Causal Consistency of Structural Equation Models

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.Comment: equal contribution between Rubenstein and Weichwald; accepted manuscrip

Recovery of non-linear cause-effect relationships from linearly mixed neuroimaging data

Causal inference concerns the identification of cause-effect relationships between variables. However, often only linear combinations of variables constitute meaningful causal variables. For example, recovering the signal of a cortical source from electroencephalography requires a well-tuned combination of signals recorded at multiple electrodes. We recently introduced the MERLiN (Mixture Effect Recovery in Linear Networks) algorithm that is able to recover, from an observed linear mixture, a causal variable that is a linear effect of another given variable. Here we relax the assumption of this cause-effect relationship being linear and present an extended algorithm that can pick up non-linear cause-effect relationships. Thus, the main contribution is an algorithm (and ready to use code) that has broader applicability and allows for a richer model class. Furthermore, a comparative analysis indicates that the assumption of linear cause-effect relationships is not restrictive in analysing electroencephalographic data

Causal and anti-causal learning in pattern recognition for neuroimaging

Pattern recognition in neuroimaging distinguishes between two types of models: encoding- and decoding models. This distinction is based on the insight that brain state features, that are found to be relevant in an experimental paradigm, carry a different meaning in encoding- than in decoding models. In this paper, we argue that this distinction is not sufficient: Relevant features in encoding- and decoding models carry a different meaning depending on whether they represent causal- or anti-causal relations. We provide a theoretical justification for this argument and conclude that causal inference is essential for interpretation in neuroimaging.Comment: accepted manuscrip

Absence of EEG correlates of self-referential processing depth in ALS

Self-referential processing is a key cognitive process, associated with the serotonergic system and the default mode network (DMN). Decreased levels of serotonin and reduced activations of the DMN observed in amyotrophic lateral sclerosis (ALS) suggest that self-referential processing might be altered in patients with ALS. Here, we investigate the effects of ALS on the electroencephalography correlates of self-referential thinking. We find that electroencephalography (EEG) correlates of self-referential thinking are present in healthy individuals, but not in those with ALS. In particular, thinking about themselves or others significantly modulates the bandpower in the medial prefrontal cortex in healthy individuals, but not in ALS patients. This finding supports the view of ALS as a complex multisystem disorder which, as shown here, includes dysfunctional processing of the medial prefrontal cortex. It points towards possible alterations of self-consciousness in ALS patients, which might have important consequences for patients' self-conceptions, personal relations, and decision-making

Causal Consistency of Structural Equation Models

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs

Improving 1-year mortality prediction in ACS patients using machine learning.

The Global Registry of Acute Coronary Events (GRACE) score is an established clinical risk stratification tool for patients with acute coronary syndromes (ACS). We developed and internally validated a model for 1-year all-cause mortality prediction in ACS patients. Between 2009 and 2012, 2'168 ACS patients were enrolled into the Swiss SPUM-ACS Cohort. Biomarkers were determined in 1'892 patients and follow-up was achieved in 95.8% of patients. 1-year all-cause mortality was 4.3% (n = 80). In our analysis we consider all linear models using combinations of 8 out of 56 variables to predict 1-year all-cause mortality and to derive a variable ranking. 1.3% of 1'420'494'075 models outperformed the GRACE 2.0 Score. The SPUM-ACS Score includes age, plasma glucose, NT-proBNP, left ventricular ejection fraction (LVEF), Killip class, history of peripheral artery disease (PAD), malignancy, and cardio-pulmonary resuscitation. For predicting 1-year mortality after ACS, the SPUM-ACS Score outperformed the GRACE 2.0 Score which achieves a 5-fold cross-validated AUC of 0.81 (95% CI 0.78-0.84). Ranking individual features according to their importance across all multivariate models revealed age, trimethylamine N-oxide, creatinine, history of PAD or malignancy, LVEF, and haemoglobin as the most relevant variables for predicting 1-year mortality. The variable ranking and the selection for the SPUM-ACS Score highlight the relevance of age, markers of heart failure, and comorbidities for prediction of all-cause death. Before application, this score needs to be externally validated and refined in larger cohorts. NCT01000701