Tyler J. VanderWeele

Mediation analysis allowing for exposure-mediator interactions and causal interpretation: theoretical assumptions and implementation with SAS and SPSS macros.

Mediation analysis is a useful and widely employed approach to studies in the field of psychology and in the social and biomedical sciences. The contributions of this article are several-fold. First we seek to bring the developments in mediation analysis for nonlinear models within the counterfactual framework to the psychology audience in an accessible format and compare the sorts of inferences about mediation that are possible in the presence of exposure-mediator interaction when using a counterfactual versus the standard statistical approach. Second, the work by VanderWeele and Vansteelandt (2009, 2010) is extended here to allow for dichotomous mediators and count outcomes. Third, we provide SAS and SPSS macros to implement all of these mediation analysis techniques automatically, and we compare the types of inferences about mediation that are allowed by a variety of software macros.

Marginal structural models for the estimation of direct and indirect effects.

The estimation of controlled direct effects can be carried out by fitting a marginal structural model and using inverse probability of treatment weighting. To use marginal structural models to estimate natural direct and indirect effects, 2 marginal structural models can be used: 1 for the effects of the treatment and mediator on the outcome and 1 for the effect of the treatment on the mediator. Unlike marginal structural models typically used in epidemiologic research, the marginal structural models used to estimate natural direct and indirect effects are made conditional on the covariates.

Odds Ratios for Mediation Analysis for a Dichotomous Outcome

For dichotomous outcomes, the authors discuss when the standard approaches to mediation analysis used in epidemiology and the social sciences are valid, and they provide alternative mediation analysis techniques when the standard approaches will not work. They extend definitions of controlled direct effects and natural direct and indirect effects from the risk difference scale to the odds ratio scale. A simple technique to estimate direct and indirect effect odds ratios by combining logistic and linear regressions is described that applies when the outcome is rare and the mediator continuous. Further discussion is given as to how this mediation analysis technique can be extended to settings in which data come from a case-control study design. For the standard mediation analysis techniques used in the epidemiologic and social science literatures to be valid, an assumption of no interaction between the effects of the exposure and the mediator on the outcome is needed. The approach presented here, however, will apply even when there are interactions between the effect of the exposure and the mediator on the outcome.

Effect of a Housing and Case Management Program on Emergency Department Visits and Hospitalizations Among Chronically Ill Homeless Adults: A Randomized Trial

CONTEXT Homeless adults, especially those with chronic medical illnesses, are frequent users of costly medical services, especially emergency department and hospital services. OBJECTIVE To assess the effectiveness of a case management and housing program in reducing use of urgent medical services among homeless adults with chronic medical illnesses. DESIGN, SETTING, AND PARTICIPANTS Randomized controlled trial conducted at a public teaching hospital and a private, nonprofit hospital in Chicago, Illinois. Participants were 407 social worker-referred homeless adults with chronic medical illnesses (89% of referrals) from September 2003 until May 2006, with follow-up through December 2007. Analysis was by intention-to-treat. INTERVENTION Housing offered as transitional housing after hospitalization discharge, followed by placement in long-term housing; case management offered on-site at primary study sites, transitional housing, and stable housing sites. Usual care participants received standard discharge planning from hospital social workers. MAIN OUTCOME MEASURES Hospitalizations, hospital days, and emergency department visits measured using electronic surveillance, medical records, and interviews. Models were adjusted for baseline differences in demographics, insurance status, prior hospitalization or emergency department visit, human immunodeficiency virus infection, current use of alcohol or other drugs, mental health symptoms, and other factors. RESULTS The analytic sample (n = 405 [n = 201 for the intervention group, n = 204 for the usual care group]) was 78% men and 78% African American, with a median duration of homelessness of 30 months. After 18 months, 73% of participants had at least 1 hospitalization or emergency department visit. Compared with the usual care group, the intervention group had unadjusted annualized mean reductions of 0.5 hospitalizations (95% confidence interval [CI], -1.2 to 0.2), 2.7 fewer hospital days (95% CI, -5.6 to 0.2), and 1.2 fewer emergency department visits (95% CI, -2.4 to 0.03). Adjusting for baseline covariates, compared with the usual care group, the intervention group had a relative reduction of 29% in hospitalizations (95% CI, 10% to 44%), 29% in hospital days (95% CI, 8% to 45%), and 24% in emergency department visits (95% CI, 3% to 40%). CONCLUSION After adjustment, offering housing and case management to a population of homeless adults with chronic medical illnesses resulted in fewer hospital days and emergency department visits, compared with usual care. TRIAL REGISTRATION clinicaltrials.gov Identifier: NCT00490581.

Bias formulas for sensitivity analysis for direct and indirect effects

A key question in many studies is how to divide the total effect of an exposure into a component that acts directly on the outcome and a component that acts indirectly, ie, through some intermediate. For example, one might be interested in the extent to which the effect of diet on blood pressure is mediated through sodium intake and the extent to which it operates through other pathways. In the context of such mediation analysis, even if the effect of the exposure on the outcome is unconfounded, estimates of direct and indirect effects will be biased if control is not made for confounders of the mediator-outcome relationship. Often data are not collected on such mediator-outcome confounding variables; the results in this paper allow researchers to assess the sensitivity of their estimates of direct and indirect effects to the biases from such confounding. Specifically, the paper provides formulas for the bias in estimates of direct and indirect effects due to confounding of the exposure-mediator relationship and of the mediator-outcome relationship. Under some simplifying assumptions, the formulas are particularly easy to use in sensitivity analysis. The bias formulas are illustrated by examples in the literature concerning direct and indirect effects in which mediator-outcome confounding may be present.

