arXiv subjects

Michael J. Daniels

Publications and source records attributed to Michael J. Daniels.

29 records · Page 2Linked to original sources

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.

stat.ME↗

arXiv2022

Inference for BART with Multinomial Outcomes

The multinomial probit Bayesian additive regression trees (MPBART) framework was proposed by Kindo et al. (KD), approximating the latent utilities in the multinomial probit (MNP) model with BART (Chipman et al. 2010). Compared to multinomial logistic models, MNP does not assume independent alternatives and the correlation structure among alternatives can be specified through multivariate Gaussian distributed latent utilities. We introduce two new algorithms for fitting the MPBART and show that the theoretical mixing rates of our proposals are equal or superior to the existing algorithm in KD. Through simulations, we explore the robustness of the methods to the choice of reference level, imbalance in outcome frequencies, and the specifications of prior hyperparameters for the utility error term. The work is motivated by the application of generating posterior predictive distributions for mortality and engagement in care among HIV-positive patients based on electronic health records (EHRs) from the Academic Model Providing Access to Healthcare (AMPATH) in Kenya. In both the application and simulations, we observe better performance using our proposals as compared to KD in terms of MCMC convergence rate and posterior predictive accuracy.

stat.ME↗

arXiv2022

Information Borrowing in Regression Models

Model development often takes data structure, subject matter considerations, model assumptions, and goodness of fit into consideration. To diagnose issues with any of these factors, it can be helpful to understand regression model estimates at a more granular level. We propose a new method for decomposing point estimates from a regression model via weights placed on data clusters. The weights are informed only by the model specification and data availability and thus can be used to explicitly link the effects of data imbalance and model assumptions to actual model estimates. The weight matrix has been understood in linear models as the hat matrix in the existing literature. We extend it to Bayesian hierarchical regression models that incorporate prior information and complicated dependence structures through the covariance among random effects. We show that the model weights, which we call borrowing factors, generalize shrinkage and information borrowing to all regression models. In contrast, the focus of the hat matrix has been mainly on the diagonal elements indicating the amount of leverage. We also provide metrics that summarize the borrowing factors and are practically useful. We present the theoretical properties of the borrowing factors and associated metrics and demonstrate their usage in two examples. By explicitly quantifying borrowing and shrinkage, researchers can better incorporate domain knowledge and evaluate model performance and the impacts of data properties such as data imbalance or influential points.

stat.ME↗

arXiv2021

Variable Selection Using Bayesian Additive Regression Trees

Variable selection is an important statistical problem. This problem becomes more challenging when the candidate predictors are of mixed type (e.g. continuous and binary) and impact the response variable in nonlinear and/or non-additive ways. In this paper, we review existing variable selection approaches for the Bayesian additive regression trees (BART) model, a nonparametric regression model, which is flexible enough to capture the interactions between predictors and nonlinear relationships with the response. An emphasis of this review is on the capability of identifying relevant predictors. We also propose two variable importance measures which can be used in a permutation-based variable selection approach, and a backward variable selection procedure for BART. We present simulations demonstrating that our approaches exhibit improved performance in terms of the ability to recover all the relevant predictors in a variety of data settings, compared to existing BART-based variable selection methods.

stat.ME↗

arXiv2021

BNPqte: A Bayesian Nonparametric Approach to Causal Inference on Quantiles in R

In this article, we introduce the BNPqte R package which implements the Bayesian nonparametric approach of Xu, Daniels and Winterstein (2018) for estimating quantile treatment effects in observational studies. This approach provides flexible modeling of the distributions of potential outcomes, so it is capable of capturing a variety of underlying relationships among the outcomes, treatments and confounders and estimating multiple quantile treatment effects simultaneously. Specifically, this approach uses a Bayesian additive regression trees (BART) model to estimate the propensity score and a Dirichlet process mixture (DPM) of multivariate normals model to estimate the conditional distribution of the potential outcome given the estimated propensity score. The BNPqte R package provides a fast implementation for this approach by designing efficient R functions for the DPM of multivariate normals model in joint and conditional density estimation. These R functions largely improve the efficiency of the DPM model in density estimation, compared to the popular DPpackage. BART-related R functions in the BNPqte R package are inherited from the BART R package with two modifications on variable importance and split probability. To maximize computational efficiency, the actual sampling and computation for each model are carried out in C++ code. The Armadillo C++ library is also used for fast linear algebra calculations.

stat.CO↗

arXiv2021

A Bayesian semi-parametric approach for inference on the population partly conditional mean from longitudinal data with dropout

Studies of memory trajectories using longitudinal data often result in highly non-representative samples due to selective study enrollment and attrition. An additional bias comes from practice effects that result in improved or maintained performance due to familiarity with test content or context. These challenges may bias study findings and severely distort the ability to generalize to the target population. In this study we propose an approach for estimating the finite population mean of a longitudinal outcome conditioning on being alive at a specific time point. We develop a flexible Bayesian semi-parametric predictive estimator for population inference when longitudinal auxiliary information is known for the target population. We evaluate sensitivity of the results to untestable assumptions and further compare our approach to other methods used for population inference in a simulation study. The proposed approach is motivated by 15-year longitudinal data from the Betula longitudinal cohort study. We apply our approach to estimate lifespan trajectories in episodic memory, with the aim to generalize findings to a target population.

