A Bayesian nonparametric approach to marginal structural models for point treatments and a continuous or survival outcome

Hierarchical Bayesian bootstrap for heterogeneous treatment effect estimation

A major focus of causal inference is the estimation of heterogeneous average treatment effects (HTE) - average treatment effects within strata of another variable of interest such as levels of a biomarker, education, or age strata. Inference involves estimating a stratum-specific regression and integrating it over the distribution of confounders in that stratum - which itself must be estimated. Standard practice involves estimating these stratum-specific confounder distributions independently (e.g. via the empirical distribution or Rubin's Bayesian bootstrap), which becomes problematic for sparsely populated strata with few observed confounder vectors. In this paper, we develop a nonparametric hierarchical Bayesian bootstrap (HBB) prior over the stratum-specific confounder distributions for HTE estimation. The HBB partially pools the stratum-specific distributions, thereby allowing principled borrowing of confounder information across strata when sparsity is a concern. We show that posterior inference under the HBB can yield efficiency gains over standard marginalization approaches while avoiding strong parametric assumptions about the confounder distribution. We use our approach to estimate the adverse event risk of proton versus photon chemoradiotherapy across various cancer types.

A BAYESIAN MACHINE LEARNING APPROACH FOR ESTIMATING HETEROGENEOUS SURVIVOR CAUSAL EFFECTS: APPLICATIONS TO A CRITICAL CARE TRIAL

Assessing heterogeneity in the effects of treatments has become increasingly popular in the field of causal inference and carries important implications for clinical decision-making. While extensive literature exists for studying treatment effect heterogeneity when outcomes are fully observed, there has been limited development in tools for estimating heterogeneous causal effects when patient-centered outcomes are truncated by a terminal event, such as death. Due to mortality occurring during study follow-up, the outcomes of interest are unobservable, undefined, or not fully observed for many participants in which case principal stratification is an appealing framework to draw valid causal conclusions. Motivated by the Acute Respiratory Distress Syndrome Network (ARDSNetwork) ARDS respiratory management (ARMA) trial, we developed a flexible Bayesian machine learning approach to estimate the average causal effect and heterogeneous causal effects among the always-survivors stratum when clinical outcomes are subject to truncation. We adopted Bayesian additive regression trees (BART) to flexibly specify separate mean models for the potential outcomes and latent stratum membership. In the analysis of the ARMA trial, we found that the low tidal volume treatment had an overall benefit for participants sustaining acute lung injuries on the outcome of time to returning home but substantial heterogeneity in treatment effects among the always-survivors, driven most strongly by biologic sex and the alveolar-arterial oxygen gradient at baseline (a physiologic measure of lung function and degree of hypoxemia). These findings illustrate how the proposed methodology could guide the prognostic enrichment of future trials in the field.

Bayesian graphical modeling for heterogeneous causal effects

There is a growing interest in current medical research to develop personalized treatments using a molecular-based approach. The broad goal is to implement a more precise and targeted decision-making process, relative to traditional treatments based primarily on clinical diagnoses. Specifically, we consider patients affected by Acute Myeloid Leukemia (AML), an hematological cancer characterized by uncontrolled proliferation of hematopoietic stem cells in the bone marrow. Because AML responds poorly to chemotherapeutic treatments, the development of targeted therapies is essential to improve patients' prospects. In particular, the dataset we analyze contains the levels of proteins involved in cell cycle regulation and linked to the progression of the disease. We evaluate treatment effects within a causal framework represented by a Directed Acyclic Graph (DAG) model, whose vertices are the protein levels in the network. A major obstacle in implementing the above program is represented by individual heterogeneity. We address this issue through a Dirichlet Process (DP) mixture of Gaussian DAG-models where both the graphical structure as well as the allied model parameters are regarded as uncertain. Our procedure determines a clustering structure of the units reflecting the underlying heterogeneity, and produces subject-specific estimates of causal effects based on Bayesian Model Averaging (BMA). With reference to the AML dataset, we identify different effects of protein regulation among individuals; moreover, our method clusters patients into groups that exhibit only mild similarities with traditional categories based on morphological features.

