arXiv subjects

Michael J. Daniels

Publications and source records attributed to Michael J. Daniels.

At least 19 recordsLinked to original sources

arXiv2026

Causal mediation analysis for zero-inflated longitudinal data in the presence of treatment non-compliance and multiple mediators

Understanding whether a digital marketing campaign is effective is central to designing effective customer engagement strategies. We analyze a large-scale, longitudinal promotional email campaign conducted by a U.S.\ retailer to evaluate how value-added incentives, such as free shipping, compare with traditional price discounts in influencing customer purchasing behavior. The analysis is complicated by non-compliance, due to not opening emails, multiple longitudinal mediators, and zero-inflated mediators and purchase outcomes. To address these challenges, we develop a Bayesian causal mediation framework based on enriched Dirichlet process mixture models and estimate the causal estimands using a scalable G-computation algorithm. We show that analyses ignoring email-opening behavior substantially attenuate estimated effects. Value-added incentives consistently outperform price discounts, yielding higher estimated potential purchase amounts, with benefits accumulating over time. We design an individualized sequential emailing strategy that optimizes expected purchase count in the observed data.

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arXiv2026

A Bayesian Approach for Nonignorable Dropout in Bivariate Longitudinal Models

Longitudinal data collected in clinical trials are almost always incomplete due to some of the participants dropping out from the study during the planned follow-up. A common strategy to handle nonresponse expresses missingness in terms of a dropout process, which is jointly analysed with the outcome process to facilitate the formulation of the missingness assumptions. However, when the outcome is multivariate, the identification of the dropout process becomes problematic, especially when individuals have different dropout times for each type of response, and sensitivity analysis is difficult. The modelling task may be also be complicated by data complexities (e.g. skewness and spikes) which are difficult to capture through standard parametric methods. An example of this analysis framework occurs in trial-based economic evaluations, where a longitudinal bivariate response, formed by suitably-defined measures of effectiveness and costs, is analysed to inform policymakers about the cost-effectiveness of alternative interventions. We present a novel Bayesian nonparametric approach to handle a missing bivariate longitudinal outcome by jointly modelling the dropout process associated with each type of response while also taking into account the complexities of the data. We specify a flexible nonparametric model for the observed data and partially identify the distribution of the missing data with identifying restrictions conditional on the dropout indicators and sensitivity parameters. We explore alternative nonignorable scenarios through different priors for the sensitivity parameters. Our approach is motivated by, and applied to, data from a trial assessing the cost-effectiveness of a new treatment for intellectual disability and challenging behaviour.

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arXiv2026

A case study of causal mediation using Bayesian nonparametrics and semiparametric corrections

We propose a Bayesian nonparametric approach using a truncated Enriched Dirichlet Process mixture (EDPM) model to estimate natural direct (NDE) and indirect (NIE) effects in causal mediation analyses in the presence of post-treatment confounders. We introduce an efficient cluster reallocation Metropolis-Hasting algorithm to improve mixing in the blocked Gibbs sampler. We implement a one-step posterior correction based on the efficient influence function for our setting. This post-processing step solves a critical problem in Bayesian nonparametrics: how to obtain reliable estimates and posteriors for a specific causal estimand of interest (the NDE and NIE) with excellent frequentist properties, such as correct coverage, from a model designed for complex joint distributions. We conduct simulation studies to assess our method's performance and apply it to evaluate causal mediation effects in a weight management clinical trial.

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arXiv2026

Variational Bayes and Truncation approximations for Enriched Dirichlet process mixtures

A common impediment in conducting inference for Bayesian nonparametric models is either the need for complex MCMC algorithms and/or computational run-time for large datasets. We propose solutions here for Enriched Dirichlet process mixtures (EDPM). We derive a variational Bayes estimator based on a previously developed truncation approximation for EDPMs. The variational Bayes estimator can be used in two ways: 1) to develop a more efficient truncation approximation; 2) as good initial values for a blocked Gibbs sampler based on this more efficient truncation approximation or for a polya urn sampler. We derive the accuracy of this more efficient truncation approximation and demonstrate how this allows for simple implementation of a blocked Gibbs Sampler EDPMs in Nimble. We confirm the validity of the approximations by simulations and illustrate on a real data set.

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arXiv2026

Causal mediation analysis for longitudinal and survival data in continuous time using Bayesian non-parametric joint models

Observational cohort data is an important source of information for understanding the causal effects of treatments on survival and the degree to which these effects are mediated through changes in disease-related risk factors. However, these analyses are often complicated by irregular data collection intervals and the presence of longitudinal confounders and mediators. We propose a causal mediation framework that jointly models longitudinal exposures, confounders, mediators, and time-to-event outcomes as continuous functions of age. This framework for longitudinal covariate trajectories enables statistical inference even at ages where the subject's covariate measurements are unavailable. The observed data distribution in our framework is modeled using an enriched Dirichlet process mixture (EDPM) model. Using data from the Atherosclerosis Risk in Communities cohort study, we apply our methods to assess how medication -- prescribed to target cardiovascular disease (CVD) risk factors -- affects the time-to-CVD death.

