Deep bootstrap for Bayesian inference.

For a Bayesian, the task to define the likelihood can be as perplexing as the task to define the prior. We focus on situations when the parameter of interest has been emancipated from the likelihood and is linked to data directly through a loss function. We survey existing work on both Bayesian parametric inference with Gibbs posteriors and Bayesian non-parametric inference. We then highlight recent bootstrap computational approaches to approximating loss-driven posteriors. In particular, we focus on implicit bootstrap distributions defined through an underlying push-forward mapping. We investigate independent, identically distributed (iid) samplers from approximate posteriors that pass random bootstrap weights through a trained generative network. After training the deep-learning mapping, the simulation cost of such iid samplers is negligible. We compare the performance of these deep bootstrap samplers with exact bootstrap as well as MCMC on several examples (including support vector machines or quantile regression). We also provide theoretical insights into bootstrap posteriors by drawing upon connections to model mis-specification. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

Improving Medicare's Hospital Compare Mortality Model.

OBJECTIVE: To improve the predictions provided by Medicare's Hospital Compare (HC) to facilitate better informed decisions regarding hospital choice by the public. DATA SOURCES/SETTING: Medicare claims on all patients admitted for Acute Myocardial Infarction between 2009 through 2011. STUDY DESIGN: Cohort analysis using a Bayesian approach, comparing the present assumptions of HC (using a constant mean and constant variance for all hospital random effects), versus an expanded model that allows for the inclusion of hospital characteristics to permit the data to determine whether they vary with attributes of hospitals, such as volume, capabilities, and staffing. Hospital predictions are then created using directly standardized estimates to facilitate comparisons between hospitals. DATA COLLECTION/EXTRACTION METHODS: Medicare fee-for-service claims. PRINCIPAL FINDINGS: Our model that included hospital characteristics produces very different predictions from the current HC model, with higher predicted mortality rates at hospitals with lower volume and worse characteristics. Using Chicago as an example, the expanded model would advise patients against seeking treatment at the smallest hospitals with worse technology and staffing. CONCLUSION: To aid patients when selecting between hospitals, the Centers for Medicare and Medicaid Services (CMS) should improve the HC model by permitting its predictions to vary systematically with hospital attributes such as volume, capabilities, and staffing.

Negotiating Multicollinearity with Spike-and-Slab Priors.

In multiple regression under the normal linear model, the presence of multicollinearity is well known to lead to unreliable and unstable maximum likelihood estimates. This can be particularly troublesome for the problem of variable selection where it becomes more difficult to distinguish between subset models. Here we show how adding a spike-and-slab prior mitigates this difficulty by filtering the likelihood surface into a posterior distribution that allocates the relevant likelihood information to each of the subset model modes. For identification of promising high posterior models in this setting, we consider three EM algorithms, the fast closed form EMVS version of Rockova and George (2014) and two new versions designed for variants of the spike-and-slab formulation. For a multimodal posterior under multicollinearity, we compare the regions of convergence of these three algorithms. Deterministic annealing versions of the EMVS algorithm are seen to substantially mitigate this multimodality. A single simple running example is used for illustration throughout.

Deregulated expression of EVI1 defines a poor prognostic subset of MLL-rearranged acute myeloid leukemias: a study of the German-Austrian Acute Myeloid Leukemia Study Group and the Dutch-Belgian-Swiss HOVON/SAKK Cooperative Group.

PURPOSE: To evaluate the prognostic value of ecotropic viral integration 1 gene (EVI1) overexpression in acute myeloid leukemia (AML) with MLL gene rearrangements. PATIENTS AND METHODS: We identified 286 patients with AML with t(11q23) enrolled onto German-Austrian Acute Myeloid Leukemia Study Group and Dutch-Belgian-Swiss Hemato-Oncology Cooperative Group prospective treatment trials. Material was available from 177 AML patients for EVI1 expression analysis. RESULTS: We divided 286 MLL-rearranged AMLs into three subgroups: t(9;11)(p22;q23) (44.8%), t(6;11)(q27;q23) (14.7%), and t(v;11q23) (40.5%). EVI1 overexpression (EVI1(+)) was found in 45.8% of all patients with t(11q23), with t(6;11) showing the highest frequency (83.9%), followed by t(9;11) at 40.0%, and t(v;11q23) at 34.8%. Concurrent gene mutations were rare or absent in all three subgroups. Within all t(11q23) AMLs, EVI1(+) was the sole prognostic factor, predicting for inferior overall survival (OS; hazard ratio [HR], 2.06; P = .003), relapse-free survival (HR, 2.28; P = .002), and event-free survival (HR, 1.79; P = .009). EVI1(+) AMLs with t(11q23) in first complete remission (CR) had a significantly better outcome after allogeneic transplantation compared with other consolidation therapies (5-year OS, 54.7% v 0%; Mantel-Byar, P = .0006). EVI1(-) t(9;11) AMLs had lower WBC counts, more commonly FAB M5 morphology, and frequently had additional trisomy 8 (39.6%; P < .001). Among t(9;11) AMLs, EVI1(+) again was the sole independent adverse prognostic factor for survival. CONCLUSION: Deregulated EVI1 expression defines poor prognostic subsets among AML with t(11q23) and AML with t(9;11)(p22;q23). Patients with EVI1(+) MLL-rearranged AML seem to benefit from allogeneic transplantation in first CR.

Mutant DNMT3A: a marker of poor prognosis in acute myeloid leukemia.

