Looking-backward probabilities for Gibbs-type exchangeable random partitions

Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems that are typically referred to as species sampling problems. In this paper, we consider the class of looking-backward species sampling problems introduced in Lijoi et al. (Ann. Appl. Probab. 18 (2008) 1519-1547) in Bayesian nonparametrics. Specifically, given some information on the random partition induced by an initial sample from a Gibbs-type random probability measure, we study the conditional distributions of statistics related to the old species, namely those species detected in the initial sample and possibly re-observed in an additional sample. The proposed results contribute to the analysis of conditional properties of Gibbs-type exchangeable random partitions, so far focused mainly on statistics related to those species generated by the additional sample and not already detected in the initial sample.Comment: Published at http://dx.doi.org/10.3150/13-BEJ559 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Bayesian Uncertainty Directed Trial Designs

Most Bayesian response-adaptive designs unbalance randomization rates toward the most promising arms with the goal of increasing the number of positive treatment outcomes during the study, even though the primary aim of the trial is different. We discuss Bayesian uncertainty directed designs (BUD), a class of Bayesian designs in which the investigator specifies an information measure tailored to the experiment. All decisions during the trial are selected to optimize the available information at the end of the study. The approach can be applied to several designs, ranging from early stage multi-arm trials to biomarker-driven and multi-endpoint studies. We discuss the asymptotic limit of the patient allocation proportion to treatments, and illustrate the finite-sample operating characteristics of BUD designs through examples, including multi-arm trials, biomarker-stratified trials, and trials with multiple co-primary endpoints. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.The work of SB was partially supported by funding from the Cantab Capital Institute for the Mathematics of Information. LT has been supported by a Burroughs Wellcome Fund Award for Innovation in Regulatory Science and the The Claudia Adams Barr Program in Innovative Basic Cancer Research

Sufficientness postulates for Gibbs-type priors and hierarchical generalizations

A fundamental problem in Bayesian nonparametrics consists of selecting a prior distribution by assuming that the corresponding predictive probabilities obey certain properties. An early discussion of such a problem, although in a parametric framework, dates back to the seminal work by English philosopher W. E. Johnson, who introduced a noteworthy characterization for the predictive probabilities of the symmetric Dirichlet prior distribution. This is typically referred to as Johnson’s “sufficientness” postulate. In this paper we review some nonparametric generalizations of Johnson’s postulate for a class of nonparametric priors known as species sampling models. In particular we revisit and discuss the “sufficientness” postulate for the two parameter Poisson-Dirichlet prior within the more general framework of Gibbs-type priors and their hierarchical generalizations.. Stefano Favaro is supported by the European Research Council through StG N-BNP 306406. Marco Battiston’s research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) ERC grant agreement number 617071

Imprints of Nuclear Symmetry Energy on Properties of Neutron Stars

Significant progress has been made in recent years in constraining the density dependence of nuclear symmetry energy using terrestrial nuclear laboratory data. Around and below the nuclear matter saturation density, the experimental constraints start to merge in a relatively narrow region. At supra-saturation densities, there are, however, still large uncertainties. After summarizing the latest experimental constraints on the density dependence of nuclear symmetry energy, we highlight a few recent studies examining imprints of nuclear symmetry energy on the binding energy, energy release during hadron-quark phase transitions as well as the $w$-mode frequency and damping time of gravitational wave emission of neutron stars.Comment: 10 pages. Invited talk given in the Nuclear Astrophysics session of INPC2010, July 4-9, 2010, Vancouver, Canada; Journal of Physics: Conference Series (2011

Genomic Profiling of Smoldering Multiple Myeloma Identifies Patients at a High Risk of Disease Progression