Bias formulas for sensitivity analysis of unmeasured confounding for general outcomes, treatments, and confounders.

Uncontrolled confounding in observational studies gives rise to biased effect estimates. Sensitivity analysis techniques can be useful in assessing the magnitude of these biases. In this paper, we use the potential outcomes framework to derive a general class of sensitivity-analysis formulas for outcomes, treatments, and measured and unmeasured confounding variables that may be categorical or continuous. We give results for additive, risk-ratio and odds-ratio scales. We show that these results encompass a number of more specific sensitivity-analysis methods in the statistics and epidemiology literature. The applicability, usefulness, and limits of the bias-adjustment formulas are discussed. We illustrate the sensitivity-analysis techniques that follow from our results by applying them to 3 different studies. The bias formulas are particularly simple and easy to use in settings in which the unmeasured confounding variable is binary with constant effect on the outcome across treatment levels.

A Tutorial on Interaction

Abstract In this tutorial, we provide a broad introduction to the topic of interaction between the effects of exposures. We discuss interaction on both additive and multiplicative scales using risks, and we discuss their relation to statistical models (e.g. linear, log-linear, and logistic models). We discuss and evaluate arguments that have been made for using additive or multiplicative scales to assess interaction. We further discuss approaches to presenting interaction analyses, different mechanistic forms of interaction, when interaction is robust to unmeasured confounding, interaction for continuous outcomes, qualitative or “crossover” interactions, methods for attributing effects to interactions, case-only estimators of interaction, and power and sample size calculations for additive and multiplicative interaction.

Concerning the consistency assumption in causal inference.

Cole and Frangakis (Epidemiology. 2009;20:3-5) introduced notation for the consistency assumption in causal inference. I extend this notation and propose a refinement of the consistency assumption that makes clear that the consistency statement, as ordinarily given, is in fact an assumption and not an axiom or definition. The refinement is also useful in showing that additional assumptions (referred to here as treatment-variation irrelevance assumptions), stronger than those given by Cole and Frangakis, are in fact necessary in articulating the ordinary assumptions of ignorability or exchangeability. The refinement furthermore sheds light on the distinction between intervention and choice in reasoning about causality. A distinction between the range of treatment variations for which potential outcomes can be defined and the range for which treatment comparisons are made is discussed in relation to issues of nonadherence. The use of stochastic counterfactuals can help relax what is effectively being presupposed by the treatment-variation irrelevance assumption and the consistency assumption.

Why Is Spiritual Care Infrequent at the End of Life? Spiritual Care Perceptions Among Patients, Nurses, and Physicians and the Role of Training

PURPOSE To determine factors contributing to the infrequent provision of spiritual care (SC) by nurses and physicians caring for patients at the end of life (EOL). PATIENTS AND METHODS This is a survey-based, multisite study conducted from March 2006 through January 2009. All eligible patients with advanced cancer receiving palliative radiation therapy and oncology physician and nurses at four Boston academic centers were approached for study participation; 75 patients (response rate = 73%) and 339 nurses and physicians (response rate = 63%) participated. The survey assessed practical and operational dimensions of SC, including eight SC examples. Outcomes assessed five factors hypothesized to contribute to SC infrequency. RESULTS Most patients with advanced cancer had never received any form of spiritual care from their oncology nurses or physicians (87% and 94%, respectively; P for difference = .043). Majorities of patients indicated that SC is an important component of cancer care from nurses and physicians (86% and 87%, respectively; P = .1). Most nurses and physicians thought that SC should at least occasionally be provided (87% and 80%, respectively; P = .16). Majorities of patients, nurses, and physicians endorsed the appropriateness of eight examples of SC (averages, 78%, 93%, and 87%, respectively; P = .01). In adjusted analyses, the strongest predictor of SC provision by nurses and physicians was reception of SC training (odds ratio [OR] = 11.20, 95% CI, 1.24 to 101; and OR = 7.22, 95% CI, 1.91 to 27.30, respectively). Most nurses and physicians had not received SC training (88% and 86%, respectively; P = .83). CONCLUSION Patients, nurses, and physicians view SC as an important, appropriate, and beneficial component of EOL care. SC infrequency may be primarily due to lack of training, suggesting that SC training is critical to meeting national EOL care guidelines.

On causal inference in the presence of interference

Interference is said to be present when the exposure or treatment received by one individual may affect the outcomes of other individuals. Such interference can arise in settings in which the outcomes of the various individuals come about through social interactions. When interference is present, causal inference is rendered considerably more complex, and the literature on causal inference in the presence of interference has just recently begun to develop. In this article we summarise some of the concepts and results from the existing literature and extend that literature in considering new results for finite sample inference, new inverse probability weighting estimators in the presence of interference and new causal estimands of interest.