Covariate selection in causal learning under non-Gaussianity

Understanding causal mechanisms is a central goal in the behavioral, developmental, and social sciences. When estimating and probing causal effects using observational data, covariate adjustment is a crucial element to remove dependencies between focal predictors and the error term. Covariate selection, however, constitutes a challenging task because availability alone is not an adequate criterion to decide whether a covariate should be included in the statistical model. The present study introduces a non-Gaussian method for covariate selection and provides a forward selection algorithm for linear models (i.e., non-Gaussian forward selection; nGFS) to select appropriate covariates from a set of potential control variables to avoid inconsistent and biased estimators of the causal effect of interest. Further, we demonstrate that the forward selection algorithm has properties compatible with principles of direction of dependence, i.e., probing whether the causal target model is correctly specified with respect to the causal direction of effects. Results of a Monte Carlo simulation study suggest that the selection algorithm performs well, in particular when sample sizes are large (i.e., n ≥ 250) and data strongly deviate from Gaussianity (e.g., distributions with skewness beyond 1.5). An empirical example is given for illustrative purposes.

A Unification of Mediator, Confounder, and Collider Effects

Third-variable effects, such as mediation and confounding, are core concepts in prevention science, providing the theoretical basis for investigating how risk factors affect behavior and how interventions change behavior. Another third variable, the collider, is not commonly considered but is also important for prevention science. This paper describes the importance of the collider effect as well as the similarities and differences between these three third-variable effects. The single mediator model in which the third variable (T) is a mediator of the independent variable (X) to dependent variable (Y) effect is used to demonstrate how to estimate each third-variable effect. We provide difference in coefficients and product of coefficients estimators of the effects and demonstrate how to calculate these values with real data. Suppression effects are defined for each type of third-variable effect. Future directions and implications of these results are discussed.

Negative ability bias from conditioning on a confounded mediator: A directed interaction test and case study

Sociologists increasingly recognize the problem of endogenous selection bias in mediation analysis. Building on a sub-model of Elwert and Winship (2014), we propose that a widely-overlooked endogenous selection bias exists in the form of a negative ability bias in sociological models of economic outcomes where job attributes are often included as mediators but confounded by unobserved abilities. We use simulations to show that the bias size increases with collider selectivity under common modeling assumptions, and we leverage this property to develop a directed interaction test to detect this bias. To demonstrate the principles of the test and the practical significance of the bias, we re-examine the paradox of Communist Party Premiums in post-2000 China-the sudden disappearance of income returns to Party members, as found in recent studies. The results are strikingly consistent with the hypothesis that a negative ability bias has recently overwhelmed the persistent Party premiums in China.

Principles of confounder selection

Selecting an appropriate set of confounders for which to control is critical for reliable causal inference. Recent theoretical and methodological developments have helped clarify a number of principles of confounder selection. When complete knowledge of a causal diagram relating all covariates to each other is available, graphical rules can be used to make decisions about covariate control. Unfortunately, such complete knowledge is often unavailable. This paper puts forward a practical approach to confounder selection decisions when the somewhat less stringent assumption is made that knowledge is available for each covariate whether it is a cause of the exposure, and whether it is a cause of the outcome. Based on recent theoretically justified developments in the causal inference literature, the following proposal is made for covariate control decisions: control for each covariate that is a cause of the exposure, or of the outcome, or of both; exclude from this set any variable known to be an instrumental variable; and include as a covariate any proxy for an unmeasured variable that is a common cause of both the exposure and the outcome. Various principles of confounder selection are then further related to statistical covariate selection methods.

Sharp sensitivity bounds for mediation under unmeasured mediator-outcome confounding

It is often of interest to decompose the total effect of an exposure into a component that acts on the outcome through some mediator and a component that acts independently through other pathways. Said another way, we are interested in the direct and indirect effects of the exposure on the outcome. Even if the exposure is randomly assigned, it is often infeasible to randomize the mediator, leaving the mediator-outcome confounding not fully controlled. We develop a sensitivity analysis technique that can bound the direct and indirect effects without parametric assumptions about the unmeasured mediator-outcome confounding.

The current deconstruction of paradoxes: one sign of the ongoing methodological "revolution"

The current deconstruction of paradoxes is one among several signs that a profound renewal of methods for clinical and epidemiological research is taking place; perhaps for some basic life sciences as well. The new methodological approaches have already deconstructed and explained long puzzling apparent paradoxes, including the (non-existent) benefits of obesity in diabetics, or of smoking in low birth weight. Achievements of the new methods also comprise the elucidation of the causal structure of long-disputed and highly complex questions, as Berkson's bias and Simpson's paradox, and clarifying reasons for deep controversies, as those on estrogens and endometrial cancer, or on adverse effects of hormone replacement therapy. These are signs that the new methods can go deeper and beyond the methods in current use. A major example of a highly relevant idea is: when we condition on a common effect of a pair of variables, then a spurious association between such pair is likely. The implications of these ideas are potentially vast. A substantial number of apparent paradoxes may simply be the result of collider biases, a source of selection bias that is common not just in epidemiologic research, but in many types of research in the health, life, and social sciences. The new approaches develop a new framework of concepts and methods, as collider, instrumental variables, d-separation, backdoor path and, notably, Directed Acyclic Graphs (DAGs). The current theoretical and methodological renewal-or, perhaps, "revolution"-may be changing deeply how clinical and epidemiological research is conceived and performed, how we assess the validity and relevance of findings, and how causal inferences are made. Clinical and basic researchers, among others, should get acquainted with DAGs and related concepts.