The prevalence, the prognostic effect, and interaction with other molecular markers of DNMT3A mutations was studied in 415 patients with acute myeloid leukemia (AML) younger than 60 years. We show mutations in DNMT3A in 96 of 415 patients with newly diagnosed AML (23.1%). Univariate Cox regression analysis showed that patients with DNMT3A(mutant) AML show significantly worse overall survival (OS; P = .022; hazard ratio [HR], 1.38; 95% confidence interval [CI], 1.04-1.81), and relapse-free survival (RFS; P = .005; HR, 1.52; 95% CI, 1.13-2.05) than DNMT3A(wild-type) AMLs. In a multivariable analysis, DNMT3A mutations express independent unfavorable prognostic value for OS (P = .003; HR, 1.82; 95% CI, 1.2-2.7) and RFS (P < .001; HR, 2.2; 95% CI, 1.4-3.3). In a composite genotypic subset of cytogenetic intermediate-risk AML without FLT3-ITD and NPM1 mutations, this association is particularly evident (OS: P = .013; HR, 2.09; 95% CI, 1.16-3.77; RFS: P = .001; HR, 2.65; 95% CI, 1.48-4.89). The effect of DNMT3A mutations in human AML remains elusive, because DNMT3A(mutant) AMLs did not express a methylation or gene expression signature that discriminates them from patients with DNMT3A(wild-type) AML. We conclude that DNMT3A mutation status is an important factor to consider for risk stratification of patients with AML.

Hierarchical Bayesian formulations for selecting variables in regression models.

The objective of finding a parsimonious representation of the observed data by a statistical model that is also capable of accurate prediction is commonplace in all domains of statistical applications. The parsimony of the solutions obtained by variable selection is usually counterbalanced by a limited prediction capacity. On the other hand, methodologies that assure high prediction accuracy usually lead to models that are neither simple nor easily interpretable. Regularization methodologies have proven to be useful in addressing both prediction and variable selection problems. The Bayesian approach to regularization constitutes a particularly attractive alternative as it is suitable for high-dimensional modeling, offers valid standard errors, and enables simultaneous estimation of regression coefficients and complexity parameters via computationally efficient MCMC techniques. Bayesian regularization falls within the versatile framework of Bayesian hierarchical models, which encompasses a variety of other approaches suited for variable selection such as spike and slab models and the MC(3) approach. In this article, we review these Bayesian developments and evaluate their variable selection performance in a simulation study for the classical small p large n setting. The majority of the existing Bayesian methodology for variable selection deals only with classical linear regression. Here, we present two applications in the contexts of binary and survival regression, where the Bayesian approach was applied to select markers prognostically relevant for the development of rheumatoid arthritis and for overall survival in acute myeloid leukemia patients.

Retroviral integration mutagenesis in mice and comparative analysis in human AML identify reduced PTP4A3 expression as a prognostic indicator.

Acute myeloid leukemia (AML) results from multiple genetic and epigenetic aberrations, many of which remain unidentified. Frequent loss of large chromosomal regions marks haplo-insufficiency as one of the major mechanisms contributing to leukemogenesis. However, which haplo-insufficient genes (HIGs) are involved in leukemogenesis is largely unknown and powerful experimental strategies aimed at their identification are currently lacking. Here, we present a new approach to discover HIGs, using retroviral integration mutagenesis in mice in which methylated viral integration sites and neighbouring genes were identified. In total we mapped 6 genes which are flanked by methylated viral integration sites (mVIS). Three of these, i.e., Lrmp, Hcls1 and Prkrir, were up regulated and one, i.e., Ptp4a3, was down regulated in the affected tumor. Next, we investigated the role of PTP4A3 in human AML and we show that PTP4A3 expression is a negative prognostic indicator, independent of other prognostic parameters. In conclusion, our novel strategy has identified PTP4A3 to potentially have a role in AML, on one hand as a candidate HIG contributing to leukemogenesis in mice and on the other hand as a prognostic indicator in human AML.

Risk stratification of intermediate-risk acute myeloid leukemia: integrative analysis of a multitude of gene mutation and gene expression markers.

Numerous molecular markers have been recently discovered as potential prognostic factors in acute myeloid leukemia (AML). It has become of critical importance to thoroughly evaluate their interrelationships and relative prognostic importance. Gene expression profiling was conducted in a well-characterized cohort of 439 AML patients (age < 60 years) to determine expression levels of EVI1, WT1, BCL2, ABCB1, BAALC, FLT3, CD34, INDO, ERG and MN1. A variety of AML-specific mutations were evaluated, that is, FLT3, NPM1, N-RAS, K-RAS, IDH1, IDH2, and CEBPA(DM/SM) (double/single). Univariable survival analysis shows that (1) patients with FLT3(ITD) mutations have inferior overall survival (OS) and event-free survival (EFS), whereas CEBPA(DM) and NPM1 mutations indicate favorable OS and EFS in intermediate-risk AML, and (2) high transcript levels of BAALC, CD34, MN1, EVl1, and ERG predict inferior OS and EFS. In multivariable survival analysis, CD34, ERG, and CEBPA(DM) remain significant. Using survival tree and regression methodologies, we show that CEBPA(DM), CD34, and IDH2 mutations are capable of separating the intermediate group into 2 AML subgroups with highly distinctive survival characteristics (OS at 60 months: 51.9% vs 14.9%). The integrated statistical approach demonstrates that from the multitude of biomarkers a greatly condensed subset can be selected for improved stratification of intermediate-risk AML.