BackgroundEpidemiologic research is often devoted to etiologic investigation, and so techniques that may facilitate mechanistic inferences are attractive. Some of these techniques rely on rigid and/or unrealistic assumptions, making the biologic inferences tenuous. The methodology investigated here is effect decomposition: the contrast between effect measures estimated with and without adjustment for one or more variables hypothesized to lie on the pathway through which the exposure exerts its effect. This contrast is typically used to distinguish the exposure's indirect effect, through the specified intermediate variables, from its direct effect, transmitted via pathways that do not involve the specified intermediates.MethodsWe apply a causal framework based on latent potential response types to describe the limitations inherent in effect decomposition analysis. For simplicity, we assume three measured binary variables with monotonic effects and randomized exposure, and use difference contrasts as measures of causal effect. Previous authors showed that confounding between intermediate and the outcome threatens the validity of the decomposition strategy, even if exposure is randomized. We define exchangeability conditions for absence of confounding of causal effects of exposure and intermediate, and generate two example populations in which the no-confounding conditions are satisfied. In one population we impose an additional prohibition against unit-level interaction (synergism). We evaluate the performance of the decomposition strategy against true values of the causal effects, as defined by the proportions of latent potential response types in the two populations.ResultsWe demonstrate that even when there is no confounding, partition of the total effect into direct and indirect effects is not reliably valid. Decomposition is valid only with the additional restriction that the population contain no units in which exposure and intermediate interact to cause the outcome. This restriction implies homogeneity of causal effects across strata of the intermediate.ConclusionsReliable effect decomposition requires not only absence of confounding, but also absence of unit-level interaction and use of linear contrasts as measures of causal effect. Epidemiologists should be wary of etiologic inference based on adjusting for intermediates, especially when using ratio effect measures or when absence of interacting potential response types cannot be confidently asserted.

SUMMARYAdjusting for a causal intermediate is a common analytic strategy for estimating an average causal direct e ect (ACDE). The ACDE is the component of the total exposure e ect that is not relayed through the speciÿed intermediate. Even if the total e ect is unconfounded, the usual ACDE estimate may be biased when an unmeasured variable a ects the intermediate and outcome variables. Using linear programming optimization to compute non-parametric bounds, we develop new ACDE estimators for binary measured variables in this causal structure, and use root mean square confounding bias (RMSB) to compare their performance with the usual stratiÿed estimator in simulated distributions of target populations comprised of the 64 possible potential response types as well as distributions of target populations restricted to subsets of 18 or 12 potential response types deÿned by monotonicity or no-interactions assumptions of unit-level causal e ects. We also consider target population distributions conditioned on ÿxed outcome risk among the unexposed, or ÿxed true ACDE in one stratum of the intermediate. Results show that a midpoint estimator constructed from the optimization bounds has consistently lower RMSB than the usual stratiÿed estimator both unconditionally and conditioned on any risk in the unexposed. When conditioning on true ACDE, this midpoint estimator performs more poorly only when conditioned on an extreme true ACDE in one stratum of the intermediate, yet outperforms the stratiÿed estimator in the other stratum when interaction is permitted. An alternate 'limit-modiÿed crude' estimator can never perform less favourably than the stratiÿed estimator, and often has lower RMSB.

We apply a linear programming approach which uses the causal risk difference (RDC) as the objective function and provides minimum and maximum values that RDC can achieve under any set of linear constraints on the potential response type distribution. We consider two scenarios involving binary exposure X, covariate Z and outcome Y. In the first, Z is not affected by X, and is a potential confounder of the causal effect of X on Y. In the second, Z is affected by X and intermediate in the causal pathway between X and Y. For each scenario we consider various linear constraints corresponding to the presence or absence of arcs in the associated directed acyclic graph (DAG), monotonicity assumptions, and presence or absence of additive-scale interactions. We also estimate Z-stratum-specific bounds when Z is a potential effect measure modifier and bounds for both controlled and natural direct effects when Z is affected by X. In the absence of any additional constraints deriving from background knowledge, the well-known bounds on RDc are duplicated: −Pr(Y≠X) ≤ RDC ≤ Pr(Y=X). These bounds have unit width, but can be narrowed by background knowledge-based assumptions. We provide and compare bounds and bound widths for various combinations of assumptions in the two scenarios and apply these bounds to real data from two studies.

Social epidemiology is the study of relations between social factors and health status in populations. Although recent decades have witnessed a rapid development of this research program in scope and sophistication, causal inference has proven to be a persistent dilemma due to the natural assignment of exposure level based on unmeasured attributes of individuals, which may lead to substantial confounding. Some optimism has been expressed about randomized social interventions as a solution to this long-standing inferential problem. We review the causal inference problem in social epidemiology, and the potential for causal inference in randomized social interventions. Using the example of a currently on-going intervention that randomly assigns families to non-poverty housing, we review the limitations to causal inference even under experimental conditions and explain which causal effects become identifiable. We note the benefit of using the randomized trial as a conceptual model, even for design and interpretation of observational studies in social epidemiology. r

Common sensitivity analysis methods for unmeasured confounders provide a corrected point estimate of causal effect for each specified set of unknown parameter values. This article reviews alternative methods for generating deterministic nonparametric bounds on the magnitude of the causal effect using linear programming methods and potential outcomes models. The bounds are generated using only the observed table. We then demonstrate how these bound widths may be reduced through assumptions regarding the potential outcomes under various exposure regimens. We illustrate this linear programming approach using data from the Cooperative Cardiovascular Project. These bounds on causal effect under uncontrolled confounding complement standard sensitivity analyses by providing a range within which the causal effect must lie given the validity of the assumptions.