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Background Causal inference has seen an increasing popularity in medical research. Estimation of causal effects from observational data allows to draw conclusions from data when randomized controlled trials cannot be conducted. Although the identification of structural causal models (SCM) and the calculation of structural coefficients has received much attention, a key requirement for valid causal inference is that conclusions are drawn based on the true data-generating model. Methods It remains widely unknown how large the probability is to reject the true structural causal model when observational data from it is sampled. The latter probability – the causal false-positive risk – is crucial, as rejection of the true causal model can induce bias in the estimation of causal effects. In this paper, the widely used causal models of confounders and colliders are studied regarding their causal false-positive risk in linear Markovian models. A simulation study is carried out which investigates the causal false-positive risk in Gaussian linear Markovian models. Therefore, the testable implications of the DAG corresponding to confounders and colliders are analyzed from a Bayesian perspective. Furthermore, the induced bias in estimating the structural coefficients and causal effects is studied. Results Results show that the false-positive risk of rejecting a true SCM of even simple building blocks like confounders and colliders is substantial. Importantly, estimation of average, direct and indirect causal effects can become strongly biased if a true model is rejected. The causal false-positive risk may thus serve as an indicator or proxy for the induced bias. Conclusion While the identification of structural coefficients and testable implications of causal models have been studied rigorously in the literature, this paper shows that causal inference also must develop new concepts for controlling the causal false-positive risk. Although a high risk cannot be equated with a substantial bias, it is indicative of the induced bias. The latter fact calls for the development of more advanced risk measures for committing a causal type I error in causal inference.

This paper proposes a novel algorithm for optimizing decision variables with respect to an outcome variable of interest in complex problems, such as those arising from big data. The proposed algorithm builds on the notion of Markov blankets in Bayesian networks to alleviate the computational challenges associated with optimization tasks in complex datasets. Through a case study, we apply the algorithm to optimize medication prescriptions for diabetic patients, who have different characteristics, suffer from multiple comorbidities, and take multiple medications concurrently. In particular, we demonstrate how the optimal combination of diabetic medications can be found by examining the comparative effectiveness of the medications among similar patients. The case study is based on 5 years of data for 19,223 diabetic patients. Our results indicate that certain patient characteristics (e.g., clinical and demographic features) influence optimal treatment decisions. Among patients examined, monotherapy with metformin was the most common optimal medication decision. The results are consistent with the relevant clinical guidelines and reports in the medical literature. The proposed algorithm obviates the need for knowledge of the whole Bayesian network model, which can be very complex in big data problems. The procedure can be applied to any complex Bayesian network with numerous features, multiple decision variables, and a target variable.

Do-calculus is concerned with estimating the interventional distribution of an action from the observed joint probability distribution of the variables in a given causal structure. All identifiable causal effects can be derived using the rules of do-calculus, but the rules themselves do not give any direct indication whether the effect in question is identifiable or not. Shpitser and Pearl constructed an algorithm for identifying joint interventional distributions in causal models, which contain unobserved variables and induce directed acyclic graphs. This algorithm can be seen as a repeated application of the rules of do-calculus and known properties of probabilities, and it ultimately either derives an expression for the causal distribution, or fails to identify the effect, in which case the effect is non-identifiable. In this paper, the R package causaleffect is presented, which provides an implementation of this algorithm. Functionality of causaleffect is also demonstrated through examples., Comment: This is the version published in the Journal of Statistical Software

The concept of d-separation (Pearl, 1988) was originally defined for acyclic directed graphs, but there is a natural extension of the concept to directed graphs with cycles. When exactly the same set of d-separation relations hold in two directed graphs, no matter whether respectively cyclic or acyclic, we say that they are markov equivalent. In other words, when two directed cyclic graphs are Markov equivalent, the set of distributions that satisfy a natural extension of the global directed Markov condition (Lauritzen et al., 1990) is exactly the same for each graph. There is an obvious exponential (in the number of vertices) time algorithm for deciding Markov equivalence of two directed cyclic graphs: simply check all of the d-separation relations in each graph. In this paper I prove a theorem that gives necessary and sufficient conditions for two directed cyclic graphs to be Markov equivalent, where each of the conditions can be checked in polynomial time. Hence, the theorem can be easily adapted into a polynomial time algorithm for deciding the Markov equivalence of two directed cyclic graphs (Richardson, 1996).