A comparison of covariate adjustment approaches under model misspecification in individually randomized trials

Adjustment for baseline covariates in randomized trials has been shown to lead to gains in power and can protect against chance imbalances in covariates. For continuous covariates, there is a risk that the the form of the relationship between the covariate and outcome is misspecified when taking an adjusted approach. Using a simulation study focusing on individually randomized trials with small sample sizes, we explore whether a range of adjustment methods are robust to misspecification, either in the covariate-outcome relationship or through an omitted covariate-treatment interaction. Specifically, we aim to identify potential settings where G-computation, inverse probability of treatment weighting (IPTW), augmented inverse probability of treatment weighting (AIPTW) and targeted maximum likelihood estimation (TMLE) offer improvement over the commonly used analysis of covariance (ANCOVA). Our simulations show that all adjustment methods are generally robust to model misspecification if adjusting for a few covariates, sample size is 100 or larger, and there are no covariate-treatment interactions. When there is a non-linear interaction of treatment with a skewed covariate and sample size is small, all adjustment methods can suffer from bias; however, methods that allow for interactions (such as G-computation with interaction and IPTW) show improved results compared to ANCOVA. When there are a high number of covariates to adjust for, ANCOVA retains good properties while other methods suffer from under- or over-coverage. An outstanding issue for G-computation, IPTW and AIPTW in small samples is that standard errors are underestimated; they should be used with caution without the availability of small-sample corrections, development of which is needed. These findings are relevant for covariate adjustment in interim analyses of larger trials.

A flexible approach for causal inference with multiple treatments and clustered survival outcomes

When drawing causal inferences about the effects of multiple treatments on clustered survival outcomes using observational data, we need to address implications of the multilevel data structure, multiple treatments, censoring, and unmeasured confounding for causal analyses. Few off-the-shelf causal inference tools are available to simultaneously tackle these issues. We develop a flexible random-intercept accelerated failure time model, in which we use Bayesian additive regression trees to capture arbitrarily complex relationships between censored survival times and pre-treatment covariates and use the random intercepts to capture cluster-specific main effects. We develop an efficient Markov chain Monte Carlo algorithm to draw posterior inferences about the population survival effects of multiple treatments and examine the variability in cluster-level effects. We further propose an interpretable sensitivity analysis approach to evaluate the sensitivity of drawn causal inferences about treatment effect to the potential magnitude of departure from the causal assumption of no unmeasured confounding. Expansive simulations empirically validate and demonstrate good practical operating characteristics of our proposed methods. Applying the proposed methods to a dataset on older high-risk localized prostate cancer patients drawn from the National Cancer Database, we evaluate the comparative effects of three treatment approaches on patient survival, and assess the ramifications of potential unmeasured confounding. The methods developed in this work are readily available in the R $$ \mathsf{R}\kern.15em $$ package riAFTBART $$ \mathsf{riAFTBART} $$ .

Sensitivity analysis of unmeasured confounding in causal inference based on exponential tilting and super learner

Causal inference under the potential outcome framework relies on the strongly ignorable treatment assumption. This assumption is usually questionable in observational studies, and the unmeasured confounding is one of the fundamental challenges in causal inference. To this end, we propose a new sensitivity analysis method to evaluate the impact of the unmeasured confounder by leveraging ideas of doubly robust estimators, the exponential tilt method, and the super learner algorithm. Compared to other existing methods of sensitivity analysis that parameterize the unmeasured confounder as a latent variable in the working models, the exponential tilting method does not impose any restrictions on the structure or models of the unmeasured confounders. In addition, in order to reduce the modeling bias of traditional parametric methods, we propose incorporating the super learner machine learning algorithm to perform nonparametric model estimation and the corresponding sensitivity analysis. Furthermore, most existing sensitivity analysis methods require multivariate sensitivity parameters, which make its choice difficult and subjective in practice. In comparison, the new method has a univariate sensitivity parameter with a nice and simple interpretation of log-odds ratios for binary outcomes, which makes its choice and the application of the new sensitivity analysis method very easy for practitioners.

