arXiv subjects

Jami J. Mulgrave

Publications and source records attributed to Jami J. Mulgrave.

6 recordsLinked to original sources

arXiv2024

Bayesian Posterior Interval Calibration to Improve the Interpretability of Observational Studies

Observational healthcare data offer the potential to estimate causal effects of medical products on a large scale. However, the confidence intervals and p-values produced by observational studies only account for random error and fail to account for systematic error. As a consequence, operating characteristics such as confidence interval coverage and Type I error rates often deviate sharply from their nominal values and render interpretation impossible. While there is longstanding awareness of systematic error in observational studies, analytic approaches to empirically account for systematic error are relatively new. Several authors have proposed approaches using negative controls (also known as "falsification hypotheses") and positive controls. The basic idea is to adjust confidence intervals and p-values in light of the bias (if any) detected in the analyses of the negative and positive control. In this work, we propose a Bayesian statistical procedure for posterior interval calibration that uses negative and positive controls. We show that the posterior interval calibration procedure restores nominal characteristics, such as 95% coverage of the true effect size by the 95% posterior interval.

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arXiv2021

Regression-Based Bayesian Estimation and Structure Learning for Nonparanormal Graphical Models

A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations. We consider a Bayesian approach to inference in a nonparanormal graphical model in which we put priors on the unknown transformations through a random series based on B-splines. We use a regression formulation to construct the likelihood through the Cholesky decomposition on the underlying precision matrix of the transformed variables and put shrinkage priors on the regression coefficients. We apply a plug-in variational Bayesian algorithm for learning the sparse precision matrix and compare the performance to a posterior Gibbs sampling scheme in a simulation study. We finally apply the proposed methods to a real data set. KEYWORDS:

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arXiv2020

Using Data Assimilation of Mechanistic Models to Estimate Glucose and Insulin Metabolism

Motivation: There is a growing need to integrate mechanistic models of biological processes with computational methods in healthcare in order to improve prediction. We apply data assimilation in the context of Type 2 diabetes to understand parameters associated with the disease. Results: The data assimilation method captures how well patients improve glucose tolerance after their surgery. Data assimilation has the potential to improve phenotyping in Type 2 diabetes.

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arXiv2019

The Medical Deconfounder: Assessing Treatment Effects with Electronic Health Records

The treatment effects of medications play a key role in guiding medical prescriptions. They are usually assessed with randomized controlled trials (RCTs), which are expensive. Recently, large-scale electronic health records (EHRs) have become available, opening up new opportunities for more cost-effective assessments. However, assessing a treatment effect from EHRs is challenging: it is biased by unobserved confounders, unmeasured variables that affect both patients' medical prescription and their outcome, e.g. the patients' social economic status. To adjust for unobserved confounders, we develop the medical deconfounder, a machine learning algorithm that unbiasedly estimates treatment effects from EHRs. The medical deconfounder first constructs a substitute confounder by modeling which medications were prescribed to each patient; this substitute confounder is guaranteed to capture all multi-medication confounders, observed or unobserved (arXiv:1805.06826). It then uses this substitute confounder to adjust for the confounding bias in the analysis. We validate the medical deconfounder on two simulated and two real medical data sets. Compared to classical approaches, the medical deconfounder produces closer-to-truth treatment effect estimates; it also identifies effective medications that are more consistent with the findings in the medical literature.

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arXiv2019

Bayesian Analysis of Nonparanormal Graphical Models Using Rank-Likelihood

Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality assumption may be restrictive in many settings. A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables where it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformation. We consider a Bayesian approach for the nonparanormal graphical model using a rank-likelihood which remains invariant under monotone transformations, thereby avoiding the need to put a prior on the transformation functions. On the underlying precision matrix of the transformed variables, we consider a horseshoe prior on its Cholesky decomposition and use an efficient posterior Gibbs sampling scheme. We present a posterior consistency result for the precision matrix based on the rank-based likelihood. We study the numerical performance of the proposed method through a simulation study and apply it on a real dataset.

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arXiv2019

Bayesian Inference in Nonparanormal Graphical Models

Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for continuous variables where it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations on each of them. We consider a Bayesian approach in the nonparanormal graphical model by putting priors on the unknown transformations through a random series based on B-splines where the coefficients are ordered to induce monotonicity. A truncated normal prior leads to partial conjugacy in the model and is useful for posterior simulation using Gibbs sampling. On the underlying precision matrix of the transformed variables, we consider a spike-and-slab prior and use an efficient posterior Gibbs sampling scheme. We use the Bayesian Information Criterion to choose the hyperparameters for the spike-and-slab prior. We present a posterior consistency result on the underlying transformation and the precision matrix. We study the numerical performance of the proposed method through an extensive simulation study and finally apply the proposed method on a real data set.

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