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arXiv2026

Identification and estimation of causal mechanisms in cluster-randomized trials with post-treatment confounding using Bayesian nonparametrics

Causal mediation analysis in cluster-randomized trials (CRTs) is essential for explaining how cluster-level interventions affect individual outcomes, yet it is complicated by interference, post-treatment confounding, and hierarchical covariate adjustment. We develop a Bayesian nonparametric framework that simultaneously accommodates interference and a post-treatment confounder that precedes the mediator. Identification is achieved through a multivariate Gaussian copula that replaces cross-world independence with a single dependence parameter, yielding a built-in sensitivity analysis to residual post-treatment confounding. For estimation, we introduce a nested common atoms enriched Dirichlet process (CA-EDP) prior that integrates the Common Atoms Model (CAM) to share information across clusters while capturing between- and within-cluster heterogeneity, and an Enriched Dirichlet Process (EDP) structure delivering robust covariate adjustment without impacting the outcome model. We provide formal theoretical support for our prior by deriving the model's key distributional properties, including its partially exchangeable partition structure, and by establishing convergence guarantees for the practical truncation-based posterior inference strategy. We demonstrate the performance of the proposed methods in simulations and provide further illustration through a reanalysis of a completed CRT.

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arXiv2026

A sensitivity analysis approach to principal stratification with a continuous longitudinal intermediate outcome: Applications to a cohort stepped wedge trial

Causal inference in the presence of intermediate variables is a challenging problem in many applications. Principal stratification (PS) provides a framework to estimate principal causal effects (PCE) in such settings. However, existing PS methods primarily focus on settings with binary intermediate variables. We propose a novel approach to estimate PCE with continuous intermediate variables in the context of stepped wedge cluster randomized trials (SW-CRTs). Our method leverages the time-varying treatment assignment in SW-CRTs to calibrate sensitivity parameters and identify the PCE under realistic assumptions. We demonstrate the application of our approach using data from a cohort SW-CRT evaluating the effect of a crowdsourcing intervention on HIV testing uptake among men who have sex with men in China, with social norms as a continuous intermediate variable. The proposed methodology expands the scope of PS to accommodate continuous variables and provides a practical tool for causal inference in SW-CRTs.

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arXiv2025

A new algorithm for sampling parameters in a structured correlation matrix with application to estimating optimal combinations of muscles to quantify progression in Duchenne muscular dystrophy

The goal of this paper is to estimate an optimal combination of biomarkers for individuals with Duchenne muscular dystrophy (DMD), which provides the most sensitive combinations of biomarkers to assess disease progression (in this case, optimal with respect to standardized response mean (SRM) for 4 muscle biomarkers). The biomarker data is an incomplete (missing and irregular) multivariate longitudinal data. We propose a normal model with structured covariance designed for our setting. To sample from the posterior distribution of parameters, we develop a Markov Chain Monte Carlo (MCMC) algorithm to address the positive definiteness constraint on the structured correlation matrix. In particular, we propose a novel approach to compute the support of the parameters in the structured correlation matrix; we modify the approach from \cite{Barnard} on the set of largest possible submatrices of the correlation matrix, where the correlation parameter is a unique element. For each posterior sample, we compute the optimal weights of our construct. We conduct data analysis and simulation studies to evaluate the algorithm and the frequentist properties of the posteriors of correlations and weights. We found that the lower extremities are the most responsive muscles at the early and late ambulatory disease stages and the biceps brachii is the most responsive at the non-ambulatory disease stage.

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arXiv2025

A Bayesian approach for unadjudicated events in cardiovascular disease cohort studies

An important issue in joint modelling for outcomes and longitudinal risk factors in cohort studies is to have an accurate assessment of events. Events determined based on ICD-9 codes can be very inaccurate, in particular for cardiovascular disease (CVD) where ICD-9 codes may overestimate the frequency of CVD. Motivated by the lack of adjudicated events in the Established Populations for Epidemiologic Studies of the Elderly (EPESE) cohort, we develop methods that use a related cohort Atherosclerosis Risk in Communities (ARIC), with both ICD-9 code events and adjudicated events, to create a posterior predictive distribution of adjudicated events. The methods are based on the construction of flexible Bayesian joint models combined with a Bayesian additive regression trees to directly address the ICD-9 misclassification. We assessed the performance of our approach by simulation study and applied to ARIC data.