Timing matters: real-world effectiveness of early combination of biologic and conventional synthetic disease-modifying antirheumatic drugs for treating newly diagnosed polyarticular course juvenile idiopathic arthritis

OBJECTIVES

To compare real-world effectiveness of two adaptive treatment strategies of disease-modifying antirheumatic drugs (DMARDs) in treating children with newly diagnosed polyarticular course juvenile idiopathic arthritis (pcJIA): early aggressive use of biologic DMARDs (bDMARDs) in combination with conventional synthetic DMARDs (csDMARDs) versus conservative delayed use of bDMARDs following the initial csDMARD prescription.

METHODS

A single-centre newly diagnosed DMARD-naive pcJIA patient database (n=465) was derived from the electronic medical records between 1 January 2009 and 31 December 2018. The primary study endpoints were clinical Juvenile Arthritis Disease Activity Score (cJADAS) at 6 and 12 months following the first DMARD prescription. The secondary study endpoint was Pediatric Quality of Life Inventory (PedsQL) generic total score at 12 months. Averaged causal treatment effects were assessed using a Bayesian non-parametric casual inference method.

RESULTS

Both cJADAS and PedsQL improve over time, regardless of the treatment strategies. Compared with the conservative approach, early aggressive approach is more effective in reducing cJADAS (mean -2.17, 95% CI -3.77 to -0.56) by 6 months. Adding bDMARD after 6 months to the initial treatment provides very little added benefit. The averaged treatment effect was 6.35 (95% CI -5.89 to 18.58) improvement in PedsQL at 12 months.

CONCLUSIONS

Timing matters-early aggressive use with bDMARDs is more effective than conservative delayed treatment in lowering disease activity after 6 and 12 months of treatment.

A practical introduction to Bayesian estimation of causal effects: Parametric and nonparametric approaches

Substantial advances in Bayesian methods for causal inference have been made in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian models and would like an overview of what it can add to causal estimation in practical settings. In the paper, we demonstrate how priors can induce shrinkage and sparsity in parametric models and be used to perform probabilistic sensitivity analyses around causal assumptions. We provide an overview of nonparametric Bayesian estimation and survey their applications in the causal inference literature. Inference in the point-treatment and time-varying treatment settings are considered. For the latter, we explore both static and dynamic treatment regimes. Throughout, we illustrate implementation using off-the-shelf open source software. We hope to leave the reader with implementation-level knowledge of Bayesian causal inference using both parametric and nonparametric models. All synthetic examples and code used in the paper are publicly available on a companion GitHub repository.

From Real-World Patient Data to Individualized Treatment Effects Using Machine Learning: Current and Future Methods to Address Underlying Challenges

Clinical decision making needs to be supported by evidence that treatments are beneficial to individual patients. Although randomized control trials (RCTs) are the gold standard for testing and introducing new drugs, due to the focus on specific questions with respect to establishing efficacy and safety vs. standard treatment, they do not provide a full characterization of the heterogeneity in the final intended treatment population. Conversely, real-world observational data, such as electronic health records (EHRs), contain large amounts of clinical information about heterogeneous patients and their response to treatments. In this paper, we introduce the main opportunities and challenges in using observational data for training machine learning methods to estimate individualized treatment effects and make treatment recommendations. We describe the modeling choices of the state-of-the-art machine learning methods for causal inference, developed for estimating treatment effects both in the cross-section and longitudinal settings. Additionally, we highlight future research directions that could lead to achieving the full potential of leveraging EHRs and machine learning for making individualized treatment recommendations. We also discuss how experimental data from RCTs and Pharmacometric and Quantitative Systems Pharmacology approaches can be used to not only improve machine learning methods, but also provide ways for validating them. These future research directions will require us to collaborate across the scientific disciplines to incorporate models based on RCTs and known disease processes, physiology, and pharmacology into these machine learning models based on EHRs to fully optimize the opportunity these data present.

