arXiv subjects

Joseph Antonelli

Publications and source records attributed to Joseph Antonelli.

28 records · Page 2Linked to original sources

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

Spike-and-Slab Group Lassos for Grouped Regression and Sparse Generalized Additive Models

We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the first nonparametric variant of the spike-and-slab lasso methodology. Our model simultaneously performs group selection and estimation, while our fully Bayes treatment of the mixture proportion allows for model complexity control and automatic self-adaptivity to different levels of sparsity. We develop theory to uniquely characterize the global posterior mode under the SSGL and introduce a highly efficient block coordinate ascent algorithm for maximum a posteriori (MAP) estimation. We further employ de-biasing methods to provide uncertainty quantification of our estimates. Thus, implementation of our model avoids the computational intensiveness of Markov chain Monte Carlo (MCMC) in high dimensions. We derive posterior concentration rates for both grouped linear regression and sparse GAMs when the number of covariates grows at nearly exponential rate with sample size. Finally, we illustrate our methodology through extensive simulations and data analysis.

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arXiv2020

Averaging causal estimators in high dimensions

There has been increasing interest in recent years in the development of approaches to estimate causal effects when the number of potential confounders is prohibitively large. This growth in interest has led to a number of potential estimators one could use in this setting. Each of these estimators has different operating characteristics, and it is unlikely that one estimator will outperform all others across all possible scenarios. Coupling this with the fact that an analyst can never know which approach is best for their particular data, we propose a synthetic estimator that averages over a set of candidate estimators. Averaging is widely used in statistics for problems such as prediction, where there are many possible models, and averaging can improve performance and increase robustness to using incorrect models. We show that these ideas carry over into the estimation of causal effects in high-dimensional scenarios. We show theoretically that averaging provides robustness against choosing a bad model, and show empirically via simulation that the averaging estimator performs quite well, and in most cases nearly as well as the best among all possible candidate estimators. Finally, we illustrate these ideas in an environmental wide association study and see that averaging provides the largest benefit in the more difficult scenarios that have large numbers of confounders.

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arXiv2019

Estimating the health effects of environmental mixtures using Bayesian semiparametric regression and sparsity inducing priors

Humans are routinely exposed to mixtures of chemical and other environmental factors, making the quantification of health effects associated with environmental mixtures a critical goal for establishing environmental policy sufficiently protective of human health. The quantification of the effects of exposure to an environmental mixture poses several statistical challenges. It is often the case that exposure to multiple pollutants interact with each other to affect an outcome. Further, the exposure-response relationship between an outcome and some exposures, such as some metals, can exhibit complex, nonlinear forms, since some exposures can be beneficial and detrimental at different ranges of exposure. To estimate the health effects of complex mixtures we propose a flexible Bayesian approach that allows exposures to interact with each other and have nonlinear relationships with the outcome. We induce sparsity using multivariate spike and slab priors to determine which exposures are associated with the outcome, and which exposures interact with each other. The proposed approach is interpretable, as we can use the posterior probabilities of inclusion into the model to identify pollutants that interact with each other. We illustrate our approach's ability to estimate complex functions using simulated data, and apply our method to two studies to determine which environmental pollutants adversely affect health.

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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

Statistical Methods and Workflow for Analyzing Human Metabolomics Data

High-throughput metabolomics investigations, when conducted in large human cohorts, represent a potentially powerful tool for elucidating the biochemical diversity and mechanisms underlying human health and disease. Large-scale metabolomics data, generated using targeted or nontargeted platforms, are increasingly more common. Appropriate statistical analysis of these complex high-dimensional data is critical for extracting meaningful results from such large-scale human metabolomics studies. Herein, we consider the main statistical analytical approaches that have been employed in human metabolomics studies. Based on the lessons learned and collective experience to date in the field, we propose a step-by-step framework for pursuing statistical analyses of human metabolomics data. We discuss the range of options and potential approaches that may be employed at each stage of data management, analysis, and interpretation, and offer guidance on analytical considerations that are important for implementing an analysis workflow. Certain pervasive analytical challenges facing human metabolomics warrant ongoing research. Addressing these challenges will allow for more standardization in the field and lead to analytical advances in metabolomics investigations with the potential to elucidate novel mechanisms underlying human health and disease.

