arXiv subjects

Fabrizia Mealli

Publications and source records attributed to Fabrizia Mealli.

33 records · Page 2Linked to original sources

arXiv2019

The Local Randomization Framework for Regression Discontinuity Designs: A Review and Some Extensions

Regression discontinuity designs (RDDs) are a common quasi-experiment in economics and statistics. The most popular methodologies for analyzing RDDs utilize continuity-based assumptions and local polynomial regression, but recent works have developed alternative assumptions based on local randomization. The local randomization framework avoids modeling assumptions by instead placing assumptions on the assignment mechanism near the cutoff. However, most works have focused on completely randomized assignment mechanisms, which posit that propensity scores are equal for all units near the cutoff. In our review of the local randomization framework, we extend the framework to allow for any assignment mechanism, such that propensity scores may differ. We outline randomization tests that can be used to select a window around the cutoff where a particular assignment mechanism is most plausible, as well as methodologies for estimating causal effects after a window and assignment mechanism are chosen. We apply our methodology to a fuzzy RDD assessing the effects of financial aid on college dropout rates in Italy. We find that positing different assignment mechanisms within a single RDD can provide more nuanced sensitivity analyses as well as more precise inferences for causal effects.

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arXiv2019

Causal inference and machine learning approaches for evaluation of the health impacts of large-scale air quality regulations

We develop a causal inference approach to estimate the number of adverse health events prevented by large-scale air quality regulations via changes in exposure to multiple pollutants. This approach is motivated by regulations that impact pollution levels in all areas within their purview. We introduce a causal estimand called the Total Events Avoided (TEA) by the regulation, defined as the difference in the expected number of health events under the no-regulation pollution exposures and the observed number of health events under the with-regulation pollution exposures. We propose a matching method and a machine learning method that leverage high-resolution, population-level pollution and health data to estimate the TEA. Our approach improves upon traditional methods for regulation health impact analyses by clarifying the causal identifying assumptions, utilizing population-level data, minimizing parametric assumptions, and considering the impacts of multiple pollutants simultaneously. To reduce model-dependence, the TEA estimate captures health impacts only for units in the data whose anticipated no-regulation features are within the support of the observed with-regulation data, thereby providing a conservative but data-driven assessment to complement traditional parametric approaches. We apply these methods to investigate the health impacts of the 1990 Clean Air Act Amendments in the US Medicare population.

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arXiv2019

Bayesian Inference for Sequential Treatments under Latent Sequential Ignorability

We focus on causal inference for longitudinal treatments, where units are assigned to treatments at multiple time points, aiming to assess the effect of different treatment sequences on an outcome observed at a final point. A common assumption in similar studies is Sequential Ignorability (SI): treatment assignment at each time point is assumed independent of future potential outcomes given past observed outcomes and covariates. SI is questionable when treatment participation depends on individual choices, and treatment assignment may depend on unobservable quantities associated with future outcomes. We rely on Principal Stratification to formulate a relaxed version of SI: Latent Sequential Ignorability (LSI) assumes that treatment assignment is conditionally independent on future potential outcomes given past treatments, covariates and principal stratum membership, a latent variable defined by the joint value of observed and missing intermediate outcomes. We evaluate SI and LSI, using theoretical arguments and simulation studies to investigate the performance of the two assumptions when one holds and inference is conducted under both. Simulations show that when SI does not hold, inference performed under SI leads to misleading conclusions. Conversely, LSI generally leads to correct posterior distributions, irrespective of which assumption holds.

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arXiv2019

Survivor average causal effects for continuous time: a principal stratification approach to causal inference with semicompeting risks

In semicompeting risks problems, nonterminal time-to-event outcomes such as time to hospital readmission are subject to truncation by death. These settings are often modeled with illness-death models for the hazards of the terminal and nonterminal events, but evaluating causal treatment effects with hazard models is problematic due to conditioning on survival (a post-treatment outcome) that is embedded in the definition of a hazard. Extending an existing survivor average causal effect (SACE) estimand, we frame the evaluation of treatment effects in the context of semicompeting risks with principal stratification and introduce two new causal estimands: the time-varying survivor average causal effect (TV-SACE) and the restricted mean survivor average causal effect (RM-SACE). These principal causal effects are defined among units that would survive regardless of assigned treatment. We adopt a Bayesian estimation procedure that parameterizes illness-death models for both treatment arms. We outline a frailty specification that can accommodate within-person correlation between nonterminal and terminal event times, and we discuss potential avenues for adding model flexibility. The method is demonstrated in the context of hospital readmission among late-stage pancreatic cancer patients.

