obtain approximate analytic expressions to check results and gain insight. A small simulation study examines finite sample bias and mild violations of the normality assumption. For our simple data-generating model, we find that the Wald estimator is asymptotically biased with a bias of around 10% in fairly typical Mendelian randomization scenarios but which can be larger in more extreme situations. Recently developed methods such as structural mean models require fewer untestable assumptions and we recommend their use when the individual-level data they require are available. The Wald-type estimator may retain a role as an approximate method for meta-analysis based on summary data.

Examining the Causal Mediating Role of Cardiovascular Disease on the Effect of Subclinical Cardiovascular Disease on Cognitive Impairment via Separable Effects.

BACKGROUND: An important epidemiological question is understanding how vascular risk factors contribute to cognitive impairment. Using data from the Cardiovascular Health Cognition Study, we investigated how subclinical cardiovascular disease (sCVD) relates to cognitive impairment risk and the extent to which the hypothesized risk is mediated by the incidence of clinically manifested cardiovascular disease (CVD), both overall and within apolipoprotein E-4 (APOE-4) subgroups. METHODS: We adopted a novel "separable effects" causal mediation framework that assumes that sCVD has separably intervenable atherosclerosis-related components. We then ran several mediation models, adjusting for key covariates. RESULTS: We found that sCVD increased overall risk of cognitive impairment (risk ratio [RR] = 1.21, 95% confidence interval [CI]: 1.03, 1.44); however, there was little or no mediation by incident clinically manifested CVD (indirect effect RR = 1.02, 95% CI: 1.00, 1.03). We also found attenuated effects among APOE-4 carriers (total effect RR = 1.09, 95% CI: 0.81, 1.47; indirect effect RR = 0.99, 95% CI: 0.96, 1.01) and stronger findings among noncarriers (total effect RR = 1.29, 95% CI: 1.05, 1.60; indirect effect RR = 1.02, 95% CI: 1.00, 1.05). In secondary analyses restricting cognitive impairment to only incident dementia cases, we found similar effect patterns. CONCLUSIONS: We found that the effect of sCVD on cognitive impairment does not seem to be mediated by CVD, both overall and within APOE-4 subgroups. Our results were critically assessed via sensitivity analyses, and they were found to be robust. Future work is needed to fully understand the relationship between sCVD, CVD, and cognitive impairment.