arXiv subjects

Corwin M. Zigler

Publications and source records attributed to Corwin M. Zigler.

8 recordsLinked to original sources

arXiv2025

Bayesian Nonhomogeneous hidden Markov models to leverage routine in physical activity monitoring with informative wear time

Missing data is among the most prominent challenges in the analysis of physical activity (PA) data collected from wearable devices, with the threat of nonignorabile missingness arising when patterns of device wear relate to underlying activity patterns. We offer a rigorous consideration of assumptions about missing data mechanisms in the context of the common modeling paradigm of state space models with a finite, meaningful, set of underlying PA states. Focusing in particular on hidden Markov models, we identify inherent limitations in the presence of missing data when covariates are required to satisfy common missing data assumptions. In response to this limitation, we propose a Bayesian non-homogeneous state space model that can accommodate covariate dependence in the transitions between latent activity states, which in this case relates to whether patients' routine behavior can inform how they transition between PA states and thus support imputation of missing PA data. We show the benefits of the proposed model for missing data imputation and inference for relevant PA summaries. Our development advances analytic capacity to confront the ubiquitous challenge of missing data when analyzing PA studies using wearables. We illustrate with the analysis of a cohort of adolescent and young adult (AYA) cancer patients who wore commercial Fitbit devices for varying durations during the course of treatment.

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arXiv2024

Causal health impacts of power plant emission controls under modeled and uncertain physical process interference

Causal inference with spatial environmental data is often challenging due to the presence of interference: outcomes for observational units depend on some combination of local and non-local treatment. This is especially relevant when estimating the effect of power plant emissions controls on population health, as pollution exposure is dictated by (i) the location of point-source emissions, as well as (ii) the transport of pollutants across space via dynamic physical-chemical processes. In this work, we estimate the effectiveness of air quality interventions at coal-fired power plants in reducing two adverse health outcomes in Texas in 2016: pediatric asthma ED visits and Medicare all-cause mortality. We develop methods for causal inference with interference when the underlying network structure is not known with certainty and instead must be estimated from ancillary data. Notably, uncertainty in the interference structure is propagated to the resulting causal effect estimates. We offer a Bayesian, spatial mechanistic model for the interference mapping which we combine with a flexible non-parametric outcome model to marginalize estimates of causal effects over uncertainty in the structure of interference. Our analysis finds some evidence that emissions controls at upwind power plants reduce asthma ED visits and all-cause mortality, however accounting for uncertainty in the interference renders the results largely inconclusive.

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arXiv2022

Evaluating Federal Policies Using Bayesian Time Series Models: Estimating the Causal Impact of the Hospital Readmissions Reduction Program

Researchers are often faced with evaluating the effect of a policy or program that was simultaneously initiated across an entire population of units at a single point in time, and its effects over the targeted population can manifest at any time period afterwards. In the presence of data measured over time, Bayesian time series models have been used to impute what would have happened after the policy was initiated, had the policy not taken place, in order to estimate causal effects. However, the considerations regarding the definition of the target estimands, the underlying assumptions, the plausibility of such assumptions, and the choice of an appropriate model have not been thoroughly investigated. In this paper, we establish useful estimands for the evaluation of large-scale policies. We discuss that imputation of missing potential outcomes relies on an assumption which, even though untestable, can be partially evaluated using observed data. We illustrate an approach to evaluate this key causal assumption and facilitate model elicitation based on data from the time interval before policy initiation and using classic statistical techniques. As an illustration, we study the Hospital Readmissions Reduction Program (HRRP), a US federal intervention aiming to improve health outcomes for patients with pneumonia, acute myocardial infraction, or congestive failure admitted to a hospital. We evaluate the effect of the HRRP on population mortality among the elderly across the US and in four geographic subregions, and at different time windows. We find that the HRRP increased mortality from pneumonia and acute myocardial infraction across at least one geographical region and time horizon, and is likely to have had a detrimental effect on public health.

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arXiv2020

A Mechanistic Model of Annual Sulfate Concentrations in the United States

We develop a mechanistic model to analyze the impact of sulfur dioxide emissions from coal-fired power plants on average sulfate concentrations in the central United States. A multivariate Ornstein-Uhlenbeck (OU) process is used to approximate the dynamics of the underlying space-time chemical transport process, and its distributional properties are leveraged to specify novel probability models for spatial data (i.e., spatially-referenced data with no temporal replication) that are viewed as either a snapshot or a time-averaged observation of the OU process. Air pollution transport dynamics determine the mean and covariance structure of our atmospheric sulfate model, allowing us to infer which process dynamics are driving observed air pollution concentrations. We use these inferred dynamics to assess the regulatory impact of flue-gas desulfurization (FGD) technologies on human exposure to sulfate aerosols.

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arXiv2018

Bipartite Causal Inference with Interference

Statistical methods to evaluate the effectiveness of interventions are increasingly challenged by the inherent interconnectedness of units. Specifically, a recent flurry of methods research has addressed the problem of interference between observations, which arises when one observational unit's outcome depends not only on its treatment but also the treatment assigned to other units. We introduce the setting of bipartite causal inference with interference, which arises when 1) treatments are defined on observational units that are distinct from those at which outcomes are measured and 2) there is interference between units in the sense that outcomes for some units depend on the treatments assigned to many other units. Basic definitions and formulations are provided for this setting, highlighting similarities and differences with more commonly considered settings of causal inference with interference. Several types of causal estimands are discussed, and a simple inverse probability of treatment weighted estimator is developed for a subset of simplified estimands. The estimators are deployed to evaluate how interventions to reduce air pollution from 473 power plants in the U.S. causally affect cardiovascular hospitalization among Medicare beneficiaries residing at 23,458 zip code locations.

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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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arXiv2014

The central role of Bayes theorem for joint estimation of causal effects and propensity scores

Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal effects. Underlying this recent body of literature on Bayesian propensity score estimation is an implicit discordance between the goal of the propensity score and the use of Bayes theorem. The propensity score condenses multivariate covariate information into a scalar to allow estimation of causal effects without specifying a model for how each covariate relates to the outcome. Avoiding specification of a detailed model for the outcome response surface is valuable for robust estimation of causal effects, but this strategy is at odds with the use of Bayes theorem, which presupposes a full probability model for the observed data. The goal of this paper is to explicate this fundamental feature of Bayesian estimation of causal effects with propensity scores in order to provide context for the existing literature and for future work on this important topic.

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arXiv2011

The potential for bias in principal causal effect estimation when treatment received depends on a key covariate

Motivated by a potential-outcomes perspective, the idea of principal stratification has been widely recognized for its relevance in settings susceptible to posttreatment selection bias such as randomized clinical trials where treatment received can differ from treatment assigned. In one such setting, we address subtleties involved in inference for causal effects when using a key covariate to predict membership in latent principal strata. We show that when treatment received can differ from treatment assigned in both study arms, incorporating a stratum-predictive covariate can make estimates of the "complier average causal effect" (CACE) derive from observations in the two treatment arms with different covariate distributions. Adopting a Bayesian perspective and using Markov chain Monte Carlo for computation, we develop posterior checks that characterize the extent to which incorporating the pretreatment covariate endangers estimation of the CACE. We apply the method to analyze a clinical trial comparing two treatments for jaw fractures in which the study protocol allowed surgeons to overrule both possible randomized treatment assignments based on their clinical judgment and the data contained a key covariate (injury severity) predictive of treatment received.

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