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arXiv2018

Estimating Population Average Causal Effects in the Presence of Non-Overlap: The Effect of Natural Gas Compressor Station Exposure on Cancer Mortality

Most causal inference studies rely on the assumption of overlap to estimate population or sample average causal effects. When data exhibit non-overlap, estimation of these estimands requires reliance on model specifications, due to poor data support. All existing methods to address non-overlap, such as trimming or down-weighting data in regions of poor support, change the estimand. In environmental health research, where study results are often intended to influence policy, changes in the estimand can diminish the study's impact, because estimates may not be representative of effects in the population of interest to policymakers. Researchers may be willing to make additional, minimal modeling assumptions in order to preserve the ability to estimate population average causal effects. We seek to make two contributions on this topic. First, we propose a flexible, data-driven definition of propensity score overlap and non-overlap regions. Second, we develop a novel Bayesian framework to estimate population average causal effects with minor model dependence and appropriately large uncertainties in the presence of non-overlap. In this approach, the tasks of estimating causal effects in the overlap and non-overlap regions are delegated to two distinct models, suited to the degree of data support in each region. Tree ensembles are used to non-parametrically estimate individual causal effects in the overlap region, where the data can speak for themselves. In the non-overlap region, where insufficient data support means reliance on model specification is necessary, individual causal effects are estimated by extrapolating trends from the overlap region via a spline model. The promising performance of our method is demonstrated in simulations. Finally, we utilize our method to perform a novel investigation of the causal effect of natural gas compressor station exposure on cancer outcomes.

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arXiv2018

Estimating Causal Effects Under Interference Using Bayesian Generalized Propensity Scores

In most real-world systems units are interconnected and can be represented as networks consisting of nodes and edges. For instance, in social systems individuals can have social ties, family or financial relationships. In settings where some units are exposed to a treatment and its effect spills over connected units, estimating both the direct effect of the treatment and spillover effects presents several challenges. First, assumptions on the way and the extent to which spillover effects occur along the observed network are required. Second, in observational studies, where the treatment assignment is not under the control of the investigator, confounding and homophily are potential threats to the identification and estimation of causal effects on networks. Here, we make two structural assumptions: i) neighborhood interference, which assumes interference operates only through a function of the immediate neighbors' treatments ii) unconfoundedness of the individual and neighborhood treatment, which rules out the presence of unmeasured confounding variables, including those driving homophily. Under these assumptions we develop a new covariate-adjustment estimator for treatment and spillover effects in observational studies on networks. Estimation is based on a generalized propensity score that balances individual and neighborhood covariates across units under different levels of individual treatment and of exposure to neighbors' treatment. Adjustment for propensity score is performed using a penalized spline regression. Inference capitalizes on a three-step Bayesian procedure which allows to take into account the uncertainty in the propensity score estimation and avoiding model feedback. Finally, correlation of interacting units is taken into account using a community detection algorithm and incorporating random effects in the outcome model.

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arXiv2018

Causal inference for interfering units with cluster and population level treatment allocation programs

Interference arises when an individual's potential outcome depends on the individual treatment level, but also on the treatment level of others. A common assumption in the causal inference literature in the presence of interference is partial interference, implying that the population can be partitioned in clusters of individuals whose potential outcomes only depend on the treatment of units within the same cluster. Previous literature has defined average potential outcomes under counterfactual scenarios where treatments are randomly allocated to units within a cluster. However, within clusters there may be units that are more or less likely to receive treatment based on covariates or neighbors' treatment. We define new estimands that describe average potential outcomes for realistic counterfactual treatment allocation programs, extending existing estimands to take into consideration the units' covariates and dependence between units' treatment assignment. We further propose entirely new estimands for population-level interventions over the collection of clusters, which correspond in the motivating setting to regulations at the federal (vs. cluster or regional) level. We discuss these estimands, propose unbiased estimators and derive asymptotic results as the number of clusters grows. Finally, we estimate effects in a comparative effectiveness study of power plant emission reduction technologies on ambient ozone pollution.

