Did the Military Interventions in the Mexican Drug War Increase Violence?

We analyze publicly available data to estimate the causal effects of military interventions on the homicide rates in certain problematic regions in Mexico. We use the Rubin causal model to compare the post-intervention homicide rate in each intervened region to the hypothetical homicide rate for that same year had the military intervention not taken place. Because the effect of a military intervention is not confined to the municipality subject to the intervention, a nonstandard definition of units is necessary to estimate the causal effect of the intervention under the standard no-interference assumption of stable-unit treatment value assumption (SUTVA). Donor pools are created for each missing potential outcome under no intervention, thereby allowing for the estimation of unit-level causal effects. A multiple imputation approach accounts for uncertainty about the missing potential outcomes.     

Sufficient dimension reduction via distance covariance with multivariate responses

In this article, we propose a new method for sufficient dimension reduction when both response and predictor are vectors. The new method, using distance covariance, keeps the model-free advantage, and can fully recover the central subspace even when many predictors are discrete. We then extend this method to the dual central subspace, including a special case of canonical correlation analysis. We illustrated estimators through extensive simulations and real datasets, and compared to some existing methods, showing that our estimators are competitive and robust.     

SAVE: Robust or not?

Abstract

Sliced average variance estimation (SAVE) is one of the best methods for estimating central dimension-reduction subspace in semi parametric regression models when covariates are normal. In recent days SAVE is being used to analyze DNA microarray data especially in tumor classification but most important drawback is normality of covariates. In this article, the asymptotic behavior of estimates of CDR space under varying slice size is studied through simulation studies when covariates are non normal but follows linearity condition as well as when covariates slightly perturbed from normal distribution and we observed that serious error may occur under violation normality assumption.     

Using adaptively weighted large margin classifiers for robust sufficient dimension reduction

In this paper, we combine adaptively weighted large margin classifiers with Support Vector Machine (SVM)-based dimension reduction methods to create dimension reduction methods robust to the presence of extreme outliers. We discuss estimation and asymptotic properties of the algorithm. The good performance of the new algorithm is demonstrated through simulations and real data analysis.     

A Shrinkage Estimation of Central Subspace in Sufficient Dimension Reduction

Sliced regression is an effective dimension reduction method by replacing the original high-dimensional predictors with its appropriate low-dimensional projection. It is free from any probabilistic assumption and can exhaustively estimate the central subspace. In this article, we propose to incorporate shrinkage estimation into sliced regression so that variable selection can be achieved simultaneously with dimension reduction. The new method can improve the estimation accuracy and achieve better interpretability for the reduced variables. The efficacy of proposed method is shown through both simulation and real data analysis.     

Detecting multiple confounders

This paper proposes an approach for detecting multiple confounders which combines the advantages of two causal models, the potential outcome model and the causal diagram. The approach need not use a complete causal diagram as long as it is known that a known covariate set Z$Z$ contains the parent set of the exposure E  . On the other hand, whether a covariate is or not a confounder may depend on its categorization. We introduce uniform non-confounding which implies non-confounding in any subpopulation defined by the interval of a covariate (or any pooled level for a discrete covariate). We show that the conditions in Miettinen and Cook's criteria for non-confounding also imply uniform non-confounding. Further we present an algorithm for deleting non-confounders from the potential confounder set Z$Z$, which extends Greenland et al.'s [1999a. Causal diagrams for epidemiologic research. Epidemiology 10, 37–48] approach by splitting Z$Z$ into a series of potential confounder subsets. We also discuss conditions for non-confounding bias in the subpopulations in which we are interested, where the subpopulations may be defined by non-confounders.     

A Note on the Role of the Propensity Score for Estimating Average Treatment Effects

Hahn [Hahn, J. (1998). On the role of the propensity score in efficient semiparametric estimation of average treatment effects. Econometrica 66:315-331] derived the semiparametric efficiency bounds for estimating the average treatment effect (ATE) and the average treatment effect on the treated (ATET). The variance of ATET depends on whether the propensity score is known or unknown. Hahn attributes this to “dimension reduction.” In this paper, an alternative explanation is given: Knowledge of the propensity score improves upon the estimation of the distribution of the confounding variables.     

Dimension reduction for the conditional kth moment in regression

The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction. Here, we introduce the central k th-moment subspace to capture information from the mean, variance and so on up to the k th conditional moment of the regression. New methods are studied for estimating these subspaces. Connections with sliced inverse regression are established, and examples illustrating the theory are presented.     

Propensity score model specification for estimation of average treatment effects

Treatment effect estimators that utilize the propensity score as a balancing score, e.g., matching and blocking estimators are robust to misspecifications of the propensity score model when the misspecification is a balancing score. Such misspecifications arise from using the balancing property of the propensity score in the specification procedure. Here, we study misspecifications of a parametric propensity score model written as a linear predictor in a strictly monotonic function, e.g. a generalized linear model representation. Under mild assumptions we show that for misspecifications, such as not adding enough higher order terms or choosing the wrong link function, the true propensity score is a function of the misspecified model. Hence, the latter does not bring bias to the treatment effect estimator. It is also shown that a misspecification of the propensity score does not necessarily lead to less efficient estimation of the treatment effect. The results of the paper are highlighted in simulations where different misspecifications are studied.     

