Causality was at the center of the early history of structural equation models (SEMs) which continue to serve as the most popular approach to causal analysis in the social sciences. Through decades of development, critics and defenses of the capability of SEMs to support causal inference have accumulated. A variety of misunderstandings and myths about the nature of SEMs and their role in causal analysis have emerged, and their repetition has led some to believe they are true. Our chapter is organized by presenting eight myths about causality and SEMs in the hope that this will lead to a more accurate understanding. More specifically, the eight myths are the following: (1) SEMs aim to establish causal relations from associations alone, (2) SEMs and regression are essentially equivalent, (3) no causation without manipulation, (4) SEMs are not equipped to handle nonlinear causal relationships, (5) a potential outcome framework is more principled than SEMs, (6) SEMs are not applicable to experiments with randomized treatments, (7) mediation analysis in SEMs is inherently noncausal, and (8) SEMs do not test any major part of the theory against the data. We present the facts that dispel these myths, describe what SEMs can and cannot do, and briefly present our critique of current practice using SEMs. We conclude that the current capabilities of SEMs to formalize and implement causal inference tasks are indispensible; its potential to do more is even greater.

/pdf/eight-myths-about-causality-and-structural-equation-models-poohavb6ub.pdf

Eight myths about causality and structural equation models

This paper reviews the foundations of causal mediation analysis and offers a general and transparent account of the conditions necessary for the identification of natural direct and indirect effects, thus facilitating a more informed judgment of the plausibility of these conditions in specific applications. We show that the conditions usually cited in the literature are overly restricted, and can be relaxed substantially, without compromising identification. In particular, we show that natural effects can be identified by methods that go beyond standard adjustment for confounders, applicable to observational studies in which treatment assignment remains confounded with the mediator or with the outcome. These identification conditions can be validated algorithmically from the diagramatic description of one's model, and are guaranteed to produce unbiased results whenever the description is correct. The identification conditions can be further relaxed in parametric models, possibly including interactions, and permit us to compare the relative importance of several pathways, mediated by interdependent variables.

Interpretation and Identification of Causal Mediation

This article reviews the foundations of causal mediation analysis and offers a general and transparent account of the conditions necessary for the identification of natural direct and indirect effects, thus facilitating a more informed judgment of the plausibility of these conditions in specific applications. I show that the conditions usually cited in the literature are overly restrictive and can be relaxed substantially without compromising identification. In particular, I show that natural effects can be identified by methods that go beyond standard adjustment for confounders, applicable to observational studies in which treatment assignment remains confounded with the mediator or with the outcome. These identification conditions can be validated algorithmically from the diagrammatic description of one's model and are guaranteed to produce unbiased results whenever the description is correct. The identi- fication conditions can be further relaxed in parametric models, possibly including interactions, and permit one to compare the relative importance of several pathways, mediated by interdependent variables. Mediation analysis aims to uncover causal pathways along which changes are transmitted from causes to effects. Interest in mediation analysis stems from both scientific and practical con- siderations. Scientifically, mediation tells us how nature works, and practically, it enables us to predict behavior under a rich variety of conditions and policy interventions. For example, in coping with the age-old problem of gender discrimination (Bickel, Hammel, & O'Connell, 1975; Goldberger, 1984), a policymaker may be interested in assessing the extent to which gender disparity in hiring can be reduced by making hiring decisions gender-blind, compared with eliminating gender inequality in education or job qualifications. The former concerns the direct effect of gender on hiring, while the latter concerns the indirect effect or the effect mediated via job qualification. The example illustrates two essential ingredients of modern mediation analysis. First, the indirect effect is not merely a mod- eling artifact formed by suggestive combinations of parameters but an intrinsic property of reality that has tangible policy implica- tions. In this example, reducing employers' prejudices and launch- ing educational reforms are two contending policy options that involve costly investments and different implementation efforts. Knowing in advance which of the two, if successful, has a greater impact on reducing hiring disparity is essential for planning and depends critically on mediation analysis for resolution. Second, the policy decisions in this example concern the enabling and dis- abling of processes (hiring vs. education) rather than lowering or raising values of specific variables. These two considerations lead to the analysis of natural direct and indirect effects. Mediation analysis has its roots in the literature of structural equation models (SEMs), going back to Wright's (1923, 1934) method of path analysis and continuing in the social sciences from the 1960s to 1980s through the works of Baron and Kenny (1986), Bollen (1989), Duncan (1975), and Fox (1980). The bulk of this work was carried out in the context of linear models, in which effect sizes are represented as sums and products of structural coefficients. The definition, identification, and estimation of these coefficients required a commitment to a particular parametric and distributional model and fell short of providing a general, causally defensible measure of mediation (Glynn, 2012; Hayes, 2009; Kraemer, Kiernan, Essex, & Kupfer, 2008; MacKinnon, 2008).

