arXiv subjects

Francesca Dominici

Publications and source records attributed to Francesca Dominici.

At least 55 records · Page 3Linked to original sources

arXiv2022

Assessing the causal effects of a stochastic intervention in time series data: Are heat alerts effective in preventing deaths and hospitalizations?

The methodological development of this paper is motivated by the need to address the following scientific question: does the issuance of heat alerts prevent adverse health effects? Our goal is to address this question within a causal inference framework in the context of time series data. A key challenge is that causal inference methods require the overlap assumption to hold: each unit (i.e., a day) must have a positive probability of receiving the treatment (i.e., issuing a heat alert on that day). In our motivating example, the overlap assumption is often violated: the probability of issuing a heat alert on a cooler day is zero. To overcome this challenge, we propose a stochastic intervention for time series data which is implemented via an incremental time-varying propensity score (ItvPS). The ItvPS intervention is executed by multiplying the probability of issuing a heat alert on day $t$ -- conditional on past information up to day $t$ -- by an odds ratio $δ_t$. First, we introduce a new class of causal estimands that relies on the ItvPS intervention. We provide theoretical results to show that these causal estimands can be identified and estimated under a weaker version of the overlap assumption. Second, we propose nonparametric estimators based on the ItvPS and derive an upper bound for the variances of these estimators. Third, we extend this framework to multi-site time series using a spatial meta-analysis approach. Fourth, we show that the proposed estimators perform well in terms of bias and root mean squared error via simulations. Finally, we apply our proposed approach to estimate the causal effects of increasing the probability of issuing heat alerts on each warm-season day in reducing deaths and hospitalizations among Medicare enrollees in $2,837$ U.S. counties.

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arXiv2021

Matching on Generalized Propensity Scores with Continuous Exposures

In the context of a binary treatment, matching is a well-established approach in causal inference. However, in the context of a continuous treatment or exposure, matching is still underdeveloped. We propose an innovative matching approach to estimate an average causal exposure-response function under the setting of continuous exposures that relies on the generalized propensity score (GPS). Our approach maintains the following attractive features of matching: a) clear separation between the design and the analysis; b) robustness to model misspecification or to the presence of extreme values of the estimated GPS; c) straightforward assessment of covariate balance. We first introduce an assumption of identifiability, called local weak unconfoundedness. Under this assumption and mild smoothness conditions, we provide theoretical guarantees that our proposed matching estimator attains point-wise consistency and asymptotic normality. In simulations, our proposed matching approach outperforms existing methods under settings of model misspecification or the presence of extreme values of the estimated GPS. We apply our proposed method to estimate the average causal exposure-response function between long-term PM$_{2.5}$ exposure and all-cause mortality among 68.5 million Medicare enrollees, 2000-2016. We found strong evidence of a harmful effect of long-term PM$_{2.5}$ exposure on mortality. Code for the proposed matching approach is provided in the CausalGPS R package, which is available on CRAN and provides a computationally efficient implementation.

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arXiv2021

Measuring performance for end-of-life care

Although not without controversy, readmission is entrenched as a hospital quality metric, with statistical analyses generally based on fitting a logistic-Normal generalized linear mixed model. Such analyses, however, ignore death as a competing risk, although doing so for clinical conditions with high mortality can have profound effects; a hospitals seemingly good performance for readmission may be an artifact of it having poor performance for mortality. In this paper we propose novel multivariate hospital-level performance measures for readmission and mortality, that derive from framing the analysis as one of cluster-correlated semi-competing risks data. We also consider a number of profiling-related goals, including the identification of extreme performers and a bivariate classification of whether the hospital has higher-/lower-than-expected readmission and mortality rates, via a Bayesian decision-theoretic approach that characterizes hospitals on the basis of minimizing the posterior expected loss for an appropriate loss function. In some settings, particularly if the number of hospitals is large, the computational burden may be prohibitive. To resolve this, we propose a series of analysis strategies that will be useful in practice. Throughout the methods are illustrated with data from CMS on N=17,685 patients diagnosed with pancreatic cancer between 2000-2012 at one of J=264 hospitals in California.