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arXiv2025

Personalized feature threshold estimation in joint modelling of longitudinal and time-to-event data

Cardiovascular disease (CVD) cohort studies collect longitudinal data on numerous CVD risk factors including body mass index (BMI), systolic blood pressure (SBP), diastolic blood pressure (DBP), glucose, and total cholesterol. The commonly used threshold values for identifying subjects at high risk are 30 kg/$m^2$ for BMI, 120 mmHg for SBP, 80 mmHg for DBP, 126 mg/dL for glucose, and 230 mg/dL for total cholesterol. When studying the association between features of longitudinal risk factors and time to a CVD event, an important research question is whether these CVD risk factor thresholds should vary based on individual characteristics as well as the type of longitudinal feature being considered. Using data from the Atherosclerosis Risk in Communities (ARIC) Study, we develop methods to estimate risk factor thresholds in joint models with multiple features for each longitudinal risk factor. These thresholds are allowed to vary by sex, race, and type of feature. Our methods have the potential for personalized CVD prevention strategies as well as better estimates of CVD risk.

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arXiv2025

Integrating tumor burden with survival outcome for treatment effect evaluation in oncology trials

In early-phase cancer clinical trials, the limited availability of data presents significant challenges in developing a framework to efficiently quantify treatment effectiveness. To address this, we propose a novel utility-based Bayesian approach for assessing treatment effects in these trials, where data scarcity is a major concern. Our approach synthesizes tumor burden, a key biomarker for evaluating patient response to oncology treatments, and survival outcome, a widely used endpoint for assessing clinical benefits, by jointly modeling longitudinal and survival data. The proposed method, along with its novel estimand, aims to efficiently capture signals of treatment efficacy in early-phase studies and holds potential for development as an endpoint in Phase 3 confirmatory studies. We conduct simulations to investigate the frequentist characteristics of the proposed estimand in a simple setting, which demonstrate relatively controlled Type I error rates when testing the treatment effect on outcomes.

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arXiv2024

Bayesian feature selection in joint models with application to a cardiovascular disease cohort study

Cardiovascular disease (CVD) cohorts collect data longitudinally to study the association between CVD risk factors and event times. An important area of scientific research is to better understand what features of CVD risk factor trajectories are associated with the disease. We develop methods for feature selection in joint models where feature selection is viewed as a bi-level variable selection problem with multiple features nested within multiple longitudinal risk factors. We modify a previously proposed Bayesian sparse group selection (BSGS) prior, which has not been implemented in joint models until now, to better represent prior beliefs when selecting features both at the group level (longitudinal risk factor) and within group (features of a longitudinal risk factor). One of the advantages of our method over the BSGS method is the ability to account for correlation among the features within a risk factor. As a result, it selects important features similarly, but excludes the unimportant features within risk factors more efficiently than BSGS. We evaluate our prior via simulations and apply our method to data from the Atherosclerosis Risk in Communities (ARIC) study, a population-based, prospective cohort study consisting of over 15,000 men and women aged 45-64, measured at baseline and at six additional times. We evaluate which CVD risk factors and which characteristics of their trajectories (features) are associated with death from CVD. We find that systolic and diastolic blood pressure, glucose, and total cholesterol are important risk factors with different important features associated with CVD death in both men and women.

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arXiv2024

A Bayesian semi-parametric approach to causal mediation for longitudinal mediators and time-to-event outcomes with application to a cardiovascular disease cohort study

Causal mediation analysis of observational data is an important tool for investigating the potential causal effects of medications on disease-related risk factors, and on time-to-death (or disease progression) through these risk factors. However, when analyzing data from a cohort study, such analyses are complicated by the longitudinal structure of the risk factors and the presence of time-varying confounders. Leveraging data from the Atherosclerosis Risk in Communities (ARIC) cohort study, we develop a causal mediation approach, using (semi-parametric) Bayesian Additive Regression Tree (BART) models for the longitudinal and survival data. Our framework allows for time-varying exposures, confounders, and mediators, all of which can either be continuous or binary. We also identify and estimate direct and indirect causal effects in the presence of a competing event. We apply our methods to assess how medication, prescribed to target cardiovascular disease (CVD) risk factors, affects the time-to-CVD death.

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arXiv2024

Approximate Cross-validated Mean Estimates for Bayesian Hierarchical Regression Models

We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). Bayesian hierarchical models are popular for their ability to model complex dependence structures and provide probabilistic uncertainty estimates, but can be computationally expensive to run. Cross-validation (CV) is therefore not a common practice to evaluate the predictive performance of BHRMs. Our method circumvents the need to re-run computationally costly estimation methods for each cross-validation fold and makes CV more feasible for large BHRMs. By conditioning on the variance-covariance parameters, we shift the CV problem from probability-based sampling to a simple and familiar optimization problem. In many cases, this produces estimates which are equivalent to full CV. We provide theoretical results and demonstrate its efficacy on publicly available data and in simulations.