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arXiv2018

Quantitative Comparison of Statistical Methods for Analyzing Human Metabolomics Data

Background. Emerging technologies now allow for mass spectrometry based profiling of up to thousands of small molecule metabolites (metabolomics) in an increasing number of biosamples. While offering great promise for revealing insight into the pathogenesis of human disease, standard approaches have yet to be established for statistically analyzing increasingly complex, high-dimensional human metabolomics data in relation to clinical phenotypes including disease outcomes. To determine optimal statistical approaches for metabolomics analysis, we sought to formally compare traditional statistical as well as newer statistical learning methods across a range of metabolomics dataset types. Results. In simulated and experimental metabolomics data derived from large population-based human cohorts, we observed that with an increasing number of study subjects, univariate compared to multivariate methods resulted in a higher false discovery rate due to substantial correlations among metabolites. In scenarios wherein the number of assayed metabolites increases, as in the application of nontargeted versus targeted metabolomics measures, multivariate methods performed especially favorably across a range of statistical operating characteristics. In nontargeted metabolomics datasets that included thousands of metabolite measures, sparse multivariate models demonstrated greater selectivity and lower potential for spurious relationships. Conclusion. When the number of metabolites was similar to or exceeded the number of study subjects, as is common with nontargeted metabolomics analysis of relatively small sized cohorts, sparse multivariate models exhibited the most robust statistical power with more consistent results. These findings have important implications for the analysis of metabolomics studies of human disease.

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arXiv2018

Doubly robust matching estimators for high dimensional confounding adjustment

Valid estimation of treatment effects from observational data requires proper control of confounding. If the number of covariates is large relative to the number of observations, then controlling for all available covariates is infeasible. In cases where a sparsity condition holds, variable selection or penalization can reduce the dimension of the covariate space in a manner that allows for valid estimation of treatment effects. In this article, we propose matching on both the estimated propensity score and the estimated prognostic scores when the number of covariates is large relative to the number of observations. We derive asymptotic results for the matching estimator and show that it is doubly robust, in the sense that only one of the two score models need be correct to obtain a consistent estimator. We show via simulation its effectiveness in controlling for confounding and highlight its potential to address nonlinear confounding. Finally, we apply the proposed procedure to analyze the effect of gender on prescription opioid use using insurance claims data.

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arXiv2017

A Single Visualization Technique for Displaying Multiple Metabolite-Phenotype Associations

More advanced visualization tools are needed to assist with the analyses and interpretation of human metabolomics data, which are rapidly increasing in quantity and complexity. Using a dataset of several hundred bioactive lipid metabolites profiled in a cohort of over 1400 individuals sampled from a population-based community study, we performed a comprehensive set of association analyses relating all metabolites with eight demographic and cardiometabolic traits and outcomes. We then compared existing graphical approaches with an adapted rain plot approach to display the results of these analyses. The rain plot combines the features of a raindrop plot and a parallel heatmap approach to succinctly convey, in a single visualization, the results of relating complex metabolomics data with multiple phenotypes. This approach complements existing tools, particularly by facilitating comparisons between individual metabolites and across a range of pre-specified clinical outcomes. We anticipate that this single visualization technique may be further extended and applied to alternate study designs using different types of molecular phenotyping data.

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arXiv2016

Spatial Multiresolution Analysis of the Effect of PM2.5 on Birth Weights

Fine particulate matter (PM2.5) measured at a given location is a mix of pollution generated locally and pollution traveling long distances in the atmosphere. Therefore, the identification of spatial scales associated with health effects can inform on pollution sources responsible for these effects, resulting in more targeted regulatory policy. Recently, prediction methods that yield high-resolution spatial estimates of PM2.5 exposures allow one to evaluate such scale-specific associations. We propose a two-dimensional wavelet decomposition that alleviates restrictive assumptions required for standard wavelet decompositions. Using this method we decompose daily surfaces of PM2.5 to identify which scales of pollution are most associated with adverse health outcomes. A key feature of the approach is that it can remove the purely temporal component of variability in PM2.5 levels and calculate effect estimates derived solely from spatial contrasts. This eliminates the potential for unmeasured confounding of the exposure - outcome associations by temporal factors, such as season. We apply our method to a study of birth weights in Massachusetts, U.S.A from 2003-2008 and find that both local and urban sources of pollution are strongly negatively associated with birth weight. Results also suggest that failure to eliminate temporal confounding in previous analyses attenuated the overall effect estimate towards zero, with the effect estimate growing in magnitude once this source of variability is removed.

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