Affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributions

In observational studies designed to estimate the effects of interventions or exposures, such as cigarette smoking, it is desirable to try to control background differences between the treated group (e.g., current smokers) and the control group (e.g., never smokers) on covariates $X$ (e.g., age, education). Matched sampling attempts to effect this control by selecting subsets of the treated and control groups with similar distributions of such covariates. This paper examines the consequences of matching using affinely invariant methods when the covariate distributions are ``discriminant mixtures of proportional ellipsoidally symmetric'' (DMPES) distributions, a class herein defined, which generalizes the ellipsoidal symmetry class of Rubin and Thomas [Ann. Statist. 20 (1992) 1079--1093]. The resulting generalized results help indicate why earlier results hold quite well even when the simple assumption of ellipsoidal symmetry is not met [e.g., Biometrics 52 (1996) 249--264]. Extensions to conditionally affinely invariant matching with conditionally DMPES distributions are also discussed.Comment: Published at http://dx.doi.org/10.1214/009053606000000407 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Clarifying causal mediation analysis for the applied researcher: Defining effects based on what we want to learn

The incorporation of causal inference in mediation analysis has led to theoretical and methodological advancements -- effect definitions with causal interpretation, clarification of assumptions required for effect identification, and an expanding array of options for effect estimation. However, the literature on these results is fast-growing and complex, which may be confusing to researchers unfamiliar with causal inference or unfamiliar with mediation. The goal of this paper is to help ease the understanding and adoption of causal mediation analysis. It starts by highlighting a key difference between the causal inference and traditional approaches to mediation analysis and making a case for the need for explicit causal thinking and the causal inference approach in mediation analysis. It then explains in as-plain-as-possible language existing effect types, paying special attention to motivating these effects with different types of research questions, and using concrete examples for illustration. This presentation differentiates two perspectives (or purposes of analysis): the explanatory perspective (aiming to explain the total effect) and the interventional perspective (asking questions about hypothetical interventions on the exposure and mediator, or hypothetically modified exposures). For the latter perspective, the paper proposes tapping into a general class of interventional effects that contains as special cases most of the usual effect types -- interventional direct and indirect effects, controlled direct effects and also a generalized interventional direct effect type, as well as the total effect and overall effect. This general class allows flexible effect definitions which better match many research questions than the standard interventional direct and indirect effects

Matching Methods for Causal Inference: A Review and a Look Forward

When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970s, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods---or developing methods related to matching---do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.Comment: Published in at http://dx.doi.org/10.1214/09-STS313 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

MatchIt: Nonparametric Preprocessing for Parametric Causal Inference

MatchIt implements the suggestions of Ho, Imai, King, and Stuart (2007) for improving parametric statistical models by preprocessing data with nonparametric matching methods. MatchIt implements a wide range of sophisticated matching methods, making it possible to greatly reduce the dependence of causal inferences on hard-to-justify, but commonly made, statistical modeling assumptions. The software also easily fits into existing research practices since, after preprocessing data with MatchIt, researchers can use whatever parametric model they would have used without MatchIt, but produce inferences with substantially more robustness and less sensitivity to modeling assumptions. MatchIt is an R program, and also works seamlessly with Zelig.

Choosing the Estimand When Matching or Weighting in Observational Studies

Matching and weighting methods for observational studies require the choice of an estimand, the causal effect with reference to a specific target population. Commonly used estimands include the average treatment effect in the treated (ATT), the average treatment effect in the untreated (ATU), the average treatment effect in the population (ATE), and the average treatment effect in the overlap (i.e., equipoise population; ATO). Each estimand has its own assumptions, interpretation, and statistical methods that can be used to estimate it. This article provides guidance on selecting and interpreting an estimand to help medical researchers correctly implement statistical methods used to estimate causal effects in observational studies and to help audiences correctly interpret the results and limitations of these studies. The interpretations of the estimands resulting from regression and instrumental variable analyses are also discussed. Choosing an estimand carefully is essential for making valid inferences from the analysis of observational data and ensuring results are replicable and useful for practitioners

Using Sensitivity Analyses for Unobserved Confounding to Address Covariate Measurement Error in Propensity Score Methods

Propensity score methods are a popular tool to control for confounding in observational data, but their bias-reduction properties are threatened by covariate measurement error. There are few easy-to-implement methods to correct for such bias. We describe and demonstrate how existing sensitivity analyses for unobserved confounding---propensity score calibration, Vanderweele and Arah\u27s bias formulas, and Rosenbaum\u27s sensitivity analysis---can be adapted to address this problem. In a simulation study, we examined the extent to which these sensitivity analyses can correct for several measurement error structures: classical, systematic differential, and heteroscedastic covariate measurement error. We then apply these approaches to address covariate measurement error in estimating the association between depression and weight gain in a cohort of adults in Baltimore City. We recommend the use of Vanderweele and Arah\u27s bias formulas and propensity score calibration (assuming it is adapted appropriately for the measurement error structure), as both approaches perform well for a variety of propensity score estimators and measurement error structures

Organic geochemistry of particulate matter in the eastern tropical North Pacific Ocean: Implications for particle dynamics

Samples of marine particulate matter were collected in sediment traps and by in-situ filtration to depths of 1500 m during VERTEX II and III cruises in the eastern tropical North Pacific. Wax esters, triacylglycerols, fatty acids, sterols and steroidal ketones were analyzed in these samples to compare the compositions of organic matter associated with large sinking particulate aggregates sampled by sediment traps and with fine suspended material obtained by in-situ filtration. Distributions of specific compounds indicated that the organic chemical composition of large sinking particles and small suspended particles both in the euphotic zone and at mid-depth result from very distinct particle pools, not only in terms of particle size but also in their sources and transport mechanisms. Suspended particles in the epipelagic zone contain a mix of organic compounds derived from both phytoplankton and zooplankton sources, whereas sinking particles are dominated by zooplankton-derived compounds. In the mesopelagic zone, large, sinking particles contain organic compounds which are indicative of intensive alteration of organic matter, even though transport from the euphotic zone may have been rapid. On the other hand, it is the suspended particle pool which contains a remarkable abundance of labile organic compounds which can be attributed to undegraded phytoplankton cells rapidly delivered from surface waters. These organic geochemical results lead to a modified model of particle dynamics in which there are two distinct large, sinking particle pools which are differentially sampled by the two sampling techniques

Multiple imputation for propensity score analysis with covariates missing at random: some clarity on within and across methods

In epidemiology and social sciences, propensity score methods are popular for estimating treatment effects using observational data, and multiple imputation is popular for handling covariate missingness. However, how to appropriately use multiple imputation for propensity score analysis is not completely clear. This paper aims to bring clarity on the consistency (or lack thereof) of methods that have been proposed, focusing on the within approach (where the effect is estimated separately in each imputed dataset and then the multiple estimates are combined) and the across approach (where typically propensity scores are averaged across imputed datasets before being used for effect estimation). We show that the within method is valid and can be used with any causal effect estimator that is consistent in the full-data setting. Existing across methods are inconsistent, but a different across method that averages the inverse probability weights across imputed datasets is consistent for propensity score weighting. We also comment on methods that rely on imputing a function of the missing covariate rather than the covariate itself, including imputation of the propensity score and of the probability weight. Based on consistency results and practical flexibility, we recommend generally using the standard within method. Throughout, we provide intuition to make the results meaningful to the broad audience of applied researchers