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arXiv2023

Dirichlet process mixture models for the Analysis of Repeated Attempt Designs

In longitudinal studies, it is not uncommon to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful provides useful information for the purposes of assessing missing data assumptions. This is because measurements from subjects who provide the data after numerous failed attempts may differ from those who provide the measurement after fewer attempts. Previous models for these designs were parametric and/or did not allow sensitivity analysis. For the former, there are always concerns about model misspecification and for the latter, sensitivity analysis is essential when conducting inference in the presence of missing data. Here, we propose a new approach which minimizes issues with model misspecification by using Bayesian nonparametrics for the observed data distribution. We also introduce a novel approach for identification and sensitivity analysis. We re-analyze the repeated attempts data from a clinical trial involving patients with severe mental illness and conduct simulations to better understand the properties of our approach.

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arXiv2023

A Bayesian Non-parametric Approach for Causal Mediation with a Post-treatment Confounder

We propose a new Bayesian non-parametric (BNP) method for estimating the causal effects of mediation in the presence of a post-treatment confounder. We specify an enriched Dirichlet process mixture (EDPM) to model the joint distribution of the observed data (outcome, mediator, post-treatment confounders, treatment, and baseline confounders). The proposed BNP model allows more confounder-based clusters than clusters for the outcome and mediator. For identifiability, we use the extended version of the standard sequential ignorability as introduced in \citet{hong2022posttreatment}. The observed data model and causal identification assumptions enable us to estimate and identify the causal effects of mediation, $i.e.$, the natural direct effects (NDE), and indirect effects (NIE). We conduct simulation studies to assess the performance of our proposed method. Furthermore, we apply this approach to evaluate the causal mediation effect in the Rural LITE trial, demonstrating its practical utility in real-world scenarios. \keywords{Causal inference; Enriched Dirichlet process mixture model.}

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arXiv2023

Truncation Approximation for Enriched Dirichlet Process Mixture Models

Enriched Dirichlet process mixture (EDPM) models are Bayesian nonparametric models which can be used for nonparametric regression and conditional density estimation and which overcome a key disadvantage of jointly modeling the response and predictors as a Dirichlet process mixture (DPM) model: when there is a large number of predictors, the clusters induced by the DPM will be overwhelmingly determined by the predictors rather than the response. A truncation approximation to a DPM allows a blocked Gibbs sampling algorithm to be used rather than a Polya urn sampling algorithm. The blocked Gibbs sampler offers potential improvement in mixing. The truncation approximation also allows for implementation in standard software ($\textit{rjags}$ and $\textit{rstan}$). In this paper we introduce an analogous truncation approximation for an EDPM. We show that with sufficiently large truncation values in the approximation of the EDP prior, a precise approximation to the EDP is available. We verify that the truncation approximation and blocked Gibbs sampler with minimum truncation values that obtain adequate error bounds achieve similar accuracy to the truncation approximation and blocked Gibbs sampler with large truncation values using a simulated example. Further, we use the simulated example to show that the blocked Gibbs sampler improves upon the mixing in the Polya urn sampler, especially as the number of covariates increases.

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arXiv2022

A Bayesian nonparametric approach for causal inference with multiple mediators

Mediation analysis with contemporaneously observed multiple mediators is an important area of causal inference. Recent approaches for multiple mediators are often based on parametric models and thus may suffer from model misspecification. Also, much of the existing literature either only allow estimation of the joint mediation effect, or, estimate the joint mediation effect as the sum of individual mediator effects, which often is not a reasonable assumption. In this paper, we propose a methodology which overcomes the two aforementioned drawbacks. Our method is based on a novel Bayesian nonparametric (BNP) approach, wherein the joint distribution of the observed data (outcome, mediators, treatment, and confounders) is modeled flexibly using an enriched Dirichlet process mixture with three levels: the first level characterizing the conditional distribution of the outcome given the mediators, treatment and the confounders, the second level corresponding to the conditional distribution of each of the mediators given the treatment and the confounders, and the third level corresponding to the distribution of the treatment and the confounders. We use standardization (g-computation) to compute causal mediation effects under three uncheckable assumptions that allow identification of the individual and joint mediation effects. The efficacy of our proposed method is demonstrated with simulations. We apply our proposed method to analyze data from a study of Ventilator-associated Pneumonia (VAP) co-infected patients, where the effect of the abundance of Pseudomonas on VAP infection is suspected to be mediated through antibiotics.

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