Bayesian nonparametric for causal inference and missing data by Michael J. Daniels, Antonio Linero, and Jason Roy, CRC Press, 2023 ISBN-13: 978-0367341008, https://www.routledge.com/Bayesian-Nonparametrics-for-Causal-Inference-and-Missing-Data/Daniels-Linero-Roy/p/book/9780367341008
Li‐Pang Chen · Biometrics · 2024
Causal inference has been one of the popular topics in recent years, and it has been widely used in observational studies or dynamic treatment regimes (eg, reviewed by Chen 2020). Many monographs based on the frequentist inference are available, but analysis based on the Bayesian methods is rarely explored. This review paper aims to introduce a book entitled Bayesian Nonparametric for Causal Inference and Missing Data, which comprehensively discusses the estimation in causal inference by using the various Bayesian approaches. In addition, the authors also introduce several strategies to handle missing value problems. Moreover, case studies under various methods and models are key advantages in this book, which make readers understand applications for real datasets. This book has 15 chapters, which are divided into 3 topics. Topic I summarizes the overview of causal inference, missing value problems, Bayesian methods, and identifiability issues in chapters 1–4, respectively. Specifically, chapter 1 introduces some fundamental concepts of causal inference, such as various types of causal effects, g-formula, propensity score, marginal structural models, and causal mediation. Chapter 2 discusses missing data and relevant mechanisms, including missing completely at random (MCAR), missing at random (MAR), missing not at random (MNAR). In addition, the authors also outline ignorable and nonignorable missingness, where the latter scenario can be characterized by various models, including selection models, pattern mixture models, and shared parameter models. Chapter 3 focuses on the Bayesian methods and their applications on causal inference. The authors first introduce the priors and the posterior distribution, and summarize several methods to deal with the posterior, such as Markov chain Monte Carlo (MCMC), Gibbs sampling, the Metropolis-Hastings algorithm, slice sampling, and Hamiltonian Monte Carlo. In addition, model checking, data augmentation, and Bayesian g-computation are outlined. Chapter 4 discusses an issue of identifiability in causal inference, and examines sensitivity analyses to assess the performance if some assumptions are violated. Topic II focuses on nonparametric estimation based on the Bayesian approach. The authors separate methods in 3 chapters. Chapter 5 considers generalized additive models (GAM) to characterize the potential outcome, and proposes the Bayesian additive regression trees (BART) to address the estimation of the GAM, where the implementation includes priors over decision trees and their specification for BART, ensembles of decision trees, and posterior computation for BART. Finally, the estimator derived by BART is further applied to estimate the average causal effect. To handle non-mean causal effects as well as missing covariates that cannot be addressed by BART, chapter 6 provides the Dirichlet process mixtures (DPMs) model. Several algorithms, such as the blocked Gibbs sampler, the slice sampler, and Pólya sampler, are introduced to solve the DPM model. Moreover, the authors also introduce the enriched DPMs (EDPMs) to handle a dataset with multivariate covariates accommodated. Chapter 7 introduces Gaussian process (GP) priors and dependent Dirichlet process (DDP) priors, which enable one to model a conditional distribution directly and model the random variables being conditioned on. Finally, Topic III contains case studies for various settings in chapters 8-15. Specifically, chapter 8 analyzes electronic health records (EHR) data and aims to estimate quantile causal effects by using the DPMs and BART methods. Chapter 9 applies the causal relative risk to analyze the ratio of the probability of death where subjects received the antiretroviral drugs that include mNRTI or other NRTIs. The authors apply the EDPMs method to address this estimation. In chapter 10, the authors apply the DDP and GP (DDP+GP) method to a marginal structural model and use it to characterize main effects for alcohol use and high active antiretroviral therapy. Chapter 11 considers a longitudinal study from the schizophrenia clinical trial, where the challenges include missingness due to dropout and categorical treatment effects. The authors propose an infinite mixture model to tackle this problem and adopt the MCMC algorithm to deal with posterior computation. In chapter 12, the authors analyze the breast cancer prevention trial data that are subject to MNAR missingness. In this study, the main interest is to estimate the treatment effect on the change-from-baseline. The authors apply the DPM multinomial distribution to model the data. Chapters 13 and 14 analyze causal mediation by the DPMs and BART methods, respectively. Finally, chapter 15 discusses an application of the DDP+GP method to causal analysis for semicompeting risks. In summary, this book is a nice reference for the research of causal inference because it gives good insight on Bayesian methods and summarizes their applications to causal inference as well as missing value problems. Its comprehensive introduction and useful case studies enable readers to learn strategies to solve their future research problems.