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arXiv2021

Accounting for recall bias in case-control studies: a causal inference approach

A case-control study is designed to help determine if an exposure is associated with an outcome. However, since case-control studies are retrospective, they are often subject to recall bias. Recall bias can occur when study subjects do not remember previous events accurately. In this paper, we first define the estimand of interest: the causal odds ratio (COR) for a case-control study. Second, we develop estimation approaches for the COR and present estimates as a function of recall bias. Third, we define a new quantity called the \textit{R-factor}, which denotes the minimal amount of recall bias that leads to altering the initial conclusion. We show that a failure to account for recall bias can significantly bias estimation of the COR. Finally, we apply the proposed framework to a case-control study of the causal effect of childhood physical abuse on adulthood mental health.

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arXiv2020

From controlled to undisciplined data: estimating causal effects in the era of data science using a potential outcome framework

This paper discusses the fundamental principles of causal inference - the area of statistics that estimates the effect of specific occurrences, treatments, interventions, and exposures on a given outcome from experimental and observational data. We explain the key assumptions required to identify causal effects, and highlight the challenges associated with the use of observational data. We emphasize that experimental thinking is crucial in causal inference. The quality of the data (not necessarily the quantity), the study design, the degree to which the assumptions are met, and the rigor of the statistical analysis allow us to credibly infer causal effects. Although we advocate leveraging the use of big data and the application of machine learning (ML) algorithms for estimating causal effects, they are not a substitute of thoughtful study design. Concepts are illustrated via examples.

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arXiv2020

Causal Inference in high dimensions: A marriage between Bayesian modeling and good frequentist properties

We introduce a framework for estimating causal effects of binary and continuous treatments in high dimensions. We show how posterior distributions of treatment and outcome models can be used together with doubly robust estimators. We propose an approach to uncertainty quantification for the doubly robust estimator which utilizes posterior distributions of model parameters and (1) results in good frequentist properties in small samples, (2) is based on a single MCMC, and (3) improves over frequentist measures of uncertainty which rely on asymptotic properties. We show that our proposed variance estimation strategy is consistent when both models are correctly specified and that it is conservative in finite samples or when one or both models are misspecified. We consider a flexible framework for modeling the treatment and outcome processes within the Bayesian paradigm that reduces model dependence, accommodates nonlinearity, and achieves dimension reduction of the covariate space. We illustrate the ability of the proposed approach to flexibly estimate causal effects in high dimensions and appropriately quantify uncertainty, and show that it performs well relative to existing approaches. Finally, we estimate the effect of continuous environmental exposures on cholesterol and triglyceride levels. An R package is available at github.com/jantonelli111/DoublyRobustHD.

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arXiv2020

A causal exposure response function with local adjustment for confounding: Estimating health effects of exposure to low levels of ambient fine particulate matter

The Clean Air Act mandates that the National Ambient Air Quality Standards (NAAQS) must be routinely assessed to protect populations based on the latest science. Therefore, researchers should continue to address whether exposure to levels of air pollution below the NAAQS is harmful to human health. The contentious nature surrounding environmental regulations urges us to cast this question within a causal inference framework. Parametric and semi-parametric regression approaches have been used to estimate the exposure-response (ER) curve between ambient air pollution and health outcomes. Most of these approaches are not formulated within a causal framework, adjust for the same covariates across all levels of exposure, and do not account for model uncertainty. We introduce a Bayesian framework for the estimation of a causal ER curve called LERCA (Local Exposure Response Confounding Adjustment), which allows for different confounders and different strength of confounding at the different exposure levels; and propagates uncertainty regarding confounders' selection and the shape of the ER. LERCA provides a principled way of assessing the covariates' confounding importance at different exposure levels, providing researchers with information regarding the variables to adjust for in regression models. Using simulations, we show that state of the art approaches perform poorly in estimating the ER curve in the presence of local confounding. LERCA is used to evaluate the relationship between exposure to ambient PM2.5 and cardiovascular hospitalizations for 5,362 zip codes in the US, while adjusting for a potentially varying set of confounders across the exposure range. Ambient PM2.5 leads to an increase in cardiovascular hospitalization rates when focusing at the low exposure range. Our results indicate that there is no threshold for the effect of PM2.5 on cardiovascular hospitalizations.