/pdf/interpretation-and-identification-of-causal-mediation-mj7ik9ag6a.pdf

Interpretation and identification of causal mediation.

Imagine an oncologist knocks on your door with the following problem: she wants to know how much she could reduce mortality among her bone marrow transplant patients by prescribing a new drug that prevents graft-versus-host disease, a side effect of allogeneic marrow transplantation.1 While graft-versus-host disease is associated in observational studies with an increased risk of mortality, it also reduces the risk of leukemia relapse – thus, any drug that prevents graft-versus-host disease may have the very undesirable side effect of increasing the rate of relapse.2 She wants to compare the mortality in her cohort with what mortality would be in that same cohort if they had taken this new drug. We cannot answer this question with a regression model because leukemia relapse is a risk factor for mortality and subsequent graft-versus-host disease and it will also decrease the incidence of subsequent relapse (i.e. relapse is a confounder affected by exposure).3, 4 However, we can answer this question using the g-formula.

The g-formula is an analytic tool for estimating standardized outcome distributions using covariate (exposure and confounders) specific estimates of the outcome distribution.5The g-formula can be used to estimate familiar measures of association, such as the hazard ratio. In the current paper, we address the oncologist’s question: we compare observed mortality in our cohort with the expected mortality in that cohort under the new treatment.

Epidemiologists often use regression models (for example, the Cox proportional hazards model) to adjust for confounding; this is equivalent to estimating stratum-specific hazard ratios and then averaging the information-weighted hazard ratios. When some of those confounders are also causal intermediates, this amounts to adjusting away some of the effect of exposure.6, 7 The g-formula works differently: first, one finds weighted averages of the stratum-specific hazards, and then those averaged (standardized) hazards are combined in a summary hazard ratio. Thus, bias resulting from time-varying covariates that can be both confounders and causal intermediates is a shortcoming of using regression models to control for confounding, rather than a general principle of observational data analysis.8, 9 The g-formula is a tool that overcomes this shortcoming, but its use in the literature has been sparse – we could find only 9 examples using observational data.8, 10-17 We hypothesize that the dearth of software packages and lack of useful, yet simple, examples of the g-formula have been the main barriers to broader use.

We show how the g-formula can be used with standard software tools that many epidemiologists already employ, and we illustrate it using publicly-available data from a small cohort study with accompanying SAS code in an eAppendix. We illustrate how we can estimate the net (total) effect of a hypothetical treatment to prevent graft-versus-host disease on mortality and compare the g-formula approach with a regression approach. The g-formula (as with any statistical method) relies on making assumptions in order to make sense of the complex processes underlying the data. We discuss possible ways to assess how well we meet the assumptions as well as the robustness of the g-formula to violations of these assumptions.

/pdf/the-parametric-g-formula-for-time-to-event-data-intuition-1c8k0tp9vx.pdf

The parametric g-formula for time-to-event data: intuition and a worked example.