PURPOSE: Smoldering multiple myeloma (SMM) is a precursor condition of multiple myeloma (MM) with a 10% annual risk of progression. Various prognostic models exist for risk stratification; however, those are based on solely clinical metrics. The discovery of genomic alterations that underlie disease progression to MM could improve current risk models. METHODS: We used next-generation sequencing to study 214 patients with SMM. We performed whole-exome sequencing on 166 tumors, including 5 with serial samples, and deep targeted sequencing on 48 tumors. RESULTS: We observed that most of the genetic alterations necessary for progression have already been acquired by the diagnosis of SMM. Particularly, we found that alterations of the mitogen-activated protein kinase pathway (KRAS and NRAS single nucleotide variants [SNVs]), the DNA repair pathway (deletion 17p, TP53, and ATM SNVs), and MYC (translocations or copy number variations) were all independent risk factors of progression after accounting for clinical risk staging. We validated these findings in an external SMM cohort by showing that patients who have any of these three features have a higher risk of progressing to MM. Moreover, APOBEC associated mutations were enriched in patients who progressed and were associated with a shorter time to progression in our cohort. CONCLUSION: SMM is a genetically mature entity whereby most driver genetic alterations have already occurred, which suggests the existence of a right-skewed model of genetic evolution from monoclonal gammopathy of undetermined significance to MM. We identified and externally validated genomic predictors of progression that could distinguish patients at high risk of progression to MM and, thus, improve on the precision of current clinical models

TBCRC 030: a phase II study of preoperative cisplatin versus paclitaxel in triple-negative breast cancer: evaluating the homologous recombination deficiency (HRD) biomarker

Background: Cisplatin and paclitaxel are active in triple-negative breast cancer (TNBC). Despite different mechanisms of action, effective predictive biomarkers to preferentially inform drug selection have not been identified. The homologous recombination deficiency (HRD) assay (Myriad Genetics, Inc.) detects impaired double-strand DNA break repair and may identify patients with BRCA1/2-proficient tumors that are sensitive to DNA-targeting therapy. The primary objective of TBCRC 030 was to detect an association of HRD with pathologic response [residual cancer burden (RCB)-0/1] to single-agent cisplatin or paclitaxel. Patients and methods: This prospective phase II study enrolled patients with germline BRCA1/2 wild-type/unknown stage I–III TNBC in a 12-week randomized study of preoperative cisplatin or paclitaxel. The HRD assay was carried out on baseline tissue; positive HRD was defined as a score ≥33. Crossover to an alternative chemotherapy was offered if there was inadequate response. Results: One hundred and thirty-nine patients were evaluable for response, including 88 (63.3%) who had surgery at 12 weeks and 51 (36.7%) who crossed over to an alternative provider-selected preoperative chemotherapy regimen due to inadequate clinical response. HRD results were available for 104 tumors (74.8%) and 74 (71.1%) were HRD positive. The RCB-0/1 rate was 26.4% with cisplatin and 22.3% with paclitaxel. No significant association was observed between HRD score and RCB response to either cisplatin [odds ratio (OR) for RCB-0/1 if HRD positive 2.22 (95% CI: 0.39–23.68)] or paclitaxel [OR for RCB-0/1 if HRD positive 0.90 (95% CI: 0.19–4.95)]. There was no evidence of an interaction between HRD and pathologic response to chemotherapy. Conclusions: In this prospective preoperative trial in TNBC, HRD was not predictive of pathologic response. Tumors were similarly responsive to preoperative paclitaxel or cisplatin chemotherapy

Improving prediction from Dirichlet process mixtures via enrichment

Flexible covariate-dependent density estimation can be achieved by modelling the joint density of the response and covariates as a Dirichlet process mixture. An appealing aspect of this approach is that computations are relatively easy. In this paper, we examine the predictive performance of these models with an increasing number of covariates. Even for a moderate number of covariates, we find that the likelihood for x tends to dominate the posterior of the latent random partition, degrading the predictive performance of the model. To overcome this, we suggest using a different nonparametric prior, namely an enriched Dirichlet process. Our proposal maintains a simple allocation rule, so that computations remain relatively simple. Advantages are shown through both predictive equations and examples, including an application to diagnosis Alzheimer’s disease