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arXiv2018

Identification and estimation of treatment and interference effects in observational studies on networks

Causal inference on a population of units connected through a network often presents technical challenges, including how to account for interference. In the presence of local interference, for instance, potential outcomes of a unit depend on its treatment as well as on the treatments of other local units, such as its neighbors according to the network. In observational studies, a further complication is that the typical unconfoundedness assumption must be extended - say, to include the treatment of neighbors, and indi- vidual and neighborhood covariates - to guarantee identification and valid inference. Here, we propose new estimands that define treatment and interference effects. We then derive analytical expressions for the bias of a naive estimator that wrongly assumes away interference. The bias depends on the level of interference but also on the degree of association between individual and neighborhood treatments. We propose an extended unconfoundedness assumption that accounts for interference, and we develop new covariate-adjustment methods that lead to valid estimates of treatment and interference effects in observational studies on networks. Estimation is based on a generalized propensity score that balances individual and neighborhood covariates across units under different levels of individual treatment and of exposure to neighbors' treatment. We carry out simulations, calibrated using friendship networks and covariates in a nationally representative longitudinal study of adolescents in grades 7-12, in the United States, to explore finite-sample performance in different realistic settings.

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arXiv2016

Potential outcome approach to causal inference in assessing the short term impact of air pollution on mortality

The opportunity to assess short term impact of air pollution relies on the causal interpretation of the exposure-outcome association, but up to now few studies explicitly faced this issue within a causal inference framework. In this paper, we reformulated the problem of assessing the short term impact of air pollution on health using the potential outcome approach to causal inference. We focused on the impact of high daily levels of PM10 on mortality within two days from the exposure in the metropolitan area of Milan (Italy), during the period 2003-2006. After defining the number of attributable deaths in terms of difference between potential outcomes, we used the estimated propensity score to match each high exposure-day with a day with similar background characteristics but lower PM10 level. Then, we estimated the impact by comparing mortality between matched days. We found that during the study period daily exposures larger than 40 microgram per cubic meter were responsible of 1079 deaths (116; 2042). The impact was more evident among the elderly than in the younger classes of age. The propensity score matching turned out to be an appealing method to assess historical impacts in this field.

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arXiv2016

Principal Score Methods: Assumptions and Extensions

Researchers addressing post-treatment complications in randomized trials often turn to principal stratification to define relevant assumptions and quantities of interest. One approach for estimating causal effects in this framework is to use methods based on the "principal score," typically assuming that stratum membership is as-good-as-randomly assigned given a set of covariates. In this paper, we clarify the key assumption in this context, known as Principal Ignorability, and argue that versions of this assumption are quite strong in practice. We describe different estimation approaches and demonstrate that weighting-based methods are generally preferable to subgroup-based approaches that discretize the principal score. We then extend these ideas to the case of two-sided noncompliance and propose a natural framework for combining Principal Ignorability with exclusion restrictions and other assumptions. Finally, we apply these ideas to the Head Start Impact Study, a large-scale randomized evaluation of the Head Start program. Overall, we argue that, while principal score methods are useful tools, applied researchers should fully understand the relevant assumptions when using them in practice.

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arXiv2016

Posterior Predictive P-values with Fisher Randomization Tests in Noncompliance Settings: Test Statistics vs Discrepancy Variables

