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Treatment effects in before-after data Gelman, Andrew Uploaded 04-27-2004 Keywords correlation experiments interactions hierarchical models observational studies variance components Abstract In experiments and observations with before-after data, the correlation between "before" and "after" measurements is typically higher among the controls than among the treated units, violating the usual assumptions of equal variance and a constant treatment effect. We illustrate with three applied examples and then discuss models that could be used to fit this phenomenon, which we argue is related to the

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Causal Inference with General Treatment Regimes: Generalizing the Propensity Score Imai, Kosuke van Dyk, David A. Uploaded 07-08-2003 Keywords causal inference income medical expenditure non-random treatment observational studies schooling smoking subclassification Abstract In this article, we develop the theoretical properties of the propensity function which is a generalization of the propensity score of Rosenbaum and Rubin (1983). Methods based on the propensity score have long been used for causal inference in observational studies; they are easy to use and can effectively reduce the bias caused by non-random treatment assignment. Although treatment regimes need not be binary in practice, the propensity score methods are generally confined to binary treatment scenarios. Two possible exceptions were suggested by Joffe and Rosenbaum (1999) and Imbens (2000) for ordinal and categorical treatments, respectively. In this article, we develop theory and methods which encompass all of these techniques and widen their applicability by allowing for arbitrary treatment regimes. We illustrate our propensity function methods by applying them to two data sets; we estimate the effect of smoking on medical expenditure and the effect of schooling on wages. We also conduct Monte Carlo experiments to investigate the performance of our methods.

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Causal inference with general treatment regimes: Generalizing the propensity score Imai, Kosuke van Dyk, David A. Uploaded 11-18-2002 Keywords causal inference income medical expenditure non-random treatment observational studies schooling smoking subclassification Abstract In this article, we develop the theoretical properties of the propensity function which is a generalization of the propensity score of Rosenbaum and Rubin (1983). Methods based on the propensity score have long been used for causal inference in observational studies; they are easy to use and can effectively reduce the bias caused by non-random treatment assignment. Although treatment regimes are often not binary in practice, the propensity score methods are generally confined to binary treatment scenarios. Two possible exceptions were suggested by Joffe and Rosenbaum (1999) and Imbens (2000) for ordinal and categorical treatments, respectively. In this article, we develop theory and methods which encompass all of these techniques and widen their applicability by allowing for arbitrary treatment regimes. We illustrate our propensity function methods by applying them to two data sets; we estimate the effect of smoking on medical expenditure and the effect of schooling on wages. We also conduct Monte Carlo experiments to investigate the performance of our methods.

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Misunderstandings among Experimentalists and Observationalists about Causal Inference Imai, Kosuke King, Gary Stuart, Elizabeth Uploaded 09-16-2007 Keywords matching blocking causal inference experimental design observational studies average treatment effects covariate balance field experiments survey experiments Abstract We attempt to clarify, and suggest how to avoid, several serious misunderstandings about and fallacies of causal inference in experimental and observational research. These issues concern some of the most basic advantages and disadvantages of each basic research design. Problems include improper use of hypothesis tests for covariate balance between the treated and control groups, and the consequences of using randomization, blocking before randomization, and matching after treatment assignment to achieve covariate balance. Applied researchers in a wide range of scientific disciplines seem to fall prey to one or more of these fallacies, and as a result make suboptimal design or analysis choices. To clarify these points, we derive a new four-part decomposition of the key estimation errors in making causal inferences. We then show how this decomposition can help scholars from different experimental and observational research traditions better understand each other's inferential problems and attempted solutions. (This paper is forthcoming in the Journal of the Royal Statistical Society, but we have some time for revisions and would value any comments anyone might have. This is a revised and much more general version of an earlier paper, "The Balance Test Fallacy in Causal Inference".)

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A New Non-Parametric Matching Method for Bias Adjustment with Applications to Economic Evaluations Sekhon, Jasjeet Uploaded 05-11-2008 Keywords semiparametric and nonparametric matching methods observational studies randomized controlled trials health economic evaluation Abstract In health economic studies that use observational data, a key concern is how to adjust for imbalances in baseline covariates due to the non-random assignment of the programs under evaluation. Traditional methods of covariate adjustment such as regression and propensity score matching are model dependent and often fail to replicate the results of randomized controlled trials. We demonstrate a new non-parametric matching method, Genetic Matching, which is a generalization of propensity score and Mahalanobis distance matching, using two contrasting case studies. In the first, an economic evaluation of a clinical intervention (Pulmonary Artery Catheterization), applying Genetic Matching to observational data replicates the substantive results of a corresponding randomized controlled trial unlike the extant literature. And in the second case study evaluating capitation versus fee-for service, Genetic Matching radically improves balance on baseline covariates and overturns previous conclusions based on traditional methods.

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Covariate Balancing Propensity Score Imai, Kosuke Ratkovic, Marc Uploaded 07-13-2012 Keywords causal inference instrumental variables inverse propensity score weighting marginal structural models observational studies propensity score matching randomized experiments Abstract The propensity score plays a central role in a variety of settings for causal inference. In particular, matching and weighting methods based on the estimated propensity score have become increasingly common in observational studies. Despite their popularity and theoretical appeal, the main practical difficulty of these methods is that the propensity score must be estimated. Researchers have found that slight misspecification of the propensity score model can result in substantial bias of estimated treatment effects. In this paper, we introduce covariate balancing propensity score (CBPS) estimation, which simultaneously optimizes the covariate balance and the prediction of treatment assignment. We exploit the dual characteristics of the propensity score as a covariate balancing score and the conditional probability of treatment assignment and estimate the CBPS within the generalized method of moments or empirical likelihood framework. We find that the CBPS dramatically improves the poor empirical performance of propensity score matching and weighting methods reported in the literature. We also show that the CBPS can be extended to a number of other important settings, including the estimation of generalized propensity score for non-binary treatments, causal inference in longitudinal settings, and the generalization of experimental and instrumental variable estimates to a target population.