stat.ME↗

arXiv2020

Bayesian semi-parametric G-computation for causal inference in a cohort study with MNAR dropout and death

Causal inference with observational longitudinal data and time-varying exposures is often complicated by time-dependent confounding and attrition. The G-computation formula is one approach for estimating a causal effect in this setting. The parametric modeling approach typically used in practice relies on strong modeling assumptions for valid inference, and moreover depends on an assumption of missing at random, which is not appropriate when the missingness is missing not at random (MNAR) or due to death. In this work we develop a flexible Bayesian semi-parametric G-computation approach for assessing the causal effect on the subpopulation that would survive irrespective of exposure, in a setting with MNAR dropout. The approach is to specify models for the observed data using Bayesian additive regression trees, and then use assumptions with embedded sensitivity parameters to identify and estimate the causal effect. The proposed approach is motivated by a longitudinal cohort study on cognition, health, and aging, and we apply our approach to study the effect of becoming a widow on memory. We also compare our approach to several standard methods.

stat.AP↗

arXiv2019

Classification using Ensemble Learning under Weighted Misclassification Loss

Binary classification rules based on covariates typically depend on simple loss functions such as zero-one misclassification. Some cases may require more complex loss functions. For example, individual-level monitoring of HIV-infected individuals on antiretroviral therapy (ART) requires periodic assessment of treatment failure, defined as having a viral load (VL) value above a certain threshold. In some resource limited settings, VL tests may be limited by cost or technology, and diagnoses are based on other clinical markers. Depending on scenario, higher premium may be placed on avoiding false-positives which brings greater cost and reduced treatment options. Here, the optimal rule is determined by minimizing a weighted misclassification loss/risk. We propose a method for finding and cross-validating optimal binary classification rules under weighted misclassification loss. We focus on rules comprising a prediction score and an associated threshold, where the score is derived using an ensemble learner. Simulations and examples show that our method, which derives the score and threshold jointly, more accurately estimates overall risk and has better operating characteristics compared with methods that derive the score first and the cutoff conditionally on the score especially for finite samples.

stat.ML↗

arXiv2018

A Bayesian Parametric Approach to Handle Missing Longitudinal Outcome Data in Trial-Based Health Economic Evaluations

Trial-based economic evaluations are typically performed on cross-sectional variables, derived from the responses for only the completers in the study, using methods that ignore the complexities of utility and cost data (e.g. skewness and spikes). We present an alternative and more efficient Bayesian parametric approach to handle missing longitudinal outcomes in economic evaluations, while accounting for the complexities of the data. We specify a flexible parametric model for the observed data and partially identify the distribution of the missing data with partial identifying restrictions and sensitivity parameters. We explore alternative nonignorable scenarios through different priors for the sensitivity parameters, calibrated on the observed data. 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.

stat.ME↗

arXiv2017

Bayesian nonparametric generative models for causal inference with missing at random covariates

We propose a general Bayesian nonparametric (BNP) approach to causal inference in the point treatment setting. The joint distribution of the observed data (outcome, treatment, and confounders) is modeled using an enriched Dirichlet process. The combination of the observed data model and causal assumptions allows us to identify any type of causal effect - differences, ratios, or quantile effects, either marginally or for subpopulations of interest. The proposed BNP model is well-suited for causal inference problems, as it does not require parametric assumptions about the distribution of confounders and naturally leads to a computationally efficient Gibbs sampling algorithm. By flexibly modeling the joint distribution, we are also able to impute (via data augmentation) values for missing covariates within the algorithm under an assumption of ignorable missingness, obviating the need to create separate imputed data sets. This approach for imputing the missing covariates has the additional advantage of guaranteeing congeniality between the imputation model and the analysis model, and because we use a BNP approach, parametric models are avoided for imputation. The performance of the method is assessed using simulation studies. The method is applied to data from a cohort study of human immunodeficiency virus/hepatitis C virus co-infected patients.

stat.ME↗

arXiv2015

Comparing Biomarkers as Trial Level General Surrogates

An intermediate response measure that accurately predicts efficacy in a new setting can reduce trial cost and time to product licensure. In this paper, we define a trial level general surrogate as a trial level intermediate response that accurately predicts trial level clinical responses. Methods for evaluating trial level general surrogates have been developed previously. Many methods in the literature use trial level intermediate responses for prediction. However, all existing methods focus on surrogate evaluation and prediction in new settings, rather than comparison of candidate trial level surrogates, and few formalize the use of cross validation to quantify the expected prediction error. Our proposed method uses Bayesian non-parametric modeling and cross-validation to estimate the absolute prediction error for use in evaluating and comparing candidate trial level general surrogates. Simulations show that our method performs well across a variety of scenarios. We use our method to evaluate and to compare candidate trial level general surrogates in several multi-national trials of a pentavalent rotavirus vaccine. We identify two immune measures that have potential value as trial level general surrogates and use the measures to predict efficacy in a trial with no clinical outcomes measured.

stat.ME↗