Structural nested models (SNMs) and the associated method of G-estimation were first proposed by James Robins over two decades ago as approaches to modeling and estimating the joint effects of a sequence of treatments or exposures. The models and estimation methods have since been extended to dealing with a broader series of problems, and have considerable advantages over the other methods developed for estimating such joint effects. Despite these advantages, the application of these methods in applied research has been relatively infrequent; we view this as unfortunate. To remedy this, we provide an overview of the models and estimation methods as developed, primarily by Robins, over the years. We provide insight into their advantages over other methods, and consider some possible reasons for failure of the methods to be more broadly adopted, as well as possible remedies. Finally, we consider several extensions of the standard models and estimation methods.

Structural Nested Models and G-estimation: The Partially Realized Promise

In principle, G-estimation is an attractive approach for dealing with confounding by variables affected by treatment. It has rarely been applied for estimation of the effects of treatment on failure-time outcomes. Part of this is due to artificial censoring, an analytic device which considers some subjects who actually were observed to fail as if they were censored. Artificial censoring leads to a lack of smoothness in the estimating function, which can pose problems in variance estimation and in optimization. It also can lead to failure to have solutions to the usual estimating functions, which then raises questions about the appropriate criteria for optimization. To improve performance of the optimization procedures, we consider approaches for reducing the amount of artificial censoring, propose the substitution of smooth for indicator functions, and propose the use of estimating functions scaled to a measure of the information in the data; we evaluate performance of these approaches using simulation. We also consider appropriate optimization criteria in the presence of information loss due to artificial censoring. We motivate and illustrate our approaches using observational data on the effect of erythropoietin on mortality among subjects on hemodialysis.

G-estimation and artificial censoring: problems, challenges, and applications.

Most attempts at causal inference in observational studies are based on assumptions that treatment assignment is ignorable. Such assumptions are usually made casually, largely because they justify the use of available statistical methods and not because they are truly believed. It will often be the case that it is plausible that conditional independence holds at least approximately for a subset but not all of the experience giving rise to one's data. Such selective ignorability assumptions may be used to derive valid causal inferences in conjunction with structural nested models. In this paper, we outline selective ignorability assumptions mathematically and sketch how they may be used along with otherwise standard G-estimation or likelihood-based methods to obtain inference on structural nested models. We also consider use of these assumptions in the presence of selective measurement error or missing data when the missingness is not at random. We motivate and illustrate our development by considering an analysis of an observational database to estimate the effect of erythropoietin use on mortality among hemodialysis patients.

/pdf/selective-ignorability-assumptions-in-causal-inference-k1y60ybxzo.pdf

Selective Ignorability Assumptions in Causal Inference

Delayed allograft function (DGF) is a common adverse event in postrenal transplantation. The etiology of DGF is thought to include both nonimmunologic (donor age, cold ischemia time, and recipient race) and immunologic factors. We examined the association of DGF with amino acid mismatches at 66 variable sites of the HLA-A molecule in a prospective cohort study of 697 renal transplant recipients of deceased donors. Using a multivariate logistic regression model adjusted for nonimmunologic risk factors, we show that combinations of a few amino acid mismatches at crucial sites of HLA-A molecules were associated with DGF. In Caucasian recipients, a mismatch at position 62, 95, or 163, all known to be functionally important within the antigen recognition site, was associated with an increased risk for DGF. Furthermore, a decreased risk for DGF was associated with a mismatch at HLA-A family-specific sites (149, 184, 193, or 246), indicating that evolutionary features of HLA-A polymorphism separating HLA-A families and lineages among donor-recipient pairs may correlate with the magnitude of alloreactivity influencing the development of DGF. These findings suggest that amino acid polymorphisms at functionally important positions at the antigen recognition site of the HLA-A molecule have a significant influence on DGF.

Wei Peter Yang

Papers

G-estimation and artificial censoring: problems, challenges, and applications.

Selective Ignorability Assumptions in Causal Inference

HLA-A amino acid polymorphism and delayed kidney allograft function