In randomized experiments with noncompliance, tests may focus on compliers rather than on the overall sample. Rubin (1998) put forth such a method, and argued that testing for the complier average causal effect and averaging permutation based p-values over the posterior distribution of the compliance status could increase power, as compared to general intent-to-treat tests. The general scheme is to repeatedly do a two-step process of imputing missing compliance statuses and conducting a permutation test with the completed data. In this paper, we explore this idea further, comparing the use of discrepancy measures, which depend on unknown but imputed parameters, to classical test statistics and exploring different approaches for imputing the unknown compliance statuses. We also examine consequences of model misspecification in the imputation step, and discuss to what extent this additional modeling undercuts the permutation test's model independence. We find that, especially for discrepancy measures, modeling choices can impact both power and validity. In particular, imputing missing compliance statuses assuming the null can radically reduce power, but not doing so can jeopardize validity. Fortunately, covariates predictive of compliance status can mitigate these results. Finally, we compare this overall approach to Bayesian model-based tests, that is tests that are directly derived from posterior credible intervals, under both correct and incorrect model specification. We find that adding the permutation step in an otherwise Bayesian approach improves robustness to model specification without substantial loss of power.

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arXiv2015

Evaluating the Causal Effect of University Grants on Student Dropout: Evidence from a Regression Discontinuity Design Using Principal Stratification

Regression discontinuity (RD) designs are often interpreted as local randomized experiments: a RD design can be considered as a randomized experiment for units with a realized value of a so-called forcing variable falling around a pre-fixed threshold. Motivated by the evaluation of Italian university grants, we consider a fuzzy RD design where the receipt of the treatment is based on both eligibility criteria and a voluntary application status. Resting on the fact that grant application and grant receipt statuses are post-assignment (post-eligibility) intermediate variables, we use the principal stratification framework to define causal estimands within the Rubin Causal Model. We propose a probabilistic formulation of the assignment mechanism underlying RD designs, by re-formulating the Stable Unit Treatment Value Assumption (SUTVA) and making an explicit local overlap assumption for a subpopulation around the threshold. A local randomization assumption is invoked instead of more standard continuity assumptions. We also develop a model-based Bayesian approach to select the target subpopulation(s) with adjustment for multiple comparisons, and to draw inference for the target causal estimands in this framework. Applying the method to the data from two Italian universities, we find evidence that university grants are effective in preventing students from low-income families from dropping out of higher education.

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arXiv2014

Improving Inference of Gaussian Mixtures Using Auxiliary Variables

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference for mixture models by using auxiliary variables. Despite the large literature in mixture models and several empirical examples, there is no previous work that gives general theoretical justification for including auxiliary variables in mixture models, even for special cases. We provide a theoretical basis for comparing inference for mixture multivariate models with the corresponding inference for marginal univariate mixture models. Analytical results for several special cases are established. We show that the probability of correctly allocating mixture memberships and the information number for the means of the primary outcome in a bivariate model with two Gaussian mixtures are generally larger than those in each univariate model. Simulations under a range of scenarios, including misspecified models, are conducted to examine the improvement. The method is illustrated by two real applications in ecology and causal inference.

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arXiv2014

A Conversation with Donald B. Rubin

Donald Bruce Rubin is John L. Loeb Professor of Statistics at Harvard University. He has made fundamental contributions to statistical methods for missing data, causal inference, survey sampling, Bayesian inference, computing and applications to a wide range of disciplines, including psychology, education, policy, law, economics, epidemiology, public health and other social and biomedical sciences.

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arXiv2014

Exploiting multiple outcomes in Bayesian principal stratification analysis with application to the evaluation of a job training program

The causal effect of a randomized job training program, the JOBS II study, on trainees' depression is evaluated. Principal stratification is used to deal with noncompliance to the assigned treatment. Due to the latent nature of the principal strata, strong structural assumptions are often invoked to identify principal causal effects. Alternatively, distributional assumptions may be invoked using a model-based approach. These often lead to weakly identified models with substantial regions of flatness in the posterior distribution of the causal effects. Information on multiple outcomes is routinely collected in practice, but is rarely used to improve inference. This article develops a Bayesian approach to exploit multivariate outcomes to sharpen inferences in weakly identified principal stratification models. We show that inference for the causal effect on depression is significantly improved by using the re-employment status as a secondary outcome in the JOBS II study. Simulation studies are also performed to illustrate the potential gains in the estimation of principal causal effects from jointly modeling more than one outcome. This approach can also be used to assess plausibility of structural assumptions and sensitivity to deviations from these structural assumptions. Two model checking procedures via posterior predictive checks are also discussed.

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