Deep determinism and the assessment of mechanistic interaction between categorical and continuous variables

Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic interaction which acknowledges asymmetries of the kind "factor A interferes with factor B, but not viceversa". A class of tests for mechanistic interaction is proposed, which works on discrete or continuous causal variables, in any combination. Conditions under which these tests can be applied under a generic regime of data collection, be it interventional or observational, are discussed in terms of conditional independence assumptions within the framework of Augmented Directed Graphs. The scientific relevance of the method and the practicality of the graphical framework are illustrated with the aid of two studies in coronary artery disease. Our analysis relies on the "deep determinism" assumption that there exists some relevant set V - possibly unobserved - of "context variables", such that the response Y is a deterministic function of the values of V and of the causal factors of interest. Caveats regarding this assumption in real studies are discussed.Comment: 20 pages including the four figures, plus two tables. Submitted to "Biostatistics" on November 24, 201

Sufficient Covariate, Propensity Variable and Doubly Robust Estimation

Statistical causal inference from observational studies often requires adjustment for a possibly multi-dimensional variable, where dimension reduction is crucial. The propensity score, first introduced by Rosenbaum and Rubin, is a popular approach to such reduction. We address causal inference within Dawid's decision-theoretic framework, where it is essential to pay attention to sufficient covariates and their properties. We examine the role of a propensity variable in a normal linear model. We investigate both population-based and sample-based linear regressions, with adjustments for a multivariate covariate and for a propensity variable. In addition, we study the augmented inverse probability weighted estimator, involving a combination of a response model and a propensity model. In a linear regression with homoscedasticity, a propensity variable is proved to provide the same estimated causal effect as multivariate adjustment. An estimated propensity variable may, but need not, yield better precision than the true propensity variable. The augmented inverse probability weighted estimator is doubly robust and can improve precision if the propensity model is correctly specified

Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview

We consider the problem of learning about and comparing the consequences of dynamic treatment strategies on the basis of observational data. We formulate this within a probabilistic decision-theoretic framework. Our approach is compared with related work by Robins and others: in particular, we show how Robins's 'G-computation' algorithm arises naturally from this decision-theoretic perspective. Careful attention is paid to the mathematical and substantive conditions required to justify the use of this formula. These conditions revolve around a property we term stability, which relates the probabilistic behaviours of observational and interventional regimes. We show how an assumption of 'sequential randomization' (or 'no unmeasured confounders'), or an alternative assumption of 'sequential irrelevance', can be used to infer stability. Probabilistic influence diagrams are used to simplify manipulations, and their power and limitations are discussed. We compare our approach with alternative formulations based on causal DAGs or potential response models. We aim to show that formulating the problem of assessing dynamic treatment strategies as a problem of decision analysis brings clarity, simplicity and generality.Comment: 49 pages, 15 figure

Complete Graphical Characterization and Construction of Adjustment Sets in Markov Equivalence Classes of Ancestral Graphs

We present a graphical criterion for covariate adjustment that is sound and complete for four different classes of causal graphical models: directed acyclic graphs (DAGs), maximum ancestral graphs (MAGs), completed partially directed acyclic graphs (CPDAGs), and partial ancestral graphs (PAGs). Our criterion unifies covariate adjustment for a large set of graph classes. Moreover, we define an explicit set that satisfies our criterion, if there is any set that satisfies our criterion. We also give efficient algorithms for constructing all sets that fulfill our criterion, implemented in the R package dagitty. Finally, we discuss the relationship between our criterion and other criteria for adjustment, and we provide new soundness and completeness proofs for the adjustment criterion for DAGs.Comment: 58 pages, 12 figures, to appear in JML

Investigating Covariate Selection Criteria: To Draw Causal Inferences from Observational Data in the Presence of Unmeasured Covariates Using Regression and Propensity Score Methods

The aim of causal effect estimation is to find the true impact of a treatment or exposure. Observational data is employed in social sciences to estimate causal effect but is susceptible to self-selection and unobserved confounding biases. Covariates included in analysis should strive to address these biases. This research focuses on investigating covariate selection approaches––common cause criterion (CC), Disjunctive Cause Criterion (DCC), Modified Disjunctive Cause Criterion (MDCC), and modified cause criterion (MCC)––in linear regression (LR) and propensity score methods (PSM) causal effect estimation in the presence of unmeasured confounding. Realistic social science scenarios such as––inclusion of proxy variables with varying degrees of strength, misidentification of the unmeasured covariate as a confounder, small sample sizes, and measurement error in proxy covariates—were investigated. For LR and PSM, five causal effect estimation models were built using different covariate selection approaches and compared on three performance metrics––bias, coverage, and empirical SE. Results showed that in the presence of an unmeasured confounder, the causal effect estimate is biased. Study 1 results indicate that MDCC approach resulted in more consistent and efficient causal effect estimates in the presence of unmeasured confounders. Studies 2a and 2b indicate that the MDCC approach is robust to the unobserved variable being a confounder and can be employed even if the unmeasured covariate is not a confounder without adversely impacting the performance measures. Studies 3 and 4 showed including a proxy of the unmeasured confounder, even a weak proxy (r ~ 0.20) or one with measurement error, results in an improvement in the consistency of the causal effect estimate and in the efficiency of the causal effect estimator. As the correlation between the proxy covariate and the unmeasured confounder gets smaller the causal effect estimator becomes less efficient and the causal effect estimate becomes less consistent

Sufficient covariates and linear propensity analysis

Working within the decision-theoretic framework for causal inference, we study the properties of “sufficient covariates”, which support causal inference from observational data, and possibilities for their reduction. In particular we illustrate the rôle of a propensity variable by means of a simple model, and explain why such a reduction typically does not increase (and may reduce) estimation efficiency