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arXiv2019

All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously

Variable importance (VI) tools describe how much covariates contribute to a prediction model's accuracy. However, important variables for one well-performing model (for example, a linear model $f(\mathbf{x})=\mathbf{x}^{T}β$ with a fixed coefficient vector $β$) may be unimportant for another model. In this paper, we propose model class reliance (MCR) as the range of VI values across all well-performing model in a prespecified class. Thus, MCR gives a more comprehensive description of importance by accounting for the fact that many prediction models, possibly of different parametric forms, may fit the data well. In the process of deriving MCR, we show several informative results for permutation-based VI estimates, based on the VI measures used in Random Forests. Specifically, we derive connections between permutation importance estimates for a single prediction model, U-statistics, conditional variable importance, conditional causal effects, and linear model coefficients. We then give probabilistic bounds for MCR, using a novel, generalizable technique. We apply MCR to a public data set of Broward County criminal records to study the reliance of recidivism prediction models on sex and race. In this application, MCR can be used to help inform VI for unknown, proprietary models.

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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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arXiv2018

A causal inference framework for cancer cluster investigations using publicly available data

Often, a community becomes alarmed when high rates of cancer are noticed, and residents suspect that the cancer cases could be caused by a known source of hazard. In response, the CDC recommends that departments of health perform a standardized incidence ratio (SIR) analysis to determine whether the observed cancer incidence is higher than expected. This approach has several limitations that are well documented in the literature. In this paper we propose a novel causal inference approach to cancer cluster investigations, rooted in the potential outcomes framework. Assuming that a source of hazard representing a potential cause of increased cancer rates in the community is identified a priori, we introduce a new estimand called the causal SIR (cSIR). The cSIR is a ratio defined as the expected cancer incidence in the exposed population divided by the expected cancer incidence under the (counterfactual) scenario of no exposure. To estimate the cSIR we need to overcome two main challenges: 1) identify unexposed populations that are as similar as possible to the exposed one to inform estimation under the counterfactual scenario of no exposure, and 2) make inference on cancer incidence in these unexposed populations using publicly available data that are often available at a much higher level of spatial aggregation than what is desired. We overcome the first challenge by relying on matching. We overcome the second challenge by developing a Bayesian hierarchical model that borrows information from other sources to impute cancer incidence at the desired finer level of spatial aggregation. We apply our proposed approach to determine whether trichloroethylene vapor exposure has caused increased cancer incidence in Endicott, NY.

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arXiv2018

airpred: A Flexible R Package Implementing Methods for Predicting Air Pollution

Fine particulate matter (PM$_{2.5}$) is one of the criteria air pollutants regulated by the Environmental Protection Agency in the United States. There is strong evidence that ambient exposure to (PM$_{2.5}$) increases risk of mortality and hospitalization. Large scale epidemiological studies on the health effects of PM$_{2.5}$ provide the necessary evidence base for lowering the safety standards and inform regulatory policy. However, ambient monitors of PM$_{2.5}$ (as well as monitors for other pollutants) are sparsely located across the U.S., and therefore studies based only on the levels of PM$_{2.5}$ measured from the monitors would inevitably exclude large amounts of the population. One approach to resolving this issue has been developing models to predict local PM$_{2.5}$, NO$_2$, and ozone based on satellite, meteorological, and land use data. This process typically relies developing a prediction model that relies on large amounts of input data and is highly computationally intensive to predict levels of air pollution in unmonitored areas. We have developed a flexible R package that allows for environmental health researchers to design and train spatio-temporal models capable of predicting multiple pollutants, including PM$_{2.5}$. We utilize H2O, an open source big data platform, to achieve both performance and scalability when used in conjunction with cloud or cluster computing systems.