A Bayesian nonparametric causal model

Typically, in the practice of causal inference from observational studies, a parametric model is assumed for the joint population density of potential outcomes and treatment assignments, and possibly this is accompanied by the assumption of no hidden bias. However, both assumptions are questionable for real data, the accuracy of causal inference is compromised when the data violates either assumption, and the parametric assumption precludes capturing a more general range of density shapes (e.g., heavier tail behavior and possible multi-modalities). We introduce a flexible, Bayesian nonparametric causal model to provide more accurate causal inferences. The model makes use of a stick-breaking prior, which has the flexibility to capture any multi-modalities, skewness and heavier tail behavior in this joint population density, while accounting for hidden bias. We prove the asymptotic consistency of the posterior distribution of the model, and illustrate our causal model through the analysis of small and large observational data sets.     

An Approach for Estimating Causal Effects in Randomized Trials with Noncompliance

We developed methods for estimating the causal risk difference and causal risk ratio in randomized trials with noncompliance. The developed estimator is unbiased under the assumption that biases due to noncompliance are identical between both treatment arms. The biases are defined as the difference or ratio between the expectations of potential outcomes for a group that received the test treatment and that for the control group in each randomly assigned group. Although the instrumental variable estimator yields an unbiased estimate under a sharp null hypothesis but may yield a biased estimate under a non-null hypothesis, the bias of the developed estimator does not depend on whether this hypothesis holds. Then the estimate of the causal effect from the developed estimator may have a smaller bias than that from the instrumental variable estimator when the treatment effect exists. There is not yet a standard method for coping with noncompliance, and thus it is important to evaluate estimates under different assumptions. The developed estimator can serve this purpose. Its application to a field trial for coronary heart disease is provided.     

Estimating efficacy in a proposed randomized trial with initial and later non-compliance

Summary.  A controversial topic in obstetrics is the effect of walking on the probability of Caesarean section among women in labour. A major reason for the controversy is the presence of non-compliance that complicates the estimation of efficacy, the effect of treatment received on outcome. The intent-to-treat method does not estimate efficacy, and estimates of efficacy that are based directly on treatment received may be biased because they are not protected by randomization. However, when non-compliance occurs immediately after randomization, the use of a potential outcomes model with reasonable assumptions has made it possible to estimate efficacy and still to retain the benefits of randomization to avoid selection bias. In this obstetrics application, non-compliance occurs initially and later in one arm. Consequently some parameters cannot be uniquely estimated without making strong assumptions. This difficulty is circumvented by a new study design involving an additional randomization group and a novel potential outcomes model (principal stratification).     

Accommodating stochastic departures from percentile invariance in causal models

Summary.  Consider a clinical trial in which participants are randomized to a single-dose treatment or a placebo control and assume that the adherence level is accurately recorded. If the treatment is effective, then good adherers in the treatment group should do better than poor ad- herers because they received more drug; the treatment group data follow a dose–response curve. But, good adherers to the placebo often do better than poor adherers, so the observed adherence–response in the treatment group cannot be completely attributed to the treatment. Efron and Feldman proposed an adjustment to the observed adherence–response in the treatment group by using the adherence–response in the control group. It relies on a percentile invariance assumption under which each participant's adherence percentile within their assigned treatment group does not depend on the assigned group (active drug or placebo). The Efron and Feldman approach is valid under percentile invariance, but not necessarily under departures from it. We propose an analysis based on a generalization of percentile invariance that allows adherence percentiles to be stochastically permuted across treatment groups, using a broad class of stochastic permutation models. We show that approximate maximum likelihood estimates of the underlying dose–response curve perform well when the stochastic permutation process is correctly specified and are quite robust to model misspecification.     

Optimal dynamic treatment regimes

Summary. A dynamic treatment regime is a list of decision rules, one per time interval, for how the level of treatment will be tailored through time to an individual's changing status. The goal of this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response. To explicate our objective and to state the assumptions, we use the potential outcomes model. The method proposed makes smooth parametric assumptions only on quantities that are directly relevant to the goal of estimating the optimal rules. We illustrate the methodology proposed via a small simulation.     

Asymptotic convergence of dimension reduction based boosting in classification

In high dimensional classification problem, two stage method, reducing the dimension of predictor first and then applying the classification method, is a natural solution and has been widely used in many fields. The consistency of the two stage method is an important issue, since errors induced by dimension reduction method inevitably have impacts on the following classification method. As an effective method for classification problem, boosting has been widely used in practice. In this paper, we study the consistency of two stage method–dimension reduction based boosting algorithm (briefly DRB) for classification problem. Theoretical results show that Lipschitz condition on the base learner is required to guarantee the consistency of DRB. This theoretical findings provide useful guideline for application.     

Application of the Bootstrap Approach to the Choice of Dimension and the α Parameter in the SIRα Method

To reduce the dimensionality of regression problems, sliced inverse regression approaches make it possible to determine linear combinations of a set of explanatory variables X related to the response variable Y in general semiparametric regression context. From a practical point of view, the determination of a suitable dimension (number of the linear combination of X) is important. In the literature, statistical tests based on the nullity of some eigenvalues have been proposed. Another approach is to consider the quality of the estimation of the effective dimension reduction (EDR) space. The square trace correlation between the true EDR space and its estimate can be used as goodness of estimation. In this article, we focus on the SIR_α method and propose a naïve bootstrap estimation of the square trace correlation criterion. Moreover, this criterion could also select the α parameter in the SIR_α method. We indicate how it can be used in practice. A simulation study is performed to illustrate the behavior of this approach.