A Bayesian nonparametric model for zero-inflated outcomes: Prediction, clustering, and causal estimation

Researchers are often interested in predicting outcomes, detecting distinct subgroups of their data, or estimating causal treatment effects. Pathological data distributions that exhibit skewness and zero-inflation complicate these tasks-requiring highly flexible, data-adaptive modeling. In this paper, we present a multipurpose Bayesian nonparametric model for continuous, zero-inflated outcomes that simultaneously predicts structural zeros, captures skewness, and clusters patients with similar joint data distributions. The flexibility of our approach yields predictions that capture the joint data distribution better than commonly used zero-inflated methods. Moreover, we demonstrate that our model can be coherently incorporated into a standardization procedure for computing causal effect estimates that are robust to such data pathologies. Uncertainty at all levels of this model flow through to the causal effect estimates of interest-allowing easy point estimation, interval estimation, and posterior predictive checks verifying positivity, a required causal identification assumption. Our simulation results show point estimates to have low bias and interval estimates to have close to nominal coverage under complicated data settings. Under simpler settings, these results hold while incurring lower efficiency loss than comparator methods. We use our proposed method to analyze zero-inflated inpatient medical costs among endometrial cancer patients receiving either chemotherapy or radiation therapy in the SEER-Medicare database.

A note on compatibility for inference with missing data in the presence of auxiliary covariates

Imputation and inference (or analysis) models that cannot be true simultaneously are frequently used in practice when missing outcomes are present. In these situations, the conclusions can be misleading depending on how "different" the implicit inference model, induced by the imputation model, is from the inference model actually used. We introduce model-based compatibility (MBC) and compare two MBC approaches to a non-MBC approach and explore the inferential validity of the latter in a simple case. In addition, we evaluate more complex cases through a series of simulation studies. Overall, we recommend caution when making inferences using a non-MBC analysis and point out when the inferential "cost" is the largest.

Bayesian estimation of the average treatment effect on the treated using inverse weighting

We develop a Bayesian approach to estimate the average treatment effect on the treated in the presence of confounding. The approach builds on developments proposed by Saarela et al in the context of marginal structural models, using importance sampling weights to adjust for confounding and estimate a causal effect. The Bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in Bayesian causal estimation relying on a joint likelihood. We present results from simulation studies to estimate the average treatment effect on the treated, evaluating the impact of sample size and the strength of confounding on estimation. We illustrate our approach using the classic Right Heart Catheterization data set and find a negative causal effect of the exposure on 30-day survival, in accordance with previous analyses of these data. We also apply our approach to the data set of the National Center for Health Statistics Birth Data and obtain a negative effect of maternal smoking during pregnancy on birth weight.

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.

Norepinephrine Administration Is Associated with Higher Mortality in Dialysis Requiring Acute Kidney Injury Patients with Septic Shock

(1) Background: Norepinephrine (NE) is the first-line vasoactive agent used in septic shock patients; however, the effect of norepinephrine on dialysis-required septic acute kidney injury (AKI-D) patients is uncertain. (2) Methods: To evaluate the impact of NE on 90-day mortality and renal recovery in septic AKI-D patients, we enrolled patients in intensive care units from 30 hospitals in Taiwan. (3) Results: 372 patients were enrolled and were divided into norepinephrine users and non-users. After adjustment by Inverse probability of treatment weighted (IPTW), there was no significant difference of baseline comorbidities between the two groups. NE users had significantly higher 90-day mortality rate and using NE is a strong predictor of 90-day mortality in the multivariate Cox regression (HR = 1.497, p = 0.027) after adjustment. The generalized additive model disclosed norepinephrine alone exerted a dose–dependent effect on 90-day mortality, while other vasoactive agents were not. (4) Conclusion: Using norepinephrine in septic AKI-D patients is associated with higher 90-day mortality and the effect is dose-dependent. Further study to explore the potential mechanism is needed.

Bayesian Approaches for Missing Not at Random Outcome Data: The Role of Identifying Restrictions

Missing data is almost always present in real datasets, and introduces several statistical issues. One fundamental issue is that, in the absence of strong uncheckable assumptions, effects of interest are typically not nonparametrically identified. In this article, we review the generic approach of the use of identifying restrictions from a likelihood-based perspective, and provide points of contact for several recently proposed methods. An emphasis of this review is on restrictions for nonmonotone missingness, a subject that has been treated sparingly in the literature. We also present a general, fully-Bayesian, approach which is widely applicable and capable of handling a variety of identifying restrictions in a uniform manner.