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arXiv2018

High-dimensional confounding adjustment using continuous spike and slab priors

In observational studies, estimation of a causal effect of a treatment on an outcome relies on proper adjustment for confounding. If the number of the potential confounders ($p$) is larger than the number of observations ($n$), then direct control for all potential confounders is infeasible. Existing approaches for dimension reduction and penalization are generally aimed at predicting the outcome, and are less suited for estimation of causal effects. Under standard penalization approaches (e.g. Lasso), if a variable $X_j$ is strongly associated with the treatment $T$ but weakly with the outcome $Y$, the coefficient $β_j$ will be shrunk towards zero thus leading to confounding bias. Under the assumption of a linear model for the outcome and sparsity, we propose continuous spike and slab priors on the regression coefficients $β_j$ corresponding to the potential confounders $X_j$. Specifically, we introduce a prior distribution that does not heavily shrink to zero the coefficients ($β_j$s) of the $X_j$s that are strongly associated with $T$ but weakly associated with $Y$. We compare our proposed approach to several state of the art methods proposed in the literature. Our proposed approach has the following features: 1) it reduces confounding bias in high dimensional settings; 2) it shrinks towards zero coefficients of instrumental variables; and 3) it achieves good coverages even in small sample sizes. We apply our approach to the National Health and Nutrition Examination Survey (NHANES) data to estimate the causal effects of persistent pesticide exposure on triglyceride levels.

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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

Causal inference in the context of an error prone exposure: air pollution and mortality

We propose a new approach for estimating causal effects when the exposure is measured with error and confounding adjustment is performed via a generalized propensity score (GPS). Using validation data, we propose a regression calibration (RC)-based adjustment for a continuous error-prone exposure combined with GPS to adjust for confounding (RC-GPS). The outcome analysis is conducted after transforming the corrected continuous exposure into a categorical exposure. We consider confounding adjustment in the context of GPS subclassification, inverse probability treatment weighting (IPTW) and matching. In simulations with varying degrees of exposure error and confounding bias, RC-GPS eliminates bias from exposure error and confounding compared to standard approaches that rely on the error-prone exposure. We applied RC-GPS to a rich data platform to estimate the causal effect of long-term exposure to fine particles ($PM_{2.5}$) on mortality in New England for the period from 2000 to 2012. The main study consists of $2,202$ zip codes covered by $217,660$ 1km $\times$ 1km grid cells with yearly mortality rates, yearly $PM_{2.5}$ averages estimated from a spatio-temporal model (error-prone exposure) and several potential confounders. The internal validation study includes a subset of 83 1km $\times$ 1km grid cells within 75 zip codes from the main study with error-free yearly $PM_{2.5}$ exposures obtained from monitor stations. Under assumptions of non-interference and weak unconfoundedness, using matching we found that exposure to moderate levels of $PM_{2.5}$ ($8 <$ $PM_{2.5}$ $\leq 10\ {\rm μg/m^3}$) causes a $2.8\%$ ($95\%$ CI: $0.6\%, 3.6\%$) increase in all-cause mortality compared to low exposure ($PM_{2.5}$ $\leq 8\ {\rm μg/m^3}$).

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arXiv2018

Discovering Effect Modification and Randomization Inference in Air Pollution Studies

Studies have shown that exposure to air pollution, even at low levels, significantly increases mortality. As regulatory actions are becoming prohibitively expensive, robust evidence to guide the development of targeted interventions to reduce air pollution exposure is needed. In this paper, we introduce a novel statistical method that splits the data into two subsamples: (a) Using the first subsample, we consider a data-driven search for $\textit{de novo}$ discovery of subgroups that could have exposure effects that differ from the population mean; and then (b) using the second subsample, we quantify evidence of effect modification among the subgroups with nonparametric randomization-based tests. We also develop a sensitivity analysis method to assess the robustness of the conclusions to unmeasured confounding bias. Via simulation studies and theoretical arguments, we demonstrate that since we discover the subgroups in the first subsample, hypothesis testing on the second subsample can focus on theses subgroups only, thus substantially increasing the statistical power of the test. We apply our method to the data of 1,612,414 Medicare beneficiaries in New England region in the United States for the period 2000 to 2006. We find that seniors aged between 81-85 with low income and seniors aged above 85 have statistically significant higher causal effects of exposure to PM$_{2.5}$ on 5-year mortality rate compared to the population mean.

