Non-parametric recurrent events analysis with BART and an application to the hospital admissions of patients with diabetes

Nonparametric failure time: Time-to-event machine learning with heteroskedastic Bayesian additive regression trees and low information omnibus Dirichlet process mixtures

Many popular survival models rely on restrictive parametric, or semiparametric, assumptions that could provide erroneous predictions when the effects of covariates are complex. Modern advances in computational hardware have led to an increasing interest in flexible Bayesian nonparametric methods for time-to-event data such as Bayesian additive regression trees (BART). We propose a novel approach that we call nonparametric failure time (NFT) BART in order to increase the flexibility beyond accelerated failure time (AFT) and proportional hazard models. NFT BART has three key features: (1) a BART prior for the mean function of the event time logarithm; (2) a heteroskedastic BART prior to deduce a covariate-dependent variance function; and (3) a flexible nonparametric error distribution using Dirichlet process mixtures (DPM). Our proposed approach widens the scope of hazard shapes including nonproportional hazards, can be scaled up to large sample sizes, naturally provides estimates of uncertainty via the posterior and can be seamlessly employed for variable selection. We provide convenient, user-friendly, computer software that is freely available as a reference implementation. Simulations demonstrate that NFT BART maintains excellent performance for survival prediction especially when AFT assumptions are violated by heteroskedasticity. We illustrate the proposed approach on a study examining predictors for mortality risk in patients undergoing hematopoietic stem cell transplant (HSCT) for blood-borne cancer, where heteroskedasticity and nonproportional hazards are likely present.

Sparse prediction informed by genetic annotations using the logit normal prior for Bayesian regression tree ensembles

Using high-dimensional genetic variants such as single nucleotide polymorphisms (SNP) to predict complex diseases and traits has important applications in basic research and other clinical settings. For example, predicting gene expression is a necessary first step to identify (putative) causal genes in transcriptome-wide association studies. Due to weak signals, high-dimensionality, and linkage disequilibrium (correlation) among SNPs, building such a prediction model is challenging. However, functional annotations at the SNP level (e.g., as epigenomic data across multiple cell- or tissue-types) are available and could be used to inform predictor importance and aid in outcome prediction. Existing approaches to incorporate annotations have been based mainly on (generalized) linear models. Bayesian additive regression trees (BART), in contrast, is a reliable method to obtain high-quality nonlinear out of sample predictions without overfitting. Unfortunately, the default prior from BART may be too inflexible to handle sparse situations where the number of predictors approaches or surpasses the number of observations. Motivated by our real data application, this article proposes an alternative prior based on the logit normal distribution because it provides a framework that is adaptive to sparsity and can model informative functional annotations. It also provides a framework to incorporate prior information about the between SNP correlations. Computational details for carrying out inference are presented along with the results from a simulation study and a genome-wide prediction analysis of the Alzheimer's Disease Neuroimaging Initiative data.

Bayesian Additive Regression Trees (BART) with covariate adjusted borrowing in subgroup analyses

It is crucial in clinical trials to investigate treatment effect consistency across subgroups defined by patient baseline characteristics. However, there may be treatment effect variability across subgroups due to small subgroup sample size. Various Bayesian models have been proposed to incorporate this variability when borrowing information across subgroups. These models rely on the underlying assumption that patients with similar characteristics will have similar outcomes to the same treatment. Patient populations within each subgroup must subjectively be deemed similar enough Pocock (1976) to borrow response information across subgroups. We propose utilizing the machine learning method of Bayesian Additive Regression Trees (BART) to provide a method for subgroup borrowing that does not rely on an underlying assumption of homogeneity between subgroups. BART is a data-driven approach that utilizes patient-level observations. The amount of borrowing between subgroups automatically adjusts as BART learns the covariate-response relationships. Modeling patient-level data rather than treating the subgroup as a single unit minimizes assumptions regarding homogeneity across subgroups. We illustrate the use of BART in this context by comparing performance from existing subgroup borrowing methods in a simulation study and a case study in non-small cell lung cancer. The application of BART in the context of subgroup analyses alleviates the need to subjectively choose how much information to borrow based on subgroup similarity. Having the amount of borrowing be analytically determined and controlled for based on the similarity of individual patient-level characteristics allows for more objective decision making in the drug development process with many other applications including basket trials.

Bayesian phase II clinical trial design with noncompliance

Noncompliance issue is common in early phase clinical trials; and may lead to biased estimation of the intent-to-treat effect and incorrect conclusions for the clinical trial. In this work, we propose a Bayesian approach for sequentially monitoring the phase II randomized clinical trials that takes account for the noncompliance information. We adopt the principal stratification framework and propose to use Bayesian additive regression trees for selecting useful baseline covariates and estimating the complier average causal effect (CACE) for both efficacy and toxicity outcomes. The decision of early termination or not is then made adaptively based on the estimated CACE from the accumulated data. Simulation studies have confirmed the excellent performance of the proposed design in the presence of noncompliance.

Nonparametric machine learning for precision medicine with longitudinal clinical trials and Bayesian additive regression trees with mixed models

Precision medicine is an active area of research that could offer an analytic paradigm shift for clinical trials and the subsequent treatment decisions based on them. Clinical trials are typically analyzed with the intent of discovering beneficial treatments if the same treatment is applied to the entire population under study. But, such a treatment strategy could be suboptimal if subsets of the population exhibit varying treatment effects. Identifying subsets of the population experiencing differential treatment effect and forming individualized treatment rules is a task well-suited to modern machine learning methods such as tree-based ensemble predictive models. Specifically, Bayesian additive regression trees (BART) has shown promise in this regard because of its exceptional performance in out-of-sample prediction. Due to the unique inferential needs of precision medicine for clinical trials, we have proposed the BART extensions explicated here. We incorporate random effects for longitudinal repeated measures and subject clustering within medical centers. The addition of a novel interaction detection prior to identify treatment heterogeneity among clinical trial patients and its association with patient characteristics. These extensions are unified under a framework that we call mixedBART. Simulation studies and applications of precision medicine based on real randomized clinical trials data examples are presented.

Bayesian additive regression trees and the General BART model

Bayesian additive regression trees (BART) is a flexible prediction model/machine learning approach that has gained widespread popularity in recent years. As BART becomes more mainstream, there is an increased need for a paper that walks readers through the details of BART, from what it is to why it works. This tutorial is aimed at providing such a resource. In addition to explaining the different components of BART using simple examples, we also discuss a framework, the General BART model that unifies some of the recent BART extensions, including semiparametric models, correlated outcomes, and statistical matching problems in surveys, and models with weaker distributional assumptions. By showing how these models fit into a single framework, we hope to demonstrate a simple way of applying BART to research problems that go beyond the original independent continuous or binary outcomes framework.