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arXiv2015

Generalized Quantile Treatment Effect: A Flexible Bayesian Approach Using Quantile Ratio Smoothing

We propose a new general approach for estimating the effect of a binary treatment on a continuous and potentially highly skewed response variable, the generalized quantile treatment effect (GQTE). The GQTE is defined as the difference between a function of the quantiles under the two treatment conditions. As such, it represents a generalization over the standard approaches typically used for estimating a treatment effect (i.e., the average treatment effect and the quantile treatment effect) because it allows the comparison of any arbitrary characteristic of the outcome's distribution under the two treatments. Following Dominici et al. (2005), we assume that a pre-specified transformation of the two quantiles is modeled as a smooth function of the percentiles. This assumption allows us to link the two quantile functions and thus to borrow information from one distribution to the other. The main theoretical contribution we provide is the analytical derivation of a closed form expression for the likelihood of the model. Exploiting this result we propose a novel Bayesian inferential methodology for the GQTE. We show some finite sample properties of our approach through a simulation study which confirms that in some cases it performs better than other nonparametric methods. As an illustration we finally apply our methodology to the 1987 National Medicare Expenditure Survey data to estimate the difference in the single hospitalization medical cost distributions between cases (i.e., subjects affected by smoking attributable diseases) and controls.

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arXiv2015

Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer

Readmission following discharge from an initial hospitalization is a key marker of quality of health care in the United States. For the most part, readmission has been used to study quality of care for patients with acute health conditions, such as pneumonia and heart failure, with analyses typically based on a logistic-Normal generalized linear mixed model. Applying this model to the study readmission among patients with increasingly prevalent advanced health conditions such as pancreatic cancer is problematic, however, because it ignores death as a competing risk. A more appropriate analysis is to imbed such studies within the semi-competing risks framework. To our knowledge, however, no comprehensive statistical methods have been developed for cluster-correlated semi-competing risks data. In this paper we propose a novel hierarchical modeling framework for the analysis of cluster-correlated semi-competing risks data. The framework permits parametric or non-parametric specifications for a range of model components, including baseline hazard functions and distributions for key random effects, giving analysts substantial flexibility as they consider their own analyses. Estimation and inference is performed within the Bayesian paradigm since it facilitates the straightforward characterization of (posterior) uncertainty for all model parameters including hospital-specific random effects. The proposed framework is used to study the risk of readmission among 5,298 Medicare beneficiaries diagnosed with pancreatic cancer at 112 hospitals in the six New England states between 2000-2009, specifically to investigate the role of patient-level risk factors and to characterize variation in risk across hospitals that is not explained by differences in patient case-mix.

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arXiv2010

A smoothing approach for masking spatial data

Individual-level health data are often not publicly available due to confidentiality; masked data are released instead. Therefore, it is important to evaluate the utility of using the masked data in statistical analyses such as regression. In this paper we propose a data masking method which is based on spatial smoothing techniques. The proposed method allows for selecting both the form and the degree of masking, thus resulting in a large degree of flexibility. We investigate the utility of the masked data sets in terms of the mean square error (MSE) of regression parameter estimates when fitting a Generalized Linear Model (GLM) to the masked data. We also show that incorporating prior knowledge on the spatial pattern of the exposure into the data masking may reduce the bias and MSE of the parameter estimates. By evaluating both utility and disclosure risk as functions of the form and the degree of masking, our method produces a risk-utility profile which can facilitate the selection of masking parameters. We apply the method to a study of racial disparities in mortality rates using data on more than 4 million Medicare enrollees residing in 2095 zip codes in the Northeast region of the United States.

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